**Special Issue: Aspects of Game Theory and Institutional Economics—Editorial**

#### **Wolfram Elsner, Torsten Heinrich, Henning Schwardt and Claudius Gräbner**

Reprinted from Special Issue: Aspects of Game Theory and Institutional Economics, *Games*. Cite as: Elsner, W.; Heinrich, T.; Schwardt, H.; Gräbner, C. Special Issue: Aspects of Game Theory and Institutional Economics (Editorial). *Games* **2014**, *5*, 188–190.

#### **1. Towards a Complexity Economics**

Classical economists from Adam Smith to Thomas Malthus and to Karl Marx have considered the importance of *direct interdependence* and direct interactions for the economy. This was even more the case for original institutionalist thinkers such as Thorstein Veblen, John Commons, and Clarence Ayres. In their writings, direct interdependence, interactions (or transactions) among agents, with all beneficial and with all problematic consequences, took center stage in economic analysis. Why, for instance, do people adhere to a particular new fashion or trend? Because others do, after eminent people, wealthy people, the "leisure class" (T. Veblen), have made it a symbol for status. The new fashion, however, ceases to serve as such a symbol once too many people follow it. The constant effort put into following trends and adopting fashion turns out to be a *social dilemma*, driven by Veblenian instincts, such as invidious distinction in predatory societies, conspicuous consumption and emulation.

The general issues of herd behavior and myopic individualistic decision making, both under opacity and highly bounded rationality in complex systems, and both possibly carrying the problem of *negative unintended consequences* for the economy as a whole, for society and the natural commons, have taken center stage again in the global financial crisis of 2007, which still lingers around as the "Great Recession".

The "*representative agent*" of the economic mainstream's theoretical core model, whose decisions may simplistically be summed up into the aggregates of the related macroeconomics, has most overtly failed to enable economists to even realize inherent tendencies towards crises in realworld complex systems, based on intricate common and collective decision structures.

Of course, both classical political economy and original institutional economics lacked the formal methods to describe intricate interdependencies and decision structures in exact and mathematical terms—even if they wanted to (while some of them have been rather critical with respect to any formalism). In particular, they could not employ modern *game theory*, *evolutionary algorithms*, or *agent-based simulation*. Today, we can. As it happens, these methods are much better suited to describe classical and evolutionary-institutionalist theories and complex economies of interactive agents than, for instance, vector fields and nonlinear optimization that were *en vogue* in economics at the time of Veblen's writings. The ex-post aggregates that emerge in simulations show one instance in which analytical advantages can in fact be realized utilizing such methods.

Among economists, the interest in these approaches has continued to grow. Making classical and evolutionary-institutional theories accessible to formal methods, and in this way even shedding new light on different aspects of traditional subjects has been at the core of a new development in economics—using game theory, agent-based modelling, simulation, and lab experiments to tackle complex dynamic, evolutionary, and institutional phenomena. *Elinor Ostrom*, well-known for her experimental as well as theoretical and field research on the commons and social dilemmas, received the Nobel memorial prize in 2009, but many other scholars (including a number of other Nobel laureates) have been active in this field as well. In fact, such *complexity economics* has apparently become a new vanishing point of the economics discipline, at least in research (albeit not in textbooks and academic mass education).

#### **2. The Contributions to this Special Issue**

The current Special Issue of "games" is an attempt to highlight some recent work in this field and to bring some papers of the field together in a single publication.

While two of the papers (by Wolfgang Radax, Bernhard Rengs, and Manuel Wäckerle, and that of Jürgen Fleiß and Stefan Palan) in this issue pursue the question of the *emergence and coevolution of institutions and hierarchy*, a third paper (by Tassos Patokos) analyzes algorithms of strategy change in evolutionary game models, and the fourth paper (by Alexander Field) takes a historical (history-of-economic-thought) point of view on the development of game theory during the cold war.

*Radax et al.* ("An Agent-Based Model of Institutional Life-Cycles") offer an application of an agent-based simulation on the *formation and development of institutions*. They consider the development of institutions in a population of agents playing repeated *prisoners' dilemma* games. The paper models institutions as voluntary associations of agents with cooperation enforced by a leader. Simulations show three sharply differing possible scenarios: universal institutionalized cooperation, universal defection with stable institutions of internal cooperation, and a scenario with non-trivial *institutional life-cycles*. In an elegant way, the authors connect the paper metaphorically and practically to Ilya Prigogine's and Stuart Kauffman's concepts of complexity as a *transition regime between ordered and chaotic states*, identifying these three regimes, each with one of the dominant three scenarios they found in their simulation study.

*Fleiß and Palan* ("Of Coordinators and Dictators: A Public Goods Experiment") consider a similar question with a methodologically different and, in fact, complementary approach. They conducted *laboratory experiments* and find that human subjects are generally willing—at an overwhelming margin—to pay for being part of an *institution* with enforced cooperation when faced with a *social dilemma* situation. The context was the production of a public good; agents could freely choose between a setting with voluntary and one with enforced contribution. In their experiments, agents strongly favor *enforced contribution* even if the randomly selected leader of the institution can exploit her position and free-ride.

*Patokos* ("Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results") pursues a subject that is of central importance to many *evolutionary game theory* and *replicator models* (those with a reassignment of strategies instead of exit and entry): the mode of *strategy updating* on the part of the agents. He considers three commonly used algorithms, immediate updating in the event of sub-optimal outcomes, updating based on the outcomes of several iterations, and updating based on a threshold outcome-level. Analyzing the

algorithms against a *number of game structures* for evolutionary game theory interaction settings and again with stochastic perturbation, sharply diverging outcomes are found.

*Field* ("Schelling, von Neumann, and the Event that Didn't Occur"), in a quite different kind of paper, a historical review, discusses the evolution of game theory during the cold war. He argues that the historical standoff confrontation at the edge of a nuclear war had a profound impact on, not only the scholars, but also the ideas, concepts, and methods of game theory itself. While this historical reconstruction of a critical phase of development, application, and identity finding of game theory, may easily be controversial, it offers a number of truly challenging thoughts and reflections that are as original as they are unorthodox—provided, in this case, by an established institutional(ist) game theorist.

#### **3. An Outlook**

The study of institutions is not a new subject in economics at all. But it has attracted a continuing scholarly interest for decades, and many conceptual, theoretical, and methodological breakthroughs have been accomplished in this field, particularly since the dawn of modern game theory and the use of computers for simulation and economic experiments. The seminal works by Robert Axelrod and Elinor Ostrom are merely two examples. These too were centered on the *evolution of institutions in a context of social dilemma situations*—a research project that is vigorously continued by the first two papers in this issue. Of course, these efforts must always be accompanied by an equally firm resolution to work on other questions of evolutionary and institutional economics (and beyond); further on methodology and, finally, to critically question the institutional history of both game theory formal methods and evolutionary and institutional economics (on which this issue also contains one paper each).

*Bremen, Germany, May 2014* 

## **An Agent-Based Model of Institutional Life-Cycles**

#### **Manuel Wäckerle, Bernhard Rengs and Wolfgang Radax**

**Abstract:** We use an agent-based model to investigate the interdependent dynamics between individual agency and emergent socioeconomic structure, leading to institutional change in a generic way. Our model simulates the emergence and exit of institutional units, understood as generic governed social structures. We show how endogenized trust and exogenously given leader authority influences institutional change, *i.e.*, diversity in institutional life-cycles. It turns out that these governed institutions (de)structure in cyclical patterns dependent on the overall evolution of trust in the artificial society, while at the same time, influencing this evolution by supporting social learning. Simulation results indicate three scenarios of institutional life-cycles. Institutions may, (1) build up very fast and freeze the artificial society in a stable but fearful pattern (ordered system); (2) exist only for a short time, leading to a very trusty society (highly fluctuating system); and (3) structure in cyclical patterns over time and support social learning due to cumulative causation of societal trust (complex system).

Reprinted from Special Issue: Aspects of Game Theory and Institutional Economics, *Games*. Cite as: Wäckerle, M.; Rengs, B.; Radax, W. An Agent-Based Model of Institutional Life-Cycles. *Games* **2014**, *5*, 160–187.

#### **1. Introduction**

The central research question of this paper deals with the emergent effects originating from dynamic interdependencies of individual strategies and social structures—see [1] for the latter. The theory of games originally established by von Neumann and Morgenstern is perfectly suited to approach such a problem, since it provides a formal mathematical body to model social interaction and basic communication structures. Thus far, game theory was used to model a multitude of socioeconomic problems, assigning relevance to strategy formation as a major influence on economic behavior, see [2] for a recent overview on the integration of game theory and the behavioral sciences. However, with the rise of evolutionary game theory the notion of learning became a central issue of investigation, in particular within population dynamics, see [3] for one of the first elaborations. In this context population dynamics have become central in phylogenetic terms, where evolutionary stable strategies (ESS) enhanced the fitness of a group compared to others within a population. The evolutionary turn has revealed a very important finding, namely that certain strategies of conditional cooperation may lead to an ESS, thereby outplaying the strict dominance of the defective strategy, thus, transforming non-cooperative games into cooperative games, see [4,5]. Obviously this strand of research has also influenced findings about our own origin and heritage as a human species, see [6]. Although we have gathered tremendous knowledge on our social preferences and the strategic sources for cooperation in non-kin large-scale societies, we have not properly connected these findings yet with the emergence, life and exit of institutions in economy and society, *i.e.*, institutional change. This research topic opens up a multitude of interesting research questions, first attempts to cope with them are given in [7]. Furthermore Ostrom [8] has clarified that institutions coordinate individual strategies concerning collective action problems. They represent more than just constraints on behavior [9], but may even lead to the emergence of new forms of behavior. Institutions evolve along strategies and rules, in consequence, they evolve in diverse forms from social interaction and reconstitute economic behavior. Seemingly, it stands to reason, that institutions are meta-stabilized sets of established and culturally transmitted [10] rules forming the cornerstones of political economy and its evolution. In this perspective, the theory of games can play a decisive role in explaining the political economic causes of endogenous crisis [11] via the accumulation of historically established strategies, habits, and their potential lock-in resulting in unequal patterns of social stratification, see [12] for Bourdieu's sociological analysis of the problem at hand. A similar socioeconomic approach got established almost 100 years earlier by Thorstein Veblen [13]. Veblen has looked into the cumulative causation of habits of thought resulting in institutional change. This first socio-cybernetic approach was interpreted by him as an evolutionary contribution to economics [14], because evolving institutions depend on the variation, selection and retention of habits of thought and social norms, such as conspicuous consumption for instance. Thereby, institutions are understood as social structures, which, again, feed-back to the establishment of new habits and norms. These spiral dynamics are crucial for what has been called the old institutional economics. The old approach to institutionalism stands in contrast to the new institutional economics research program where attention is turned to the transaction costs of socioeconomic activities, compare [15] for the demarcation problem between old and new institutional economics. Obviously, it is the notion of contingent path-dependent evolution, which makes the former approach richer in scope but more difficult to model. However, today we have the analytical tools to compete with such a challenge, as the original attempt by [16] has recently shown.

In order to fully integrate the theory of games into an evolutionary approach of institutional change as the central sub-field of evolutionary political economy, [11] suggests considering a computational and algorithmic methodology of agent-based modeling (ABM) and socioeconomic simulation. Recently this attempt has received increasing attention within a certain part of evolutionary economics, concerned with institutional evolution, see [17] for a computational multi-agent approach to meso-economics and critical platform size. The ABM approach suits the problem at hand well, because it is able to mimic the complex non-equilibrium dynamics of an evolving economy. The analyzed emergent properties are revealed on a meso-economic level, between micro and macro [18], acknowledged recently by Arthur [19]. Institutions play a central role in this process as social structures of rule correspondence, however, in the history of economic thought, heuristics were always explained differently, compare [20]. The advantage of the agent-based methodology over evolutionary game theory is given by the possibility to model institutions as accumulating social structures, once certain rules are introduced about governance and regulation. From a static analytical perspective, Aoki [21] has provided the first theoretical framework to analyze institutional complementarities via one-shot games as strategic systems of shared beliefs. Still, in this realm of research, dynamic models of interdependent agency-structure relations causing institutional change are rare and need further attention.

### **2. Model**

We propose a framework to model the emergence, life and exit of institutions (institutional life cycles) in an artificial political economy based on the interactions of individuals on a micro level. In the model we treat institutions as social accumulating structures instead of mere sets of agents with common properties, where the frequency and coordination of strategies and behavioral motivations plays the superior role (*i.e.*, an artificial society without social structure). The former anticipation is essential for a game theoretical approach of institutional change as understood in old Veblenian institutional economics, *i.e.*, basically a co-evolutionary process between agency and structure leading to differentiation in the population of agents. Particularly, we model institutions as governed social structures with clearly codified entry and exit conditions for agents as members (compare Hodgson ([22], p. 18) for this particular aspect of institutions). To this extent they represent generic regulatory mechanisms that make societies stable on a large scale. Thereby, it is important to note that institutions are neither conceived as general-purpose vehicles, nor just as spontaneously emerging and exiting, but underlie individual life-cycles. Respectively, they evolve within a contingent path-dependent process that is dependent on the general level of societal trust. This aspect of accumulation makes agents endogenously heterogeneous and institutions diverse evolving aggregate structures, see [23] for a differentiation between heterogeneity and diversity.

In our model, agents populate an abstract topological space and interact with each other locally on a regular grid with linked edges (a torus) to avoid edge cell problems. The interaction is based on a prisoner's dilemma logic, *i.e.*, in every time step agents play the prisoner's dilemma game with their von-Neumann neighbors. According to the logic of the ordinary 2 × 2 prisoner's dilemma, agents can either cooperate or defect. In our model, agents are endowed with cognitive capabilities (a memory of events in the recent past, and a decision mechanism using this memory), which feed their individual decisions. In the course of the simulation, different agents accumulate different memories due to individual spatial interaction, and thus naturally evolve into a heterogeneous set of individual decision makers1 . Repeated cooperation between agents builds up trust, which in turn influences the emergence and exit of institutions as exclusive governed structures. It is important to distinguish between "institution-building proper", which by itself just constitutes part of the "rules of the game" [24], of the simulation, and its materialization as some special form of governance. Thereby, some members of this institution enforce compliance to the rule set. The special form, the realization of an institution, needs to be modeled explicitly by some agents taking over the role of enforcers, the role of executive power. As history teaches, executive power is needed for two distinct tasks: (1) It guarantees internal stability (compliance to the institutional rules); and (2) it warrants security from external threats (others trying to invade from outside). The institutional apparatus necessary to exert executive power is always financed by tribute payments of its members to their ruling executive. With a similar (and consistent) logic the model also takes care of the possibility of the break-up of institutions.

<sup>1</sup> Heterogeneity is thus not only an exogenous assumption replacing the (mainstream economic) assumption of a set of homogeneous representative agents; it indeed is a *process*, which evolves as part of the overall dynamics.

In this respect, we follow Hooper *et al.* [25], who highlight that leadership may get accepted in cooperative groups, if it crowds out free-riding or coordination errors. Moreover, the authors specify in their model that members may prefer to pay for the supervision instead of staying in an unsupervised group. Thereby, agents accept a hierarchical organization of social complexity, which is in line with our approach. Still, we do not implement public good games, as in [25], where mutual monitors punish defectors, but institutions with hegemonic leaders enforcing cooperation within clearly structural bounds, instead of more loose groups of agents sharing common properties. To this extent, our approach wants to emphasize the explicit character of a governed institution in comparison to more implicit group selection dynamics. However, our model shares some basic characteristics with [25], e.g., enforcement of cooperation becomes more costly with increasing group size, as we will outline in more detail. Where [25] investigates just one emerging group and the dynamics within group members and agents outside the group, we are able to investigate a whole number of institutions in a common spatial environment. This constraint is given by the methodology of dynamic evolutionary games in continuous time, building upon [26]. In the agent-based framework, time is mostly considered discrete and various interaction topologies can be implemented. Elsewhere, Smaldino and Lubell [27] show that a multi-agent approach may indeed help to investigate a diversity of solutions to social dilemmas. The authors investigate an "ecology of games", where each game is analyzed with two different institutional mechanisms, capacity constraints and observation of behavior. The model we put forward implements the former institutional mechanism building upon a capacity constraint, *i.e.*, in our case a diminishing leader influence based on distance ("leadership distance decrement") since we work with an interaction topology (2D space with finite, small neighborhoods) that clearly contrasts our approach from the aforementioned ones.

Our model is based on Sanchez-Pages and Straub [28], who analytically investigate the emergence of institutions in a multi-stage one-shot game where homogeneous agents are pairwise matched to play a game of prisoner's dilemma. Each of the two agents participating in the prisoner's dilemma (PD) has the choice between the two actions of cooperation (C) and defection (D). Since the game is played simultaneously and communication is prohibited, *a priori* the two players are not aware of their respective opponent's choice of action, therefore, starting in a Hobbesian state of nature. If both players cooperate, they both achieve a payoff of R (reward), if they both choose to defect, they both end up with a payoff of P (punishment). Finally, if one agent cooperates and the other defects, then the cooperator gets a payoff of S (sucker's payoff) and the defector receives T (temptation). Payoffs therefore satisfy - and - . Which strategy is chosen depends on the exogenously given level of trust within the society in the model of Sanchez-Pages and Straub [28]. As agents have the same level of trust, they always choose the same strategy, thus, only the two symmetrical outcomes of mutual cooperation (C,C) and mutual defection (D,D) are can be realized. Every agent in our model on the other hand has an individual trust level, which evolves over time as a result of her past experiences, thus, all four possible outcomes are considered. However, in their static model agents have the option to establish an institution that enforces cooperation between its members. To this end, they must choose a leader whom they can delegate the work of enforcing cooperation. The leader may not participate in the PD game but it may set a fee that all agents willing to join the institution have to pay to at least cover his opportunity costs. Games between members of

the institution always reach the cooperative outcome. Games between a member of the institution and an outsider, however, are not under institutional supervision and are treated like games in the state of nature. For convenience, Sanchez-Pages and Straub [28] label the former case (enforced cooperation) as "formal games" (*i.e.*, game partners comply with the formalities/rules of the institution) and the latter, as well as games between two institution-less agents, as "informal games". With this basic setup, the authors of [28] go on to analyze equilibrium solutions on the number of agents within the institution, optimal fees and threats of secession. While their approach is instructive with respect to a number of issues, it considers only the case of one institution *versus* no institution in a one-shot static game. We argue in favor of a dynamic approach to catch the subtleties of the emergence, life, and exit of such coalitions between individual agents. Furthermore, we are able to study the evolution of a whole society of agents and institutions over time and to analyze these societies using a kind of institutional demography. These are all aspects that are impossible to derive from the static game described above.

Since an analytical model of such a dynamic complex adaptive version would hardly be tractable mathematically, we resort to the method of ABM. In the model, the artificial world is represented by a two-dimensional grid on which the agents can move around freely. Borders are wrapped around so that the matrix topographically corresponds to a torus. If an agent happens to meet other agents within her von-Neumann-neighborhood she plays a game of PD with each of them. If a cluster of at least three agents exists, these agents may decide to become sedentary, choose a leader and build an institution. Members of institutions are able to leave the institution each time step and the leader of an institution is allowed to set a new fee in each period. In what follows, all steps are presented in detail.

#### *2.1. Initialization*

At the start of a simulation run, agents are distributed randomly across the grid. The random numbers are drawn from a pseudo-random number generator following a uniform distribution. Each agent is endowed with a memory of size . In this memory the agent cognitively stores the opponents' choices of the last  informal games. We define informal games as games played between (1) two agents who are not members of an institution; (2) an agent who is member of an institution and an agent who isn't; or (3) two agents who are members of different institutions. In short, informal games are those games that are not supervised by the same leader. On the other hand, games played by two agents, who are members of the same institution, *i.e.*, those games where the cooperative outcome is enforced, are labeled formal games.

We further define the share of cooperative actions stored in an agent's memory as her personal value for , in this respect it is not comparable to the institutional mechanism of reputation suggested by [27], since we do not track the reputation of encounters. In contrast, we model the agent's memory as personal perception of trust in the society based on past encounters independent from intersubjective reputation. If we assume, for instance, each agent to have a memory of the last ten informal encounters, *i.e.*,  , then is equivalent to the case that in any six out of the last ten informal encounters the agent's opponents cooperated. The size of memory thus represents an assumption on the flexibility of an agent to adjust to new experiences. In this way, we endogenize

the evolution of trust according to those new experiences of an agent. If, for instance, an agent meets a lot of other agents who cooperate, her personal , *i.e.*, her trust in society, will rise and the agent will be more likely to cooperate in the future. Since we state that only informal games are memorized, we assume that enforced cooperation within an institution does not influence an agent's personal level of trust in cooperation between strangers. Obviously, at the initialization of a simulation run, no games have been played and therefore no actions would be stored in the agents' memories. We start with all agents having the same initial value of alpha at the start, which is a simulation parameter. With this starting value, we construct a random history of encounters for each agent, *i.e.*, a hypothetical history of events that corresponds to the given value of her personal at initialization. The histories are a list of encountered strategies, *i.e.*, the strategies that opponents played during the last  informal encounters and are stored as a string with length , where each character represents a past encounter (with "C" representing an encounter with a cooperating agent and "D" having faced a defecting agent). Each agent has only one such list for all informal encounters, which contains no information to identify former opponents. Though the two extreme exemplary histories "CCCCCCDDDD" and "DDDDCCCCCC" both represent the same (60% remembered cooperative informal encounters), they still represent heterogeneous histories. In the first example another cooperative encounter would push out the oldest remembered encounter (*i.e.*, the oldest memory would be forgotten) and change agent 's memory to "CCCCCCCDDD" whereas, in the latter case, it would change to "CDDDDCCCCC" ( . Note that, although these encounters are stored in the proper historical order, the agents do not have any information as to how much simulation time has passed since the individual encounter happened, *i.e.*, the agents have an event based memory.

In contrast to the perfectly homogeneous agents in [28], the agents in our model are heterogeneous with regards to their location, their personal history and trust level within the simulated world. Though simulation time progresses in discrete intervals in our simulation, we employ full asynchronous updating with random ordering for our agents, which means that every agent performs all her actions in one go, before the next agent is activated. The consequences of all actions are effective immediately, e.g., informal games have an influence on the memory, and, thus, , of encountered agents, whether they have already been active in this round or not. This is a much more realistic assumption than synchronous updating, which introduces game phases for specific agent's actions during each round. The latter method was shown to be very problematic with some simulations by [29], who showed that some simulation outcomes could only be reached because the agents were activated in a specific static non-random order and were updated synchronously.

At the beginning of each time step, the activation order of every agent is shuffled randomly. Then, every agent is activated and takes all her actions before the next agent is activated. The following subsections describe the actions, which every agent may take during her round.

#### *2.2. Movement*

An agent who is currently not member of an institution, looks for an unoccupied site within her immediate von-Neumann-neighborhood (with a sight of one), randomly selects one of these and moves to its location if at least one such file exists. Thus, the agent can only move to a free location

directly above, below, right, or left of his current location or not at all if all cells are currently occupied.

#### *2.3. Playing the PD*

Leaving institutions aside for a while, the next step lets the agent play a game of PD against each of her von-Neumann-neighbors in random order, *i.e.*, up to a maximum of four games per round. In informal games, each agent plays a mixed strategy of cooperating with probability and defecting with probability . As stated above, the parameter evolves endogenously for each agent. This setup stands in contrast to [28], who consider only cases of mutual cooperation or mutual defection, whereas our model allows for the cases of (D,C) and (C,D) as well.

Please note that, in contrast to [28], in our model, leaders are allowed to play PD games. The reason is that leaders can also have informal encounters and, thus, changes in their trust level during their time as leaders of an institution. It would be counterintuitive that only the leaders are isolated from this societal evolutionary learning process.

#### *2.4. Building an Institution*

A cluster of at least three agents connected through their von-Neumann-neighborhoods may decide whether to build an institution. This cluster is formed by all agents directly or indirectly connected to each other, who currently are not members of an existing institution, *i.e.*, there is a path (unbroken chain) that traverses only members of the cluster, each of who is a von-Neumann neighbor of the former. An example for such a small cluster can be seen in Figure 1, which shows properly positioned neighbors (*i.e.*, members of the cluster) in green and unreachable neighbors in red.

An institution warrants enforced cooperation between its members at the cost of a membership fee. The process of institution formation proceeds in four steps. (1) Each agent within the cluster calculates if it pays to participate in the future institution; (2) Each agent willing to join the institution proposes a fee she would collect from the members of the institution, in case that the agent would become leader; (3) The agent proposing the lowest fee is appointed as leader; (4) Each agent aside from the leader decides whether to effectively participate in the institution under the designated leader and her proposed fee. If after these four steps, a connected set of two members and the leader remains, *i.e.*, at least three agents, then this connected set becomes a formal institution.

#### 2.4.1. Step 1: Decision of Participation

At first each of the agents in the cluster calculates if it pays to participate in the future institution by comparing her potential informal payoff with her potential formal payoff as a member of the institution. The agent assumes that her further encounters will be similar to previous ones, *i.e.*, she expects to encounter the same mixed strategy that she herself currently employs. Thus the agent expects that she will encounter a cooperating agent with probability and a defecting agent with probability . She then sums up the four possible payoffs weighted by their expected probability to occur. This results in an expected potential profit of a single informal encounter of agent with another agent as given in Equation (1).

$$
\pi\_l^l = \alpha\_l [\alpha\_l R + (1 - \alpha\_l)S] + (1 - \alpha\_l)[\alpha\_l T + (1 - \alpha\_l)P] \tag{1}
$$

With and being the individual payoffs of the prisoners dilemma game for the respective situations. Superscript " stands for informal profit expectation as compared to superscript # for formal profit (within an institution).

With regards to formal games, we assume the quality of enforcement of cooperation to decrease with agent 's distance \$% to the leader &. The distance to the leader is measured as the shortest path between the agent and the leader that traverses only members of the institution, each of who is a von-Neumann neighbor of the former. The payoff for a formal game is then given in Equation (2).

$$\pi\_l^F = \begin{cases} R(1 - \lambda \delta\_{l,L}), \{\lambda \delta\_{l,L} \le 1\} \\ 0, \{\lambda \delta\_{l,L} > 1\} \end{cases} \tag{2}$$

The parameter \*-! is exogenously given and serves as a weight for the loss in quality of enforcement, *i.e.*, a decrease of leadership effectivity with increasing distance (leadership distance decrement). Thus, a value of \* ./ means that agents with a distance of at least three fields do not receive any payoff from formal games anymore, though, in the model at hand, it is only relevant at which distance the expected payoff of institutional cooperation drops below the expected payoff of informal games. Nevertheless, if only taking this decrease of effectivity into account, the above case would lead to a maximum von-Neumann distance of two fields from the leader, and a maximum institution size of 12 members and one leader. This can be seen on left hand side of Figure 2, which shows the von-Neumann distances from the leader in the center. It follows that smaller values of \* enable the emergence of much larger institutions. However, it is highly unlikely that institution size will ever come near to the theoretical maximum for that \* value as indicated before since the expected formal payoff is very low further away from the leader. Thus, the value of \* is more relevant for the question how much of the reward payoff remains on the cells near the leader, e.g., with a high value of \* even agents directly adjacent to the leader would gain very little or even too little payoff from formal games. The remaining share of the reward payoff, with respect to the distance from the leader \*\$%—again for the example of \* ./—can be seen on the right hand side of Figure 2 (./ if 1 field away, ./ if two fields away, 0 if three fields away, with 0 not being displayed).

**Figure 2.** Exemplary von-Neumann distances and remaining payoff in the case of \* ./

Since the agent might have multiple encounters per round, she tries to anticipate the number of formal and informal games she will play actively and passively2 in the next round. We assume that the agent takes all available local information into account when calculating her expected payoff. The expectation for the overall payoff in non-member state is then formulated in Equation (3).

$$
\pi\_l^{NMS} = \pi\_l^l \* n \tag{3}
$$

With representing the number of local neighbors, *i.e.*, the current number of agents occupying adjacent fields.

The expectation for overall payoff in the member state on the other hand is then given in Equation (4)

$$
\pi\_l^{MS} = \left( \langle n - m \rangle \ast \pi\_l^F \right) + \left( m \ast \pi\_l^l \right) - \left. \varphi \right| \tag{4}
$$

With 5 being the fee that will be charged by the leader to-be and 4 representing the number of those local neighbors that will almost definitely lead to informal games—against agents that currently are in another, already existing institution. Thus, 4 is the optimistically expected number of future co-members of the institution to-be, *i.e.*, the current number of non-members in their von-Neumann neighborhood.

Since the institution has not come into existence yet, and no leader has been chosen, the distance to the leader is not yet defined. Thus, for the first estimates of ( and <sup>12</sup> each agent assumes that \$% , *i.e.*, that she might be appointed leader. This estimate will be corrected and decisions will be reevaluated as soon as a potential leader was selected, before the institution is formed, *i.e.*, wrong estimates will not have a huge effect.

The initial fee for this first evaluation of <sup>12</sup> is again based on the assumption that the agent herself might be leader, and will also be proposed to the other agents in a later Step (2.4.2). We assume that an agent estimates her fee proposal according to the sum of collected fees equaling the cost of being the leader, *i.e.*, we assume that leaders do not factor in a profit margin. The cost of enforcing cooperation is then given in Equation (5).

$$\mathbf{c}(\overline{\mathbf{s}}, \mathbf{s}) = \overline{\mathbf{s}} \sqrt{\mathbf{s}} \tag{5}$$

<sup>2</sup> Passive play occurs when a game is initiated by another agent—*i.e.*, a game that is played outside of the target agent's turn.

Equation (5), thus, denotes the cost accruing to the leader from enforcing cooperation and 8 is the size of the institution, *i.e.*, the number of members including the leader. Furthermore, \$7 represents the average distance of the leader (*i.e.*, herself) to all members of the institution. Obviously, the chosen cost function is just one of many possible alternatives, but it serves as a first reasonable and parsimonious approach. Future research may well investigate the effects of different cost functions.

The initial fee 5 for this first evaluation of <sup>12</sup> is then given in Equation (6).

$$\varphi = \frac{c\{\overline{\delta}, s\}}{s - 1} \tag{6}$$

We assume that the leader agent herself does not need to pay the fee, thus, the costs are divided by the number of members without the leader 8 . Since, at this moment, it is not yet clear to the agents how large the institution will, in fact, be (since potential members-to-be will be allowed not to join, once the potential leader is known), they use the size of the cluster they are part of as an estimate.

Each agent in the cluster evaluates the benefits of participating in the institution now and compares her expected non-member state payoff <sup>012</sup> with her expected member-state payoff <sup>12</sup>. Only if the latter exceeds or equals the former, the agent is willing to participate in the institution. If all agents in the cluster come to the conclusion that they will be better off as members of the institution the formation of the institution proceeds to the next evaluation steps—else the institution will not be evaluated any further. Due to the completely asynchronous nature of the simulation, another agent might again start the evaluation of the same—or a slightly changed—cluster within the same time step.

#### 2.4.2. Step 2: Proposing a Fee

During Step 2, each agent willing to participate in the institution proposes the fee that she would collect from members, which has already been calculated in the evaluation Step of 2.4.1., as given in Equation (6).

#### 2.4.3. Step 3: Appointing a Leader

Next, the agent proposing the lowest fee is appointed as the leader of the potential institution to-be. If more than one leader proposes the lowest fee, one of them is appointed randomly.

#### 2.4.4. Step 4: Final Evaluation

Finally, each agent in the cluster recalculates the distance to the leader to-be and reevaluates her expected payoffs. If the situation changed and her expected member-state payoff is no longer higher or equal to her expected non-member state payoff, she chooses not to join the potential institution. This procedure serves as a preliminary proxy for future implementations with more complex evaluation procedures, such as voting. Any agent that is disconnected/isolated from the cluster, due to other agents leaving the cluster, will also not be part of the institution to keep institutional territory

contiguous. Only if after this final evaluation a connected set of at least three agents (including the leader) remains, an institution emerges. All agents participating in an institution become sedentary and remain so until they eventually leave the institution or the latter breaks apart. Every agent may only leave, join, or found an institution once per round, which is evaluated in the given order.

#### *2.5. Joining an Already Existing Institution*

If an agent is located in the von-Neumann neighborhood of a member of an institution after moving, the former may choose to join the institution as well. Again, this agent compares her non-member-state payoff with her hypothetical payoff from joining the institution, based on actual distance to the leader and future size of the institution. If the member-state payoff is higher than or equal to the non-member-state payoff, the agent joins the institution.

#### *2.6. Leaving an Institution (Re-Evaluating Membership)*

In each time step, every member of an institution re-evaluates her gains from participation in the institution. If due to changed circumstances (e.g., changed neighborhood or individual trust), her member-state payoff no longer exceeds or at least equals her non-member-state payoff, the agent chooses to leave the institution. All members not connected to the leader anymore are forced to leave the institution as well. If the size of an institution falls beneath three, it ceases to exist.

#### *2.7. Re-Evaluating the Fee*

In every period, each leader of an institution re-evaluates the fee she collects from the members of the institution. If the sum of fees collected in the previous period is smaller than the cost accrued to it for enforcing cooperation, the leader would suffer a loss. In this case, she raises the fee such that the collected fees would equal the cost in the current period.

Since we employ strict asynchronous updating, each agent may actively initiate one attempt to found a new institution during his turn. If such an attempt results in the foundation of an institution during one agent's turn, it is founded effective immediately for all agents that finally participated. Agents who are activated after they passively participated in the founding of an institution can only play the PD during his turn, because agents may only participate in one institutional activity per time step, *i.e.*, founding, joining, leaving—evaluation alone is not considered an institutional activity for this purpose.

#### **3. Simulation Experiments, Data Analysis and Results**

In this section we illustrate the data analysis of simulation experiments and show the main results of the model. Simulations were performed with a payoff matrix for the pairwise prisoner dilemma that is in line with the non-degeneracy condition according to [1] <sup>3</sup> . The initial parameters for our

<sup>3</sup> Basically resulting into - < and - <, for details compare [1]. This condition has strong consequences for the calculation of the informal payoff of agents. If we would pick payoff values not meeting

experiments comprise settings given in Table 1. The memory size of agents (their cognitive endowment) smoothes the level of societal trust within simulation runs and works as a behavioral inertia therefore. Particularly a higher memory size leads to fewer fluctuations in societal trust, since agents play in a more consistent way. In this respect more agents are committed to a common average societal trust. Adjustments in low memory sizes have a strong effect, whereas adjustments in high memory sizes have weaker effects; e.g., changing the memory size from 80 to 100 encounters does have a weaker effect than changing it from 10 to 20 (especially since very low numbers of remembered encounters could theoretically even result in a completely new set of memories within a single simulation step). This result is quite intuitive, for that reason the memory size is not used as an additional variable for permutations in the following analysis.


**Table 1.** Initial parameters for simulation experiments.

The motivation of the analysis put forward is to get a deeper understanding of the generic logic of institution demography, the interdependent effects of individual strategic action, societal trust and institutional accumulation. The following two initial parameters are crucial for this investigation: the initial level of societal trust and leadership distance decrement \*. Correspondingly, we kept parameters given in Table 1 constant and computed simulation runs around couples of initial and with varying permutations, see Table 2.

As elaborated in Section 2, the initial level of alpha fixes the starting distribution of individual cooperation and defection of agents. Otherwise the leadership distance decrement (\*) constrains the size of institutions during simulation runs. The two parameters serve as proxies for the dynamics of institutional life-cycles in the model. Experiments have indicated that the simulation may eventually reach a final state, either with static institutions (*i.e.*, complete cessation of institutional change) or without any institutions (only informal encounters). In order to analyze the dynamics in between these two states with more detail we could limit the parameter space due to experiences with former experiments and induce permutations of initial societal trust with a lower level of for more stable institutional settings. These simulations, experiments 1–3 (Table 2), are varied with \* =; \* and \* =. Low leadership distance decrements result into a gain of power in the periphery of an institution (*i.e.*, a higher remaining profit in the periphery) and therefore lead to larger institutions. In such settings the simulation almost instantaneously tends to converge to a static institutional scenario. Higher \* leads to smaller institutions which are not stable over time, simply because the maintenance costs do not pay off anymore. This lead us to the expectation that simulation experiments 4–6 would deliver the most exciting results in terms of a

the "nondegeneracy" condition (e.g., - ) then the informal payoff function would be in linear dependence of alpha (trust), *i.e.*, a very special and singular case.

complex evolution (between order and chaos). The simulation experiments 7–9 have been initialized with > (that means a very high initial level of trust), where participation in an institution is not tempting.


**Table 2.** Simulation experiments with permutations of and \*.

We have looked into the evolution of some crucial variables with 20 replications (with randomly generated seeds) for each simulation experiment running over 10,000 rounds/periods, resulting in 9 × 20 datasets. Preliminary experimentation has shown that the institutional landscape may stabilize after approximately 5000 simulation periods, to this end we decided to gather an overview for the long run and have doubled this crucial time horizon. For every dataset we have created aggregated measures for the evolution of the following variables: mean societal trust, mean share of non-members in the population, mean number of institutions, mean age of institutions, and heterogeneity within the age structure of institutions. At first we are interested in the evolution of societal trust.

#### *3.1. Societal Trust*

Societal trust (the average share of cooperative actions within the whole population) may theoretically converge towards (full cooperation). Otherwise (full defection) never occurs, because agents will always take refuge in institutions once the amount of defectors increases in the population. The evolution of societal trust depends on the initial values of trust ( ) and leadership distance decrement (). In general, the higher the higher is the level of societal trust during a run, since the initial memory of cooperation has a strong path-dependent effect and agents are not likely to build institutions respectively. Figure 3 shows the evolution of societal trust ( ) for all nine simulation experiments, where (a) summarizes the permutations of for , (b) the permutations for / and finally (c) for >. On the left hand side of Figure 3 we see graphs showing the evolution of the means over 20 replications and on the right hand side we see the standard deviations for these means accordingly. The data confirms that a higher initial value of societal trust leads also to higher values during the simulation when we compare Figure 3a–c. In a very similar manner a higher initial level of societal trust makes the evolution of trust more robust, as a comparison of the standard deviations in Figure 3a–c shows. However, the cause of this effect lies in the instability of institutions. Institutions are instable only if cooperation is high within the

population, because they are not tempting enough for agents to join (expected payoffs of non-member state exceed expected payoff of member state, as given, e.g., in the simulation experiments in Figure 3c. A high level of societal trust with a given memory size of  encounters indicates a stable and robust process. Otherwise, Figure 3a shows, that if agents defect, more due to a low initial level of societal trust, they take refuge in institutions (enforcing them to cooperate) in early phases of the simulation.

Taking a closer look lets us follow that a lower \* leads in general to lower levels of societal trust within the simulation experiments. In Figure 3a,b the lowest level of societal trust is given in the cases of \* = , wherelse \* = leads to the highest levels of societal trust in all permutations. Of course this relation corresponds with the basic model setup as indicated in Section 3.2: lower \* results in larger institutions (smaller loss of power dependent on the distance between member and leader). Due to the spatial interaction topology (*i.e.*, locality effects), it is more likely that agents become members thereafter. In the very long run, high leads to processes where societal trust tends to converge to full cooperation.

**Figure 3.** Evolution of societal trust ( ).

#### *3.2. Evolution of the Population Structure*

The next variable we investigate concerns the evolution of population structure, with regards to membership in institutions. Figure 4 shows the average share of non-members in the population across the conducted simulation experiments. It indicates that the population structure is quite stable over time, as the standard deviations show in Figure 4a–c. If leaders have greater influence in the periphery of institutions (low \* ) then the amount of non-members playing with randomly encountered agents settles on a low level correspondingly.

Furthermore, we have checked for the robustness of this result by looking into the average number of institutions respectively, as illustrated in Figure 5. Since the number of institutions further stabilizes after an adaptation phase of 2000–3000 periods (also visible in Figure 4) we can conclude that there is a direct relationship between leadership distance decrement \* and the amount of institutions indeed as expected. Figure 5a–c show that permutations with \* = result into 80 institutions, although this number deviates between 0–30 dependent on . Otherwise lower \* is more sensitive to the initial level of societal trust . This analysis further indicates that interesting cases of permutations are appearing around / and \* . These cases have to get investigated in more detail by looking into the mean age of institutions.

**Figure 4.** Share of non-members in the population.

#### **Figure 5.** Number of institutions.

#### *3.3. Institutional Life-Cycles*

Since the population structure is rather stable, we have anticipated that the dynamics are more volatile in the evolution of institutions, dealing with entry, (in)stability and exit of institutions. Figure 6 shows the spectrum of institutional life cycles in a grand comparison of all computed permutations in simulation experiments 1–9. Accordingly, we have derived a deeper analysis on the mean age of institutions, in particular the accumulation process dependent on individual action and social structure. This full picture illustrates that our model produces two main results concerning the demography of institutions. On the one hand, institutions accumulate quickly from start due to a high number of free-riders in the initial population. Thereby, agents take refuge in governed institutional structures under leader supervision preventing exploitation in non-member state. Simulation experiments 1 and 2 result into this finite state of the simulation, where institutions do not fall apart anymore, *i.e.*, their life-time is infinite. We call this result a *static and ordered scenario of institutional change.* On the other hand, simulation experiments 8 and 9 indicate that institutions cannot stabilize, because their leaders are not able to influence the periphery of their institutions effectively, thereby, the sum of collected membership fees remains too small for long maintenance of

larger institutions, or ultimately any institution at all. In this case institutions have a very short life-time, they "pop up" very frequently in pulses. This final state of institutional change delivers the second main result in the "*in silico*" analysis of the model. We call this result a *dynamic but highly fluctuating scenario of institutional change*.

**Figure 6.** Mean age of institutions—Full picture long run.

However, we further identify a third result characterized by a more complex behavior. This result is best illustrated via the system behavior of simulation experiments 3, 5, 6, and 7. We call this result a *dynamic and complex scenario of institutional change*. Here, institutions cycle over a long period of time where it is undecidable to which state they may converge. Simulation experiments 5 and 7 converge to the highly fluctuating (almost chaotic) state of institutional change. We dub this process *institutional learning*, since the early advancing life-time of institutions experiences a turning point, where societal trust reaches significant levels that agents are tempted to get rid of social structures and switch to non-member status. Institutions in this model support social learning, which will be described in more detail at the end of this section. Otherwise, experiments 3 and 5 tend to develop towards the static and ordered scenario of institutional change, although with continuous fluctuations in the mean age of institutions. In order to confirm these results we provide an exploded view of this picture in Figure 7 and discuss some more details. Figure 7a–c highlight these results by showing just the medium run where the diversity within the mean institutional age becomes better visible.

**Figure 7.** Mean age of institutions—Exploded view medium run.

The most interesting cases of institutional learning are given in Figure 7b,c with \* The standard deviations indicate that these processes are not as deterministic as it seems in comparison to those with lower or higher leadership distance decrement. In this generic model of institutional change institutions may act as learning vehicles even with higher values of initial societal trust. The diversity within the age structure of institutions is high in these cases fluctuating between 10 and 100 periods. A closer view on the heterogeneity of institutional life-cycles among institutions within each time step (Figure 8) confirms this finding.

We observe that the higher the initial level of societal trust, the lower the heterogeneity within the age structure. Thus different values of \* may lead to phase-transitions towards another scenario. To conclude we want to turn the attention to the similarity in the trend of the aforementioned processes, which is not recognizable from the aggregated measures shown previously. Figure 9 gives the overall trend of replications within simulation experiment 5. It shows that institutions change indeed in cyclical processes, what we have dubbed *institutional learning*. The accumulation of these generic governed structures follows a similar trend, the cyclical behavior is of course leveled out in the aggregated views we have shown previously.

**Figure 8.** Mean age of institutions—Heterogeneity within the age structure of institutions.

**Figure 9.** Similarity in trend for / and \* over replications.

The diversity within institutional change that our model produces is a distinct feature that becomes evident only in a heterogeneous multi-agent configuration. The two main results indicate the deterministic corner solutions that can also be derived from a closed form equation-based game-theoretical model in continuous time, but an analysis of the complexity between these deterministic solutions is out of range in this type of models. In this respect the discovery of *institutional learning* makes our study distinct in this realm of game-theoretical inspired evolutionary institutional economics and political economy. Again it is the interdependent interplay between agency and structure in space and time, which delivers such insights. The complex adaptive system dynamics in our model open a spectrum of potential institutional life-cycles over time. A crucial feature given by the model concerns the cognitive capabilities of agents, their potential to learn adaptively from the past and reevaluate their membership status in particular. Learning is, here, considered not just as a temporal processes, as mostly conceived in population games, but is severely dependent on the dynamically changing spatial distribution of agents, because institutions emerge and exit on certain places in the artificial political economy. Their bounded rationality in terms of [30] develops due to spatiotemporal adaptation (a mesoeconomic process), thereby depending on the complex evolution of the system as a whole but also on their institutional subsystems [31]. This finding is still in line with the socio-cybernetic theory of institutional change by Veblen, advanced by the means of evolutionary and complexity theory. Such a transdisciplinary approach to political economy may further stimulate novel modes of teaching in economics, see [32]. However it's these properties that are responsible for the likely volatile system dynamics, but they are also the major contributors to more noise and more complicated data analysis. Since the analysis of contingent path-dependent processes and emerging structures lies at the heart of evolutionary institutional economics and political economy, people are aware that results and moreover interpretations are never unambiguous.

However, we are able to conclude some major dependencies and dynamics in our model of institutional change. The evolution of societal trust is the major driving force behind the building up of institutions. If trust runs high on average, the need for institutions as we designed them decreases, because agents don't need executive protection. Consequently, this logic also works in the opposite direction, if trust runs low, agents demand institutions, and the absolute number of them will increase. Although this observation seems trivial it has some crucial ramifications dealing with the frequency of emergence and exit, *i.e.*, institutional change in cyclical patterns. These dynamics are majorly dependent on the initial values of exogenous variables, like the initial level of trust and the leadership distance decrement. As our experiments have shown, this parameter space determines the different paths and processes of institutional change. According to them we can identify three scenarios of institutional change generated by the computational simulation of our artificial political economy. Interestingly, our three scenarios share some generic characteristics of the results given by the complex system analysis in [33]. Stuart Kauffman has shown that in ordered regimes the elements freeze very fast and form a bigger cluster, which spans across the system. In the chaotic regime there is no frozen component; instead, a connected cluster of unfrozen elements appears. Small changes in the initial parameters may lead to strong reactions of the whole system. Transitions from the ordered to the chaotic state are possible through phase transitions, where the transition region is called a complex regime. In this regime frozen and unfrozen elements are percolating simultaneously with very sensitive conditions on the complex edge between chaos and order. The three scenarios found in our experiments are correspondingly called:

• *static and ordered scenario of institutional change* 

a non-cooperative world indicated by simulation experiments 1 and 2

	- a cooperative world indicated by simulation experiments 8 and 9
	- complex institutional learning indicated by simulation experiments 3, 5, 6, and 7

To give a more vivid and intuitive understanding of the different cases compare Figures 10–13, which visualize the artificial landscape of exemplary runs of experiments 1, 3, and 9. The subfigures show snapshots of the landscape of agents and institution in different points of time—please note that there are different timespans between subfigures in Figures 10–13, since the different classes have gravely varying convergence speeds. The subfigures show non-member agents, who have not yet been member of any institution depicted as blue squares and non-member agents who have already been in an institution before depicted as red squares. Furthermore, green circles depict leaders and green squares depict members of institutions, with black connections between members of the same institution. The darkness of institutional leaders and members indicates the age of the institution—*i.e.*, light green reflects a young institution, where dark green depicts a relatively old institution. Figures 11 and 13 additionally show pink (light red) squares and circles, which indicate agents in attempted institutions, *i.e.*, institutions that only existed for one evaluation period (technically these have an institution age of 0). These come into existence when the overall level of is very high and no stable institutions exist anymore and are disbanded immediately. When taking a look at the following figures, please keep in mind that we interpret the grid as a torus; it might look like there are one or two-person institutions at the edges of the landscape, but in truth they continue on the opposing edge of the landscape.

Figure 10, now, is an the visualization of the landscape of an exemplary run of experiment 1 (\* =, , other parameters as given in Table 1) and shows what we called a *static and ordered scenario of institutional change.* The first subpicture on the left hand side shows that after a very short time (at B ) most agents already are members of institutions, with a number of agents still wandering around. The next subpictures show that very quickly (at B =) most of the agents are now members of institutions, that most institutions are already relatively old and stable, with only very few agents still wandering around. Shortly after (at B =) all agents are members of institutions, which are completely stable (old). The society is now ordered, in the sense that there is only cooperation enforced in institutions and static since there are no elements of change anymore, *i.e.*, the landscape is identical for all following time steps. Since this lock-in happened so fast, there was almost no change in the societal trust level—a graph of the development of societal trust over time would show a flat line.

**Figure 10.** Institutional landscape of an exemplary simulation run (\* =, .

Figure 11 now shows the visualization of the landscape of an exemplary run of experiment 9 (\* =, >, other parameters as given in Table 1) and shows what we called a *dynamic but highly fluctuating scenario of institutional change.* The first subpicture on the left hand side shows that after a very short time (at B ) most agents have already been members in very shortly lived institutions, with only a very small number of institutions (in this example only 1), because the initial level of societal trust was very high to begin with. The next subpicture shows that in the short run a small number of institutions emerged ( B = ). This was the result of an already highly heterogeneous distribution of , which lead to agents with lower to still seek shelter in institutions—during this process, societal trust even went down a little. Nevertheless, the system quickly returns to converge against full cooperation, while institutions have not needed anymore for a long time due to the already high level of trust.

**Figure 11.** Institutional landscape of an exemplary simulation run (\* = >.

exp 9, B CDEF > exp 9, B = CDEF /G exp 9, B / CDEF G

Figure 12 shows the development of societal trust over time of the same exemplary simulation run, which was depicted in Figure 11. As can be seen, societal trust rises rather quickly, while the process of reaching full cooperation can take quite long in singular runs. There is almost no difference between member and non-member agents in terms of average trust, since there are only few, shortlived institutions early on, *i.e.*, agents are non-members almost all of the time.

**Figure 12.** Societal trust timeline of an exemplary simulation run (H = >.

Figure 13 now shows the visualization of the landscape of an exemplary run of experiment 3 (\* =, , other parameters as given in Table 1) and shows what we called a *dynamic and complex scenario of institutional change.* The first subpicture on the left hand side shows that after a very short time (at B ) a number or institutions already exist, with the majority of agents not being members of institutions. The next subpicture (B =) shows that a number of institutions have existed for some time, while there also are some quite young institutions, as well as a number of non-member agents. The following subpictures show that the number of institutions rose, since in this particular simulation run societal trust went down to quite low levels (at B = ). Nevertheless, in the medium run, as depicted in the following subpictures ( B to B = ), overall trust rose again, thus requiring less institutions and in the long run (at B /=) the artificial society arrived at full cooperation again.

**Figure 13.** Institutional landscape of an exemplary simulation run (\* =

#### **Figure 13.** *Cont.*

Figure 14 now shows the development of societal trust over time of the same exemplary simulation run, as depicted in Figure 13. As can clearly be seen initially increases and decreases again, which is then followed by a kick-in of the self-reinforcing process. In the long run, societal trust rises until full cooperation is reached.

In summary institutions in our model indirectly support social learning. Those agents with a low are more likely to join institutions and thus become sedentary—compare Figure 14, where it can be seen that the average of non-member is consistently higher than that of members (in the timeframe in which institutions are needed). In case of larger institutions a number of these low agents are even out of reach of non-members or members of other institutions, as the former are embedded deep within the institution's realm. Thus, these agents on average play fewer or even no informal games at all, during their membership in the institution. Non-member agents with a higher stay mobile and then have a higher chance to encounter other agents, which also have a higher . Thus they learn to cooperate even more over time, eventually increasing overall trust over time. These agents then function as "emissaries" of cooperation, slowly increasing the trust of agents situated on the outskirts of institutions ("teaching" them to cooperate). Since these are further away from their leader, their expected formal payoff can be quite low—depending on the \* parameter, which leads

to larger institutions, but lower formal payoff. Thus, they can be quite sensitive to changes in cooperative behavior shown by informal games with wandering non-member agents and start to leave institutions quickly.

This notion seems to be quite intuitive since in the early phases agents tend to take refuge in institutions, because trust is very low, then trust rises and then the system experiences a crucial transition, because life outside of the institution promises higher short-term payoffs on average and agents start to cooperate even more, but without institutions. Since a personal = means that the agent will cooperate more often than defect, and thus rather cause "positive" than "negative" memories in other agents. "Positive" memories lead to more cooperative behavior in other agents, which reinforces itself and, in the very long run, defection is crowded out and the society arrives at full cooperation, which is then stable.

On the other hand this scenario may also converge to a static state of frozen institutions quite quickly. This is the case when cooperation without institutions takes too high costs in the long run, or when defection is still beneficial. It is also likely to occur when setting the memory parameter ( to a small value, with the result that the wandering agents (what we called "emissaries" before) learn non-cooperative behavior through playing with members of institutions, while the level of is still low. This can also lower the emissary's to such a degree that he himself wishes to join the institution, because he now feels "safer" as a member of the institution. Consequently societal trust may converge to a constant level, once all agents have founded or attached to an institution. However the dynamic attractors for a transition in the one or the other direction are sensitively depending on certain permutations of initial societal trust and leader influence in the periphery.

#### **4. Conclusions**

In our paper we have presented an agent-based model connecting the theory of games with institutional economics via socioeconomic computational simulations, thereby providing new insights for evolutionary institutional economics and political economy. We follow the core concept of the old institutional economics, where institutions are conceived as real social structures. The Veblenian idea of institutional change via cumulative causation of habits of thought serves as the dominant proxy for this emerging field of socioeconomic research. Obviously a synthetic translation of this concept into a concrete model and its subsequent simulation rigorously cuts components of its original semantic narrative. However, our findings indicate that even an approximate, at best sufficient, simulation of this kind of institutional economics demands a transdisciplinary approach by a formal combination of evolutionary game theory and complex systems theory. Such an endeavor can be realized via the use of computational methods and simulations of heterogeneous multi-agent systems in discrete time. A modern conception of complexity as composed by Wimsatt [34] may serve as a theoretical blueprint respectively, because he advances the Simonian [31] notion of reductionist heuristics as means to more holistic theories, in contrast to linear additive methods of total aggregation he refers to decomposition. This basic argument favors a theory of practice approach, which is again in line with the old institutional economics that builds to a great extent on the philosophy of American pragmatism.

Institutions appear as diverse stabilized social structures dependent on the individual evaluation of heterogeneous agents to enter or exit them. Then the iterated PD builds the formal proxy for sequential social conflict. Traditionally it is assumed that cooperation may crowd out defection in the long run under certain conditions, such as group selection or the existence of certain beneficial topologies. Still, from a political economy perspective it is very likely that continuous defection gets never crowded out under moral assumptions such as altruistic punishment [35] or indirect reciprocity [36]. On the contrary it is more likely that individual agents will build institutions (conceived as meta-stabilized structures of culturally transmitted rules) capable of supporting social learning, especially for large scale; *i.e.*, political economy. If such a structure is established once, it is highly realistic that there are costs associated to the maintenance of it. We regard this trade-off as essential for the dynamics of institutional change since agents continuously need to evaluate their participation in stable social structures for reasons of conservation or even progress (inertia *vs.* change as discussed extensively in [16]). To this extent our third scenario represents a very realistic case of institutional change, where institutions emerge and exit over long periods in a cyclical movement. These institutions support social learning, where in times of defection agents can take refuge in protected social structures and leave them in time of cooperation. Thereby, the role of a leader executing, such a policy via institutional structures may become more and more redundant once free-riders have "learned" the benefits of cooperation. Still, it is not said that even in such a scenario the system switches again towards a protective regime eventually. Nevertheless, we have to consider that this long run decline of institutional significance would very likely not hold in a model with agent mortality and procreation, where offspring would not be exact copies of their parents.

Due to the continuous spatiotemporal contact of individual agents with institutional structures, agents share and anticipate the current societal level of trust and learn from it, thus influencing their future behavior. Of course this is only possible if the agents are equipped with a simple cognitive apparatus and a crude memory of past events, at least. The framework presented and the simulations carried out clearly encourage further research in the envisaged direction. Most of the issues explicitly studied so far are just one example of what could be seen as essential features of emergence and exit of institutions in human societies. In our framework we use very basic concepts of power and exploitation regarding the institutional leader. Even in such an environment, where coercive power relations between agents are highly stylized—centralized and monopolized by a given ruling political entity—it is possible to observe a wide variety of forms of emergence and exit of institutions, *i.e.*, *diversity in institutional life-cycles.* Those basic political economy elements point out the potential of such an evolutionary institutional economic approach for further models of power and exploitation. The rules for the fee paid to the agent leading an institution as well as the rule for choosing this leader are just typical economic concepts to keep dynamics still simple for useful exploration. Extending our approach by replacing them with ideas reflecting pre-existing power relations securing exploitation would certainly enable our example to be a more adequate image of the historical emergence of institutions—where there has been a historical primacy of coercive power and exploitation compared to voluntary interactions on markets, thereby hinting at the potential scope of the approach. Extensions of this kind clearly suggest opening up new dimensions of heterogeneity of agents leading to a richer diversity of institutions.

#### **Acknowledgments**

The authors would like to highlight that initial research and previous versions of this paper were produced during a research project granted by the Oesterreichische Nationalbank (OeNB—the central bank of the Republic of Austria) within the "Jubiläumsfonds" project 13350. Furthermore we want to thank participants and organizers of the research area sessions of RA-C "Institutional Change" at the annual conferences of the European Association for Evolutionary Political Economy (EAEPE) during the years 2009–2012; as well as at the participants and organizers of the annual conference of the Association of Heterodox Economics 2009 for fruitful and productive comments. We further want to acknowledge the highly constructive critique of three anonymous referees.

Finally the authors are very grateful and acknowledge the efforts of Hardy Hanappi inspiring this research.

#### **Author Contributions**

The author's contribution is equal in all aspects of the reported research and writing of the paper.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **References**


## **Of Coordinators and Dictators: A Public Goods Experiment**

#### **Jürgen Fleiß and Stefan Palan**

**Abstract:** We experimentally investigate whether human subjects are willing to give up individual freedom in return for the benefits of improved coordination. We conduct a modified iterated public goods game in which subjects in each period first decide which of two groups to join. One group employs a voluntary contribution mechanism, the other group an allocator contribution mechanism. The setup of the allocator mechanism differs between two treatments. In the coordinator treatment, the randomly selected allocator can set a uniform contribution for all group members, including herself. In the dictator treatment, the allocator can choose different contributions for herself and all other group members. We find that subjects willingly submit to authority in both treatments, even when competing with a voluntary contribution mechanism. The allocator groups achieve high contribution levels in both treatments.

Reprinted from Special Issue: Aspects of Game Theory and Institutional Economics, *Games*. Cite as: Fleiß, J.; Palan, S. Of Coordinators and Dictators: A Public Goods Experiment. *Games* **2013**, *4*, 584–607.

In 2005, a special issue of Science listed the 25 areas where scientists perceived the most important gaps in our knowledge to date [1]. These included the question, raised by Pennisi [2], of how cooperative behavior evolved to form the basis for the complex societal structures we observe today. She pointed out the importance of investigating which conditions and institutional settings promote cooperation in situations where individuals have an incentive not to cooperate. A famous example of such a dilemma is of course the contribution to a public good. In the standard setting, individuals have strong incentives to maximize their own payoffs by free riding and not contributing to the public good. As a result, a group of rational actors would be unable to supply a public good.

A large number of laboratory experiments have investigated cooperation in the public goods game (for reviews, see [3,4]). In the most common version of the repeatedly played public goods game, each individual in a group makes his or her own decision about how much of the endowment to contribute to a public good in every period. The results show that contributions tend to start out at an average of around 50% and decline towards zero [4,5]. Looking at individual behavior, a number of subjects are usually found to contribute in the first few periods of repeated public goods games. Over time, their contributions decline as they observe other subjects free riding and contributing nothing. In the end, because of these conditional cooperators' reactions to the free riders, the public good no longer gets produced [6–8].

These somewhat disappointing findings on human cooperative behavior in such dilemmas have been qualified by more recent results. There are mechanisms that can foster contributions to the public good. One such solution is monetary punishment, as introduced by Ostrom, Gardner and Walker [9]. Their paper, and a number of follow-up studies, show that (centralized and decentralized) punishment and reward can stabilize contributions at high levels [10–13].1 Besides punishment, voting on the implementation of different proposed contribution rules has been shown to have a positive effect [14,15].

We claim that besides the instruments of punishment and reward, direct power over the decisions of others can play an important role when it comes to the success of collective action in dilemma situations. Weber [16] defines power as "the likelihood that one person in a social relationship will be able, even despite resistance, to carry out his own will." Structures of (asymmetric) power distributions are omnipresent in everyday life and characterize whole societies, but also groups, (business) organizations and the like [16,17]. Yet, despite its obvious importance in everyday life, the discipline of economics has not devoted much time to studying power over the decisions of others (for an analogous argument and another recent experimental study regarding power, see [18]).

Kroll *et al*. [19] show that contributions to a public good increase if group members in a public goods game can vote for a binding proposal as opposed to making voluntary contributions. One particularly noteworthy recent exception builds on the idea of binding subjects to specific actions. It employs a new contribution mechanism in public good games, based on an asymmetric distribution of power: the allocator mechanism. The two studies introducing this topic are Hamman *et al*. [20] and Bolle and Vogel [21]. Both show that, under certain conditions, one way of promoting the provision of a public good is to establish an allocator who has absolute power over the decisions of all group members. In the unique rational expectations equilibrium, this allocator is then able to force all group members to contribute their full endowment to the public good, thereby maximizing the collective outcome. Hamman *et al*. [20] and Bolle and Vogel [21] largely confirm this theoretical prediction and show experimentally that the use of an allocator results in comparatively very high contributions to the public good.

Where the two studies differ is in the specifics of group members' and allocators' choice sets and in the structure of the experiment. Hamman *et al*. [20] let group members elect an allocator and find that groups ensure full provision of the public good primarily by electing pro-social allocators. Since each group of nine holds a new election every period, their setting allows for punishment by removing underperforming allocators from power. Allocators who contribute fully for everyone are found to be re-elected in almost all cases. Bolle and Vogel [21] choose a different first phase for their experiment. They initially let subjects play 10 periods of a public goods game with voluntary contributions. This is followed by one period, where an allocator is chosen (either randomly or by election) to make the allocation decision for the two other members of her three-person group. This sequence of voluntary (10 periods) and allocator contribution phases (one period) is repeated twice, such that subjects play three allocator periods in total. Like Hamman *et al*. [20], Bolle and Vogel [21] observe higher contributions in the allocator setting than in the setting with voluntary contributions. Interestingly, they find no statistically significant differences between the election and the random selection treatments.

The great success of the allocator mechanism documented in these two studies merits further research. We explore its performance characteristics by (i) systematically varying the action space of

<sup>1</sup> For a recent review, see [4].

the allocator and by (ii) studying whether subjects prefer groups governed by the allocator mechanism over groups where they can freely choose their own contribution when group choice is endogenous. Note that the two precursor studies implement the allocator mechanism in a way that either forces all subjects to participate or allows endogenous participation, such that non-participating subjects profit from the public good of participating subjects. In this second case, Hamman *et al*. [20] find that the allocator mechanism is not able to increase contributions due to free riding. Only when communication is possible do half of their groups choose to transfer their decision rights and achieve high contribution levels. We build on these results and investigate whether the transformation of the public good into a club good, from which only group members can profit, is also able to foster the allocator mechanism's efficiency. Our second question therefore is of special importance, since it captures a subject's willingness to submit to authority for her own benefit and the benefit of the whole group. This question is also closely related to a major finding in the discipline of new institutional economics [22]. It states that the voluntary participation of subjects in finding a solution to coordination problems substantially increases the likelihood of success.

Such endogenous institution choice has previously also been examined for the punishment and reward mechanisms mentioned above. One approach is to let subjects vote whether they want to implement, e.g., punishment in the public goods game they will later be playing [23]. Another is to let subjects self-select into groups with different, exogenously fixed institutional settings. Gu¨rerk *et al*. [24] find that subjects are more likely to self-select into groups with sanctioning institutions than into alternative groups and that the likelihood of choosing the group with sanctioning institution increases over time. In this way, they show that when two groups with different institutional settings compete against each other, the group with a sanctioning institution—due to the higher payoffs it generates for its members—prevails in the end. Hamman *et al*. [20] also present some of these aspects in their experiments. They allow subjects to choose whether they want to be part of electing an allocator who will then make the contribution decision on their behalf or whether they want to choose their level of contribution themselves. The important difference to the design of Gu¨rerk *et al*. [24] (and this study) is that subjects who choose not to be part of the electoral delegation mechanism in Hamman *et al*. [20] nonetheless profit from the public goods contributions made by subjects who have delegated their decision power. This allows subjects who have not joined the delegation mechanism to free ride on its outcomes. 2 Without communication, Hamman *et al*. [20] obtain an average contribution level of only 11%. In this setting, the allocator mechanism thus fails to sustain high public goods contributions. Whether groups governed by the allocator mechanism have an advantage over groups with voluntary contribution when one group does not profit from the contributions of the other is an important and unanswered question.

Building on Hamman *et al*. [20] and Bolle and Vogel [21], we thus identify two important questions. First, do subjects prefer a group governed by the allocator mechanism over a group with a voluntary contribution mechanism? Second, which factors influence subjects' group choice?

<sup>2</sup> Kosfeld *et al*. [25] showed that centralized punishment institutions are able to prevail in a setting where non-participating players can free ride on the contributions of the players participating in the centralized punishment institution. This leads to high levels of efficiency in their public goods experiments.

The present article answers both of these questions. As an additional innovation, we drill down into the role played by the allocator's action space. Specifically, we compare a treatment with what we term a coordinator—an allocator who can choose one uniform contribution level for all members of her group, including herself—to a treatment with a dictator—an allocator who can choose a contribution level for herself and a different, uniform contribution level for all other group members. This mimics many settings outside the lab where a group leader or government establishes policies that apply to all group members equally (e.g., regulations that require every able-bodied male adult to contribute to the public good of national defense by having to serve a term in the military, as exists in many countries). Consider as a loosely-related example for our setting a country's decision to join the European Union. This country faces a tradeoff between giving up the freedom to decide on its laws and regulations entirely on its own and abdicating some of its regulatory authority to the EU institutions in return for the benefits from greater cooperation. This example shares with our design the feature that leadership of the group, in this case, the presidency of the council of the EU, rotates through all member states, with each country serving only one term. (Another example would be the decision by a stone-age human to join a tribe, thus giving up individual freedom in order to gain the ability to jointly hunt larger game, which is argued to have contributed to the rise of modern civilization; see, e.g., [26]).

The remainder of this paper is structured as follows. In Section 1, we state our research questions and derive our hypotheses. Section 2 outlines the experimental design and procedures. Results are presented in Section 3 and discussed in Section 4.

#### **1. Research Question and Hypotheses**

We investigate the question of how societal coordination can arise endogenously in response to economic coordination problems. We take a standard public good game as our workhorse model and augment it by giving subjects the freedom to select into one of two groups at the beginning of every period. In the voluntary contribution group (VCG), they play a standard public good game by deciding how much of their endowment to keep for themselves and how much to invest into a public good. If subjects select into the allocator contribution group (ACG), one group member is randomly chosen to set the contribution level for all ACG members.

Given a contribution level, we use the same payoff function in both groups. Specifically, a subject's payoff for any one period in our experiment is calculated as follows:3

$$
\pi\_l = \left. E\_l - c\_l + \frac{\lambda}{n\_\theta} \cdot \sum\_{j=1}^{n\_\theta} c\_j^\theta \right. \tag{7}
$$

where *<sup>i</sup>*is the payoff of subject *i*, *Ei* = *E* = 20 is a subject's endowment in each period in experimental currency units (ECU), *ci* is the subject's contribution to the public good in this period, = 1*.*6 is a constant determining the marginal per capita return (MPCR), *n* is the number of subjects in group Q R STUV WUVX and Y 6M FN J MOP is the sum of all contributions of subjects *j* in group in this period.

<sup>3</sup> We suppress the period index in order to streamline the notation.

The return from the public good is rendered independent of the group size through the inclusion of *n*  in the denominator of the MPCR. It thus depends only on the average contribution in the group (this follows the design of Rockenbach and Milinski [27]). In the special case that only a single subject selects into one of the groups, the subject's contribution is automatically set to zero, and no public good is generated (subjects are so informed in the instructions). Note that subjects receive information about their group's size before making their contribution decision.

Hamman *et al*. [20] and Bolle and Vogel [21] implemented the allocator decision in a way that allowed the allocator to set a different contribution for herself than for the other group members. This allows for the rise of "corruption", which is how we refer to the case where the allocator does not contribute to the public good.4 Our design expands on this idea by modeling two different types of allocator decision options. We will continue to use "allocator" and ACG as the general terms, but will distinguish between a "coordinator" and a "dictator" treatment in our design. In the former, the coordinator can choose a contribution level, which then applies to all group members, including herself. In the latter, the dictator can choose two contribution levels, one of which applies to all group members excluding herself, while the other applies only to herself. In keeping with the vocabulary just laid out, we will be speaking of two forms of ACGs—the coordinator contribution group (CCG) and the dictator contribution group (DCG). Figure 1 illustrates this terminology. Finally, we wish to explore the impact of subjects' social preferences on their behavior in our experiment. For this reason, we elicit their social value orientation using the social value orientation (SVO) slider measure developed by Murphy *et al*. [28].

<sup>4</sup> Note that our instructions generally contained neutral wording, for example, referring to the VCG (ACG) as the "group with individual contribution choice" ("group with contribution choice by a randomly determined player").

#### *1.1. Rational Expectations Predictions*

To predict the group choice, we have to take a look at the expected contributions and payoffs in each of the two groups. In the VCG, the rationally5 expected behavior is not to contribute, yielding an expected payoff to every subject equal to her endowment. (This is also the minimax payoff in the VCG.) In the ACGs, there are different predictions for our two treatments. Given that the coordinator can only set one uniform contribution level for all group members, it is immediately apparent that for any  *>* 1 (and assuming *E >* 0), the profit-maximizing strategy is to set the contribution level equal to the common endowment, *E*. The payoff to both the coordinator and the other group members, then, is the payoff from full cooperation:

$$
\pi\_{i,CCG} = \frac{\lambda}{n\_{CCG}} \cdot E \cdot n\_{CCG} \tag{8}
$$

Given that = 1*.*6 and *E* = 20 in our setting, we thus derive the first part of our first hypothesis:

#### **Hypothesis 1a.** *In the CCG, coordinators always contribute the full endowment.*

In the coordinator treatment, the expected payoff as a member of the allocator group is higher6 than the minimax payoff in the voluntary contribution group, which equals the endowment *E*. 7 Under rational expectations, we would therefore expect all subjects to choose the allocator group in the coordinator treatment despite their lack of knowledge, at the time of making the decision, of the subsequently resulting group size. We use this benchmark for the derivation of the second part of our first hypothesis:

#### **Hypothesis 1b.** *All subjects in the coordinator treatment select into the CCG.*

In the dictator treatment, we assert that a rational allocator would set the contribution of all group members equal to their endowments and set a contribution of zero for herself. This yields the following payoffs:

$$
\pi\_{l,DCG} = \begin{cases}
E + \frac{\lambda}{n\_{DCG}} \cdot E \cdot (n\_{DCG} - 1) & \text{if subject } i \text{ is the dictator, and} \\
\frac{\lambda}{n\_{DCG}} \cdot E \cdot (n\_{DCG} - 1) & \text{if subject } i \text{ is not the dictator}
\end{cases}
(9)
$$

We reflect the incentives induced by this payoff function in the first part of our second hypothesis.

**Hypothesis 2a.** *In the DCG, dictators always contribute nothing themselves and the full endowment for all other group members.*

<sup>5</sup> Note that *rational* in this case includes the assumption that the actors are only interested in maximizing their own payoff without regard for the payoff of others.

<sup>6</sup> Strictly speaking, this is only true if subjects assign a positive probability to *nCCG >* 1.

<sup>7</sup> This result holds for any  *>* 1 and, thus, for any public good.

Since every player who joins the DCG has a chance of 1/*nDCG* to become the dictator, the conditionally expected payoff (assuming full contribution) of joining the DCG, given a group size of *nDCG*, would be:

$$\mathbb{E}[\pi\_{i,DCG}] = \frac{1}{n\_{DCG}} \cdot E + \left(\frac{\lambda}{n\_{DCG}} \cdot E \cdot (n\_{DCG} - 1)\right) \tag{10}$$

where o is the conditional expectations operator assuming equilibrium play (*i.e*., full contribution in the ACG; no contribution in the VCG). It follows from Equations (2) and (4), as well as from our treatment of the special case of a group size of one that o[*i,DCG*] o[*i,VCG*], with o[*i,DCG*] = o[*i,VCG*] iff *nDCG* = 1. Thus, even though the resulting group sizes are as yet undetermined when subjects make their group choice, selecting into the VCG is nonetheless a dominant strategy. This is also the case for the worst possible outcome in the DCG when only two subjects join the DCG.<sup>8</sup> This leads to the second part of our second hypothesis:

#### **Hypothesis 2b.** *All subjects in the dictator treatment select into the DCG.*

Despite their theoretical validity, we judge it likely that hypotheses 1a and 1b, as well as hypotheses 2a and 2b will not hold in our experiments. Experimental economists (among others) have shown that people do not behave in an exclusively payoff maximizing manner. In our setting, possible reasons for off-equilibrium behavior include the heterogeneity of social preferences, bounded rationality, salience effects, aversion to risk and/or losses and a dislike of competing *per se*. Unfortunately, there is a large number of different theories of, e.g., social preferences, such that it is not possible to include all of them with precise predictions. We will therefore formulate some hypotheses regarding expected deviations from perfectly rational behavior based on social value orientation and inequality aversion.

#### *1.2. Social Preference Predictions*

Social preference models (and also social value orientation) assume that individuals are not concerned about their own payoff alone, but also about the payoffs to others and the relative sizes of their own and others' payoffs. One specific form of social preferences is inequality-aversion. Outcome based models of inequality aversion assume that subjects are averse to differences in outcomes (see, e.g., [29,30]). This allows us to make a prediction regarding the differences in group choice between the coordinator and dictator treatments. Since no inequality is possible in the CCG, inequality aversion cannot be a cause for subjects choosing the VCG in the coordinator treatment. This is different in our dictator treatment. Here, the dictator can choose different contribution levels for himself and for the other DCG members, thereby increasing his payoff relative to the other group members'. This reduces the utility of inequality-averse subjects and renders the VCG relatively more

<sup>8</sup> Following from Equation (4), this assertion implies the following inequality: 1/*nACG ·E* +/*nACG ·E·*(*nACG* 1) *> E*. It is easy to show that it simplifies to  *>* 1 if *E >* 0 and *n >* 1.

attractive to them.9 Since we assume that there likely are such subjects in our subject pool, we reflect this in our next hypothesis:

### **Hypothesis 3.** *Subjects are more likely to choose the ACG in the coordinator treatment than in the dictator treatment.*

Once we drop the assumption of rational expectations, subjects can be assumed to update their expectations of other participants' behavior based on their observations of past outcomes. We expect an effect of the amount of the dictator contribution in the previous period on subjects' group choice in the subsequent period.

### **Hypothesis 4.** *Subjects' likelihood of selecting into the DCG increases in the previous period's dictator contribution.*

As Equation (3) makes clear, the negative effects of low dictator contributions in the DCG are diluted with increasing group size, since the cost of dictator free riding is jointly borne by more group members. We expect that this dilution effect will make it more likely for dictator treatment subjects to join the DCG when they expect many others to do so.10 Note, however, that our subjects do not know the group size for the period for which they are currently making their group choice. We conjecture that they will use the group size information from the previous period as a proxy for the current period's DCG size when forming their expectations of the latter.11

### **Hypothesis 5.** *Subjects' likelihood of selecting into the DCG increases in the previous period's DCG size.*

We also explore the impact of allocators' social value orientation on their decisions in the experiment. Subjects with a pro-social value orientation not only care about themselves, but also about relevant others (see, e.g., [31,32]). On the other hand, pro-self individuals are more interested in their own payoff. Previous experiments show that a pro-social value orientation correlates with cooperative behavior in economic experiments (see, e.g., [33]).12 On this basis, we expect pro-social dictators to set a higher contribution level for themselves than do pro-self dictators. In the CCG, pro-social and pro-self coordinators should behave the same way (setting the contribution of everyone equal to the endowment).

<sup>9</sup> Note that dictators with social preferences (like inequality-aversion or deriving positive utility from the payoffs of others) might themselves contribute (fully) to the public good (see hypothesis 6). We thank an anonymous referee for pointing this out.

<sup>10</sup> Note that the dilution effect is counteracted by the decrease in probability of being assigned the dictator role with the attendant higher possible payoff. Refer to the Appendix in Section 4 for a proof that the first effect outweighs the second. Strictly speaking, our argument is based on the net effect.

<sup>11</sup> While we do consider this question to be interesting, we did not judge it important enough to explicitly elicit group size expectations, which carries a risk of causing an experimenter demand effect.

<sup>12</sup> For a review, see [34].

**Hypothesis 6.** *Pro-social dictators set their own contribution higher than pro-self dictators.*

#### *1.3. Hypotheses about Dynamics*

In our final two hypotheses, we explore dynamic behavioral effects, which are not necessarily connected to social preferences. In particular, we expect the previous period's contribution behavior in the VCG to influence subjects' group choice. If there are high lagged contributions in the VCG, subjects may be induced to select into this group for two different reasons. First, with high contributions, this group becomes attractive for free riders who want to exploit the contributing members of the VCG. Second, pro-social subjects may be attracted by the high contributions, because they want to participate in the generation of a public good out of their own (and other group members') free decisions. This conjecture is founded in the work of Sen [35,36], who argues that the freedom of choice yields intrinsic value to humans. We summarize this line of reasoning in the following hypothesis:

**Hypothesis 7.** *Subjects' likelihood of selecting into the VCG increases in the previous period's average VCG contribution.*

Since high contributions in a group generally make this group more attractive, we finally also expect the contribution behavior in the ACG in the previous period to influence subjects' group choice. This leads to our final hypothesis:

**Hypothesis 8.** *Subjects' likelihood of selecting into the ACG increases in the previous period's average ACG contribution.*

#### **2. Design and Procedures**

Our experiment was part of a larger research program and comprised a total of 11 sessions with 12 subjects each. Sessions 2, 3, 4 and 6 used the coordinator treatment and sessions 7 through 13, the dictator treatment (sessions 1 and 5 used a design that is not the subject of this paper).13 The experiments were conducted at the Max-Jung laboratory at the University of Graz from April to July, 2012. The participants were recruited from a subject pool consisting mainly of students from the faculty of Social and Economic Sciences. The use of ORSEE [37] ensured that every subject could only participate in the experiment once. The experiment was programmed and conducted with z-Tree [38]. All payments were made in Euros, and the conversion rate from experimental currency

<sup>13</sup> In sessions 7 through 10, a programming error caused the period end screen to display the current period's DCG contributions also for previous periods. It is for this reason that we conducted additional sessions. To compound this unfortunate streak, an irreparable server crash then forced us to terminate the experiment after the first round in session 11. The first round data from this session are unaffected, but no questionnaires or SVO measures were elicited. We perform robustness checks of all our results to control for possible effects from the programming error and server crash using the "clean" session 12 and 13 data as a benchmark. We find no material changes in our results. For this reason, we include the session 7 through 11 data in our analyses.

units to Euros was 25 ECU = 1 EUR. Average earnings were 11.90 EUR, including a show up fee of 2.5 EUR. On average, a session lasted 45 min.

#### *2.1. Treatment Design*

Subjects participate in two rounds of ten periods each of a public good game.14 Before making their contribution decisions, they chose one of two groups to join for the current period. In the coordinator (dictator) treatment, these are the VCG and the CCG (the VCG and the DCG). The choice of group impacts how subjects' contributions are determined. Furthermore, the earnings for a period depend only on the subjects in the same group. Once every subject has entered her contribution, the payoff for this period is calculated according to Equation (1). Note that all subjects are informed about the number of subjects in their group at the time of making their contribution decision. At the end of each period, subjects see a results screen, which they can study for a maximum of 60 s (other than for the results screen, there were no time limits anywhere in the experiment). There was no deception involved in the experiment.

#### 2.1.1. Design Features Specific to the Coordinator Treatment

In the coordinator treatment, Equation (1) applies equally to subjects choosing the VCG and ones choosing the CCG. The difference to the VCG is that in the CCG, one subject is randomly chosen out of all group members to make the contribution decision for the entire group. This coordinator subject enters a contribution, which then applies to all CCG members, including the coordinator herself.

At the end of a period, subjects in the coordinator treatment see a results screen, which informs them about four parameters for each group (VCG and CCG), for the period just completed, as well as for all previous periods. These are (i) the number of subjects in the group, (ii) the average contribution in the group, (iii) the per capita earnings from the public good and (iv) the average ending wealth. In addition to this, they are informed about their personal starting endowment, their contribution, their return from the public good and their ending wealth.

#### 2.1.2. Design Features Specific to the Dictator Treatment

In the dictator treatment, one subject is randomly chosen to assume the role of the dictator, similar to the case of the coordinator just described. However, in the DCG, the dictator subject enters two parameters. The first is the contribution that applies to all group members, except the dictator. The second is the contribution that applies only to the dictator. As indicated in Section 1, the dictator can, for example, choose to let all other subjects contribute their full endowment of 20 ECU while contributing nothing herself.

<sup>14</sup> The ten periods of a round are treated as a logical uni,t and subjects are informed that "we will now move on to the second round consisting of ten periods", but the only difference between period 10 in round 1 and period 1 in round 2 is that the history of the first round's periods is no longer displayed on the results screen. The motivation for this design feature was to determine the extent of a possible restart effect.

At the end of a period, subjects in the dictator treatment see the results screen displayed in Figure 2. For the VCG, they learn the same parameters as subjects in the coordinator treatment. For the DCG, they are informed about (i) the number of subjects in the group, (ii) the contribution of the dictator, (iii) the contribution the dictator has chosen for all other DCG members, (iv) the per capita earnings from the public good and (v) the average ending wealth. Furthermore, they also receive information about their own starting endowment, contribution, return from the public good and ending wealth.

#### *2.2. Session Structure*

At the beginning of an experimental session, subjects arrive and wait outside the laboratory. At the designated starting time, subjects are welcomed by the experimenter, draw cards with their computer numbers, are led into the lab and sit down at the workstations corresponding to the numbers on their cards. They there find a printed set of instructions, which the experimenter reads out loud, asking the subjects to read along. After answering any possible remaining questions individually, the experimenter then starts the first round of 10 experimental periods.

**Figure 2.** Example dictator treatment results screen. The figure displays an example of the results screen as shown to subjects at the end of each period in the dictator treatment. Text printed in red (grey in greyscale printouts) is a translation of the original German captions.

In each period, subjects can first choose the group they want to join. If they join the ACG, they then learn whether they have been randomly chosen for the role of the allocator in this period. Following this, coordinator subjects enter the contribution they want every CCG member (including themselves) to make. Dictator subjects enter both a contribution they want to make themselves and a contribution they want their fellow DCG members to make. Subjects in the VCG enter the contribution they want to make. Once all contribution decisions have been entered, a results screen informs subjects of the outcomes of the present and previous periods in the current round. After the first round is over, the experimenter starts the second round, which proceeds analogously to the first. After the second round, one of the two is randomly selected for payoff in order to avoid portfolio effects. This is achieved by letting one of the participants publicly throw a die, the result of which determines the payoff-relevant round for all subjects. Once the experimenter has entered this information into his computer, subjects are informed about their payoffs on their screens.

The experimenter then starts a computerized questionnaire eliciting data on subject demographics and on their experiences and strategies in the experiment. The experimenter furthermore hands out a sheet for the elicitation of the SVO, which he asks every subject to fill in. Subjects who have finished filling in the questionnaire and SVO sheet [39] step outside the lab to wait until everybody else has also finished. Once this is the case, the experimenter asks subjects to step into the lab one at a time and pays them anonymously.

#### **3. Results**

#### *3.1. Summary Statistics*

We begin by discussing the summary statistics listed in Table 1. The first block of three rows already lets us reach a verdict regarding our hypotheses 1b and 2b. A one sample Wilcoxon signed-rank test confirms that the median CCG (DCG) size is significantly different from 12 (both *p*-values: 0.000). We can repeat this type of analysis for the second block of three rows in Table 1 to obtain results for hypotheses 1a and 2a. The median contribution in the CCG is significantly different from 20 (one-sample Wilcoxon signed-rank test *p*-value: 0.000). Similarly, we can reject both conjectures in hypothesis 2a: dictators' median contributions for themselves and for the other DCG members are significantly different from zero and 20, respectively (both one-sample Wilcoxon signed-rank test *p*-values: 0.000).

Next, we look at key behavioral patterns in the CCG and the DCG. In the CCG, we observe full contribution by all group members in 85% of all cases. This is a value higher than usually observed in public good games. On the other hand, this means that in 15% of all periods, the coordinator did not choose the full contribution for all members.15 This is surprising, since full contribution by coordinators maximizes both individual and collective welfare. Possible explanations for this seemingly irrational behavior include antisocial preferences, subject confusion or boredom and the wish to generate an outcome differing from the usual pattern. While we find no correlation between coordinators not fully contributing and their SVO values, thus speaking against the first explanation, further experiments would be needed to determine what is responsible for this inefficiency.

<sup>15</sup> Note that the CCG (DCG) had a minimum of six (four) members in all periods.

**Table 1.** Descriptive statistics. The table shows summary statistics for the coordinator (C) and dictator (D) treatments, separately for the voluntary contribution groups (VCG) and the allocator contribution groups (coordinator contribution group (CCG); and dictator contribution group (DCG)). Note that in the case where we report on the contributions for the first and the last period in the ACGs, the sample size is rather small, with seven observations for the DCG and four observations for the CCG.


In the DCG, the share of 41% full contributions by all group members is lower than in the CCG. This is of course an effect of our treatment differences, which allowed our dictators to let all other DCG members contribute fully, while themselves free riding. This happened in 26% of the periods. In the remaining periods, we observe other behavioral patterns. In 16% of the periods, the dictator chose full contribution for all other DCG members and contributed an amount larger than zero, but smaller than the endowment herself. In 17% of the periods, the dictator chose a contribution lower than the endowment for the other DCG members.

Figure 3 shows the mean contributions for both groups and both treatments. The observed behavioral patterns result in significantly higher contributions in both the DCG and the CCG than in the VCG (both two-sided Wilcoxon rank-sum test *p*-values: 0.000). As shown in Table 1, we observe a median contribution of 20 for the first and the last periods of both rounds in both the CCG and the DCG. On the other hand, we observe median contributions between zero and ten in the VCG in both treatments.

**Figure 3.** Contributions. Mean period contributions by treatment and group. The data of rounds 1 and 2 are pooled.

#### *3.2. Group Choice*

We continue our analysis with the average group sizes and their development over time. Figure 4 shows that the average group size of the allocator group starts at a very high level and, over time, increases even further in both treatments. Consequently, only a few subjects join the VCG.

**Figure 4.** Overall trend in average group size over time in the two treatments. The figure displays the average group size in each of the ten periods separately for the dictator and the coordinator treatments. The data of rounds 1 and 2 are pooled. The dashed lines are linear predictions. The thin lines are average group sizes in individual sessions.

Next, we conduct a regression analysis of the aggregate data, which is presented in Table 2. In the models (which we fit individually for each treatment), we control for the round, the period and the interaction between the two, allowing the slope of the periods to vary between rounds. We also include previous period data on the average size of, and the average contribution in, the ACG.

**Table 2.** Group size. The table shows the results of OLS regressions of the CCG and DCG group sizes on a number of regressors. Round is 1 (2) in the first (second) of the two 10-period sequences. Period2 equals the period number Period in round 2 and zero otherwise. The remaining variables are the lagged average contributions in the ACG and the lagged ACG group size (of the DCG in the regression of the dictator treatment, of the CCG in the analysis of the coordinator treatment) and the lagged contribution of the dictator in the DCG.


\* *p <* 0*.*1; \*\* *p <* 0*.*05; \*\*\* *p <* 0*.*01. Standard errors clustered at the session level (in parentheses).

Our results show that the time effect visible in Figure 4 is not significant in either treatment when controlling for the variables that were identified as relevant in our hypotheses in Section 1. Models 1 and 2 share one statistically significant effect: a larger average ACG contribution in the previous round results in a larger current ACG group size, supporting our hypothesis 8. It also implies that when the allocator contributes relatively little, the group size of the VCG increases in the following period. Furthermore, for the dictator treatment only, we find a significant effect of the DCG group size in the previous period. This provides support for the presence of the dilution effect, as conjectured in hypothesis 5. Finally, we find a significant effect of the dictator contribution in the previous period on the DCG group size (hypothesis 4).16

<sup>16</sup> Tobit regression censored at zero and 12 yields similar results.

We continue our analysis by investigating individual subjects' group choice behavior using Probit models.17 Table 3 presents the two regression models we believe best reflect the structural relationships in our data. In Model 3, we include the Round and Period variables, a treatment dummy and a variable containing our subjects' social value orientation as measured using the instrument defined in Murphy *et al*. [28]. Higher values of the SVO measure indicate a greater willingness to give up own income to benefit others. We also include an interaction of SVO with the treatment dummy, as well as variables containing information on the previous period's average contributions in the VCG and ACG (AvgContribVCG L and AvgContribACG L) and on the size of the ACG (and, separately, for the DCG) in the previous period (GroupSizeACG L and GroupSizeACG\_L\_x\_Dictator).

As predicted in hypothesis 3, we find a negative treatment effect. Subjects are less likely to join the ACG in the dictator treatment. Our model also shows that the likelihood of a subject selecting into the ACG as opposed to the VCG increases in the average contribution in the ACG in the previous period, thus lending further support to our hypothesis 8. Conversely, higher contributions in the VCG in the previous period decrease the likelihood of subjects joining the ACG. This result supports hypothesis 7. We also find that greater social value orientation of a subject cannot be shown to play a role.18 Finally, the results do not yield any evidence of subjects being more likely to select into the ACG in later periods or in the second round.

Model 4 differs from Model 3 in that it uses only the dictator treatment data and contains the amount of the previous period's dictator contribution as an additional variable. We find a statistically significant effect of the lagged size of the DCG, but not the ACG in general, lending further support to the dilution effect of hypothesis 5. Model 4 also shows a significant effect of the lagged average contribution in the DCG, but none of the lagged dictator contribution. Hypothesis 4 does not receive support from this result. The average contribution in the VCG in the previous period shows a highly significant negative coefficient, again, in line with our hypothesis 7. Just as in the pooled analysis, there appears not to be a material effect of SVO on group choice.

<sup>17</sup> Robustness checks confirm that our main results are stable with regard to the use of a logit model and to the inclusion or exclusion of different questionnaire items. A translation of the questions is provided in the Electronic Supplementary Information.

<sup>18</sup> Two subjects did not fill in the SVO questionnaire correctly and are, therefore, excluded from all analyses employing social value orientation data. Furthermore, the session 11 data are not included, since no SVO or other questionnaire items were elicited, due to the server crash.

**Table 3.** Determinants of allocator group choice. The table shows the results of Probit regressions of IsACG on a number of regressors. IsACG is a dummy equal to zero (one) if the subject chooses the VCG (ACG) in a period. Dictator is a dummy variable equal to zero (one) in the coordinator (dictator) treatment. Round is 1 (2) in the first (second) of the two 10- period sequences. Period2 equals the period number Period in round 2 and zero otherwise. SVO is the social value orientation of the subjects, measured using the slidermeasure from Murphy *et al*. (2011), and SVO x Dictator is SVO interacted with Dictator. The remaining variables are the lagged average contributions in the ACG and VCG, the lagged ACG group size (pooled and in the dictator treatment only) and the lagged contribution of the dictator in the dictator treatment (note that the model that includes this variable solely uses dictator treatment data). Logit estimation and logit panel regression yield similar results. Robustness checks, where we include various questionnaire response items and interaction terms, yield no clear effects from the control variables, but leave the main effects unchanged.


\* *p <* 0*.*1; \*\* *p <* 0*.*05; \*\*\* *p <* 0*.*01. Standard errors clustered at the subject level (in parentheses).

#### *3.3. Contributions*

We next focus on dictators' contribution behavior in the DCG. Table 4 contains our OLS regression results for the dictator's own contribution (Model 5). We control for a time trend, the lagged contributions, the group size of the ACG, the lagged dictator contribution and SVO. First, this is the only instance where we detect a significant influence of SVO—in this case, the SVO of the dictator subject—on experimental behavior. This lends support to our hypothesis 6. Second, the dictator's own contribution increases in the previous period's dictator contribution.

**Table 4.** Determinants of dictator contribution choice. The table shows the results of an OLS regression of the dictator's own contribution on a number of regressors. Round is 1 (2) in the first (second) of the two 10-period sequences. Period2 equals the period number Period in round 2 and zero otherwise. SVO is the social value orientation of the dictator, measured using the slider-measure from Murphy *et al*. [28]. The remaining variables are the lagged average contribution in the DCG, the concurrent DCG group size and the lagged dictator contribution. The inclusion of the lagged variables leads to the exclusion of the observations from period 1 in rounds 1 and 2. Tobit regression censored at zero and 20 yields similar results. Robustness checks, where we include various questionnaire response items and interaction terms, yield no clear effects from the control variables, but leave the main effects unchanged.


\* *p* < 0.1; \*\* *p* < 0.05; \*\*\* *p* < 0.01. Standard errors clustered at the subject level (in parentheses).

#### **4. Discussion and Conclusion**

The experimental literature on mechanisms fostering cooperation in dilemmas has lately predominantly focused on the effectiveness of punishment and reward. Recent work by Hamman *et al*. [20] and Bolle and Vogel [21] has extended this field to encompass inequalities in the power over one's own and others' decisions. Such asymmetries in the decision-making powers of economic actors are a frequent and important phenomenon outside the laboratory and, as such, merit careful analysis.

Hamman *et al*. [20] and Bolle and Vogel [21] demonstrate the possible efficiency gains from centralized decision-making in the provision of a public good. We extend their research by analyzing allocator mechanisms with different action spaces. We also implement direct competition between different contribution mechanisms by allowing for endogenous group choice and investigate to what extent social preferences drive contribution and group choice behavior. We find that the vast majority of our subjects is willing to cede decision authority to a central planner in order to reap efficiency gains from improved coordination. <sup>19</sup> We consider this result of great importance, since it clearly shows that human subjects are willing to submit to a randomly selected centralized authority if it leads to higher (expected) average payoffs. This is true both in a setting enforcing equality in payoffs and in one where the subject endowed with decision authority for the entire group can exploit this power to maximize her own payoffs at the expense of her team members'. Nonetheless, subjects are more likely to select into the allocator group in the first than in the second setting, and we investigate the factors driving this decision. Our data shows that subjects condition their group choice on historical group sizes and contribution behavior. Finally, we find that an allocator's social value orientation plays a role in her contribution choice in the setting where she has the option to exploit her fellow group members.

We summarize our findings in Table 5. Overall, they show that the allocator mechanism is not only more successful in establishing high contributions than a voluntary contribution scheme, but also wins out in a direct competition. We believe that these encouraging results merit further research into allocator contribution mechanisms for the provision of public goods and the accompanying power asymmetries.



<sup>19</sup> Note that the allocator mechanism at the same time decreases the risk of exploitation and impacts payoff inequality. Further research is needed to disentangle the differential effect of these factors.

#### **Acknowledgments**

We thank two anonymous referees and the audiences at the International Meeting of the Economic Science Association 2012, the Annual Meeting of the Austrian Economic Society 2013, the 15th International Conference on Social Dilemmas, the annual conference of the GfeW 2012, the Quantitative Sociology Colloquium at the ETH Zu¨rich and the research seminars at the Vienna Center of Experimental Economics and at the Faculty of Social and Economic Sciences at the University of Graz for valuable comments. All errors remain our own.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **Appendix**

#### **Proof of the Dilution Effect in the Dictator Treatment**

Remember that Equation (4) posited the following expected payoff in the DCG:

$$\mathbb{E}[\pi\_{l,DCG}] = \frac{1}{n\_{DCG}} \cdot E + \left(\frac{\lambda}{n\_{DCG}} \cdot E \cdot (n\_{DCG} - 1)\right)$$

*Proof*. For the dilution effect to obtain, the following inequality must then hold (for expositional convenience, we suppress the DCG subscript):

$$\frac{1}{n} \cdot E + \left(\frac{\lambda}{n} \cdot E \cdot (n-1)\right) < \frac{1}{n+c} \cdot E + \left(\frac{\lambda}{n+c} \cdot E \cdot (n+c-1)\right) \tag{5}$$

where *c* is an arbitrary, positive integer. Inequality (5) can be simplified to:

$$c < \lambda c \tag{6}$$

Inequality (6) is fulfilled for any n R wx,  *>* 1 and *E >* 0 and, thus, for any public good. This also extends to our parameterization, where = 1*.*6.

#### **References**


