Games, Volume 12, Issue 4 (December 2021) – 24 articles

The trade-off between the costs and benefits of disclosing a firm’s private information has been the object of a vast literature. The absence of incentives to share information on a common market demand prior to competition has been advocated to interpret information sharing as evidence of collusion. Recent contributions have looked at bilateral information sharing, showing that information sharing is consistent with pairwise stability, This paper studies the networked pattern of bilateral information sharing on market demand, focusing on the role of heterogeneous information (firms’ signals have different variances). We show that while pairwise stability predicts that i.i.d. signals are always shared in groups with a symmetric internal structure (both with and without side-payment and linking costs), heterogeneous signals are shared in asymmetric core-periphery architectures, in which “core” firms have more valuable information than periphery firms. Full article

Weighted committees allow shareholders, party leaders, etc. to wield different numbers of votes or voting weights as they decide between multiple candidates by a given social choice method. We consider committees that apply scoring methods such as plurality, Borda, or antiplurality rule. Many different weights induce the same mapping from committee members’ preferences to winning candidates. The numbers of respective weight equivalence classes and hence of structurally distinct plurality committees, Borda commitees, etc. differ widely. There are 6, 51, and 5 plurality, Borda, and antiplurality committees, respectively, if three players choose between three candidates and up to 163 (229) committees for scoring rules in between plurality and Borda (Borda and antiplurality). A key implication is that plurality, Borda, and antiplurality rule are much less sensitive to weight changes than other scoring rules. We illustrate the geometry of weight equivalence classes, with a map of all Borda classes, and identify minimal integer representations. Full article

Empirical investigation suggests that conflict is path-dependent, i.e., current conflict leads to more conflict in the future. However, there is very little formal theory for why conflict path dependence exists. We propose a mathematical model to explore one possible pathway to explain the persistence of conflict once it starts. In this model, there are three types of cultures in two boundedly rational populations. The two populations are State Actors and Insurgents. The three cultures are Peaceable, Warring, or Bargainers. The distribution of these types is different in each population. Evolutionary dynamics determine which of these three cultures might predominate. Our simulations suggest that it is rational for people to learn to be warlike even in environments where State Actors are willing to give large side payments to “buy” peace to avoid bargaining failure. War can also be learned when State Actors and Insurgents are extremely patient and, therefore, potentially committed to Pareto improving peace deals. The outcomes of these simulations suggest that cultural learning can be a hitherto ignored explanation for why conflict is path dependent. If culture is indeed a possible cause for conflict, the best intentions of technocratic peacemakers trying to build frameworks for resource sharing and/or institutional building may fail, simply because such structures are not suited to local conditions. On the flip side, our model also provides theoretical reasoning for the observation that conflict is not a deterministic outcome of bargaining and commitment failures. Full article

This paper analyses the voting behavior of the parliamentary groups in the Regional Assembly of Madrid to appoint the Bureau, its representative body, in all the legislatures since its inception (1983–2021). To this end, the actual result of the voting is compared with the mock result attained by following a Nash equilibrium (NE) and a d’Hondt (d’H) allocation in each vote. But the result of a d’Hondt allocation varies based on the number of stages in which the voting is performed (President, Vice-President, and Secretaries), so a bias towards disproportionality could exist as measured by the absolute index of disproportionality which calculates the number of seats non-proportionally allocated. The results show that, in view of the hypothesis on the importance of the number of seats, the NE was only followed in four of the 12 Legislatures for Vice-Presidents (it was always followed for Secretaries). Thus, parliamentary groups could gain more seats by modifying their strategies. Additionally, the absolute rate of disproportionality and the number of seats non-proportionally allocated indicate that, in general, parliamentary groups obtain voting results that are less disproportionate than they could be (due to the number of voting stages). Full article

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired number of players, starting from a minimum or minimum sum representation. We also provide closed formulas for the number of WMVG with n players having a minimum representation with quota up to three, and some subclasses of this family of games. Finally, we complement these results with some upper bounds related to weights and quotas. Full article

This paper deals with one of the possible methodological approaches to an empirical examination of game awareness. Such an outline should enable the gathering of a deeper understanding of individuals’ awareness. The questionnaire is based on a scenario technique, and it is focused on game awareness in situations with possible strategic interactions. The goal is to assess the instrument regarding its reliability and validity. Internal reliability is assessed using Cronbach’s alpha coefficient. A k-nn analysis was used to estimate divergent construct validity and criterion validity, and nonparametric factor analysis was used to estimate convergent construct validity. The questionnaire satisfies the requirements of reliability and validity. Moreover, there is an indication that each of the eight scenarios may be used separately, as they also meet the criteria for reliability and validity. Possible practical and theoretical implications involve questionnaire use as a basis for educational intervention, other instruments’ development, as well as for the collection and publication of behavioral insights about game awareness. Behavioral insights should enrich the theory and incite behavioral game theory models of game awareness and its implications. Full article

Human cooperation, occurring without reciprocation and between unrelated individuals in large populations, represents an evolutionary puzzle. One potential explanation is that cooperative behaviour may be transmitted between individuals via social learning. Using an online social dilemma experiment, we find evidence that participants’ contributions were more consistent with payoff-biased transmission than prestige-biased transmission or conformity. We also found some evidence for lower cooperation (i) when exposed to social information about peer cooperation levels than without such information, and (ii) in the prisoners’ dilemma game compared to the snowdrift game. A simulation model established that the observed cooperation was more likely to be caused by participants’ general propensity to cooperate than by the effect of social learning strategies employed within the experiment, but that this cooperative propensity could be reduced through selection. Overall, our results support previous experimental evidence indicating the role of payoff-biased transmission in explaining cooperative behaviour, but we find that this effect was small and was overwhelmed by participants’ general propensity for cooperation. Full article

Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play. In general, this problem can be modeled as a leader–follower Stackelberg equilibrium problem using a mathematical program with equilibrium constraints. We propose two interconnected dynamical systems to dynamically solve a bilevel optimization problem between a leader and follower population in a single time scale by a predictive-sensitivity conditioning interconnection. For the leader’s optimization problem, we developed a gradient descent algorithm based on the total derivative, and for the followers’ optimization problem, we used the population dynamics framework to model a population of interacting strategic agents. We extended the concept of the Stackelberg population equilibrium to the differential Stackelberg population equilibrium for population dynamics. Theoretical guarantees for the stability of the proposed Stackelberg population learning dynamics are presented. Finally, a distributed energy resource coordination problem is solved via pricing dynamics based on the proposed approach. Some simulation experiments are presented to illustrate the effectiveness of the framework. Full article

This note reconsiders the Rubinstein bargaining game under the assumption that a rejected offer is only costly to the proposer who made the rejected offer. It is shown that then, the classic result of Shaked that, in the multilateral version of this game, every division of the good can be sustained in SPE no longer holds. Specifically, there are many SPE, but players’ (expected) payoffs in SPE are unique. The assumption further leads to a responder advantage. Full article

In economic theory, an agent chooses from available alternatives—modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by the outside world in a structured way. Online search results are lists of items, wine menus are often lists of lists (grouped by type or country), and online shopping often involves filtering items which can be viewed as navigating a tree. Representations constrain how an agent can choose. At the same time, an agent can also leverage representations when choosing, simplifying their choice process. For instance, in the case of a list he or she can use the order in which alternatives are represented to make their choice. In this paper, we model representations and decision procedures operating on them. We show that choice procedures are related to classical choice functions by a canonical mapping. Using this mapping, we can ask whether properties of choice functions can be lifted onto the choice procedures which induce them. We focus on the obvious benchmark: rational choice. We fully characterize choice procedures which can be rationalized by a strict preference relation for general representations including lists, list of lists, trees and others. Our framework can thereby be used as the basis for new tests of rational behavior. Classical choice theory operates on very limited information, typically budgets or menus and final choices. This is in stark contrast to the vast amount of data that specifically web companies collect about their users’ choice process. Our framework offers a way to integrate such data into economic choice models. Full article

This paper examines the behaviour of two firms competing in a duopoly, where firms can influence demand through use of advertising. The paper simulates the strategic interaction of the two firms based on a game-theoretic Cournot analytical model. The evolution over time of the Nash equilibrium is graphically displayed for a number of different competitive scenarios. The results show that there exist threshold levels of advertising effectiveness at which duopoly behaviour bifurcates, that perfectly cooperative advertising can lead to competitive disadvantage, and that perfectly predatory advertising can lead to stagnation or losses. Full article

This paper studies the standard version of the approval mechanism with two players in a common pool resource (CPR) extraction game. In the case of disapproval, the Nash extraction level is implemented. The paper investigates, experimentally, the extent to which the Nash threat leads to Pareto-improving extraction levels. Through our experiment, we confirm the effectiveness of the Nash threat in reducing CPR over-extraction. Although participants’ behavior is mainly explained by rational thinking, inequity in payoff can also motivate their behavior. Moreover, we show that there is neither an order effect nor a framing effect. Finally, the reduction persists when the Nash threat is no longer in place. Full article

Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost. Full article

Revisionist actors are increasingly operationalising a broad number of non-violent threats in their quest to change the status quo, popularly described as hybrid conflict. From a defensive point of view, this proliferation of threats compels nations to make difficult choices in terms of force posture and composition. We examine the choice process associated with this contemporary form of state competition by modelling the interactions between two actors, i.e., a defender and a challenger. As these choices are characterised by a high degree of uncertainty, we study the choice from the framework of prospect theory. This behavioural–economic perspective indicates that the defender will give a higher weight and a higher subjective value to conventional threats, inducing a higher vulnerability in the domain of hybrid deterrence. As future conflict will increasingly involve choice dilemmas, we must balance threats according to their probability of occurrence and their consequences. This article raises awareness regarding our cognitive biases when making these choices. Full article

This paper provides a model of the repeated prisoner’s dilemma in which cheap-talk communication is necessary in order to achieve cooperative outcomes in a long-term relationship. The model is one of complete information. I consider a continuous time repeated prisoner’s dilemma game where informative signals about another player’s past actions arrive following a Poisson process; actions have to be held fixed for a certain time. I assume that signals are privately observed by players. I consider an environment where signals are noisy, and the correlation of signals is higher if both players cooperate. We show that, provided that players can change their actions arbitrary frequently, there exists an equilibrium with communication that strictly Pareto-dominates all equilibria without communication. Full article

We analyze a committee decision in which individuals with common preferences are uncertain which of two alternatives is better for them. Members can acquire costly information. Private signals and information choice are both continuous. As is consistent with Down’s rational ignorance hypothesis, each member acquires less information in a larger committee and tends to acquire zero information when the committee size goes to infinity. However, with more members, a larger committee can gather more aggregate information in equilibrium. The aggregate information is infinite with the size going to infinity if and only if marginal cost at “zero information acquisition” is zero. When the marginal cost at “zero information acquisition” is positive, the probability of making an appropriate decision tends to be less than one. Full article

Global warming, as a result of greenhouse gases, is exceeding the planet’s temperature stabilization capacities. Thus, greenhouse gas emissions must be reduced. We analyse a bankruptcy situation aimed at allocating emissions permits of CO₂, the predominant greenhouse gas emitted by human activities. Inspired by the Constrained Equal Awards (CEA) solution for bankruptcy situations, we introduce a new allocation protocol based on the extension of the CEA solution over double-weighted bankruptcy situations, including two exogenous parameters aimed at providing a balance, in the request of emissions permits, between economic activities and the production of renewable energy. In these bi-criteria allocation problems, we focus on a computational approach to find an allocation protocol that does not prioritize any particular parameter. As an application of our method, we first consider CO₂ permit allocation problems in European Union (EU) countries, using real data about the gross domestic product (GDP), the production rate of renewable energies, and countries’ ‘demands’ of CO₂ emissions from 2010 to 2014. Then, we compare our approach with the CEA solution and its single-weighted extension to show the impact of using two weights over the distribution of CO₂ emissions permits; we analyse the correlation between allocations of CO₂ emission permits and the distribution of power within the EU Council to study the acceptability of alternative allocations. Full article

This paper studies the problem of screening teams of either moral or altruistic agents, in a setting where agents choose whether or not to exert effort in order to achieve a high output for the principal. I show that there exists no separating equilibrium menu of contracts that induces the agents to reveal their types unless the principal either (i) excludes one group from the productive relationship, or (ii) demands different efforts from different preference groups. I also characterize the contract-inducing pooling equilibria in which all agents are incentivized to exert a high level of effort. Full article

This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist can manipulate a legislature decision increases with the number of elected parties, and, consequently, decreases with an electoral threshold. On the other hand, a lower electoral threshold increases the representativeness of a legislature. We combine these two effects in a notion of fairness. We show the existence of an electoral threshold that optimizes the fairness of a political system, which is close to 1–5%. Namely, the optimal threshold (in our sense) is close to thresholds that exist in most parliamentary democracies. Full article

Multi-agent collaboration is greatly important in order to reduce the frequency of errors in message communication and enhance the consistency of exchanging information. This study explores the process of evolutionary decision and stable strategies among multi-agent systems, including followers, leaders, and loners, involved in collaboration based on evolutionary game theory (EGT). The main elements that affected the strategies are discussed, and a 3D evolution model is established. The evolutionary stability strategy (ESS) and stable conditions were analyzed subsequently. Numerical simulation results were obtained through MATLAB simulation, and they manifested that leaders play an important role in exchanging information with other agents, accepting agents’ state information, and sending messages to agents. Then, with the positivity of receiving and feeding back messages for followers, implementing message communication is profitable for the system, and the high positivity can accelerate the exchange of information. At the behavior level, reducing costs can strengthen the punishment of impeding the exchange of information and improve the positivity of collaboration to facilitate the evolutionary convergence toward the ideal state. Finally, the EGT results revealed that the possibility of collaboration between loners and others is improved, and the rewards are increased, thereby promoting the implementation of message communication that encourages leaders to send all messages, improve the feedback positivity of followers, and reduce the hindering degree of loners. Full article

Individual contributions by infringing firms to the compensation of cartel victims must reflect their “relative responsibility for the harm caused” according to EU legislation. Several studies have argued that the theoretically best way to operationalize this norm is to apply the Shapley value to an equilibrium model of cartel prices. Because calibrating such a model is demanding, legal practitioners prefer workarounds based on market shares. Relative sales, revenues, and profits however fail to reflect causal links between individual behavior and prices. We develop a pragmatic alternative: use simple voting games to describe which cartel configurations can(not) cause significant price increases in an approximate, dichotomous way; then compute the Shapley-Shubik index. Simulations for a variety of market scenarios document that this captures relative responsibility better than market share heuristics can. Full article

This paper investigates disclosure by testing if the game theoretic predictions of unravelling theory are borne out in a heretofore unstudied market. We analyse TripAdvisor disclosures from hoteliers across 22 locations (N = 4357). Contrary to theoretical predictions, we find that disclosure decreases linearly with TripAdvisor ratings. We find the same pattern of disclosure occurs when consumers know the information provider has information to disclose, and when they do not. We also find evidence suggesting the most elite hotels may disclose less. We provide practical as well as theoretical implications. Full article

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer. Full article