Games, Volume 9, Issue 3 (September 2018) – 35 articles

We investigate, theoretically and experimentally, the effect of competition on risk taking in a contest in which players only decide on the level of risk they wish to take. Taking more risk implies a chance of a higher performance, but also implies a higher chance of failure. We vary the level of competition in two ways: by varying the number of players (2 players versus 8 players), and by varying the sensitivity of the contest to differences in performance (lottery contest versus all-pay auction). Our results show that there is a significant interaction effect between the two treatments, suggesting that players are particularly prone to take more risks if both the number of players and the sensitivity to performance are higher. Full article

Incentives shape how much people contribute to the welfare of a group. These incentives do not restrict the opportunities but they change the costs of contributions. This paper studies how the random assignment of such incentives affects perceived distributive justice among group members. Do people consider differences in incentives similar to unequal opportunities, that is, situations in which some people have a lower chance to make a high contribution? The results from a real effort experiment show that the economic framing of incentives matters in this context. If some people do not work for the common good because of rather large private costs, they appreciate these ‘negative incentives’ similarly to unequal opportunities. They do not do so, and become less egalitarian, if lower effort for the group increases the chance for private gains (‘positive incentives’). Interestingly, participants reward group members who do not limit their expected contributions to the group despite adverse incentives. Full article

In a context where sustainable consumption and production need to be encouraged, economic experiments can provide significant insights into how individuals consider environmental externalities in their choices and how public policy can foster the environmental public good. Experimental studies aiming to evaluate market mitigation of externalities through the provision of green goods usually choose to adopt neutral language in terms of framing. Our study implements an incentivized economics experiment to explore how supply and demand consider negative externalities. Furthermore, the study addresses the impact of using non-abstract wording when describing negative externalities. Two types of goods can be produced and bought, namely goods generating negative externalities on other consumers (either labelled as B or brown) and goods that cause no harm to others (either labelled A or green). We conclude that the provision of green goods increases from 18.1% in the abstract frame to 70% in the environmental frame. Framing is, therefore, a relevant variable for the outcome of this experimental market. This has important implications for economic experiments aiming to evaluate pro-environmental behaviours and provide policy orientations for the provision of green goods. Full article

Using a laboratory experiment, we collected data on dictator giving among student strangers and married couples in a suburban area in the United States. Confirming common belief and prior empirical evidence, we find that giving among spouses is greater than giving among anonymous students. We further investigated factors associated with spousal giving which may provide insight for the development of future theories, or into explaining other-regarding preferences. Our data shows that giving is positively associated with who manages household money and controls household income. This result is robust after controlling for each spouse’s personal income and using various econometric specifications. The results suggest that spousal giving may be due to household economic roles in addition to other-regarding preferences. Full article

To examine the stability of prosocial behavior in groups and pairs, we use an indirect approach. We conducted linear public good experiments with two and four subjects repeatedly three times at intervals of one week. All experiments were carried out without providing feedback and used a payment mechanism promoting stable behavior. We study the dynamics of behavior in repeated sessions and find that pairs are much better at establishing and stabilizing cooperation than groups of four. Furthermore, we conducted all experiments in a partner and a stranger design. As is known from the literature, cooperation in a stranger design should be lower than in a partner design. Once again, we are interested in the differences of the strength of this cooperation reducing effect between pairs and groups. Unlike pairs, groups show very low contributions to the public good in the stranger treatment and display a strong tendency to decrease cooperation in the partner treatment. The results in all treatments demonstrate that decreasing cooperation is a stable pattern of behavior in dynamic social dilemma contexts. Finally, we conducted a norm elicitation experiment using a method introduced by Krupka and Weber (2013) and find that in pairs symmetric behavior plays a very important role. Full article

We consider the problem of how to apply a generalized second price (GSP) auction to a buyer–seller network. GSP auctions are often used to sell online ads where buyers care about the position or placement of the ad. GSP auctions can also be applied to wireless data transmissions with congestion where buyers care about the speed of data transmission; however, such an auction would take place over a network as a buyer could only purchase from a seller (or cell tower) that he was linked to (or was close to). Two GSP auctions over a network are considered: separate GSP auctions, and integrated GSP auctions with pauses. The efficiency of these auctions is examined with efficiency favoring the integrated auction with pauses. Full article

We study the strategies used by experimental subjects in repeated sequential prisoners’ dilemma games to identify the underlying motivations behind instrumental reciprocity, that is, reciprocation of cooperation only if there is future interaction. Importantly, we designed the games so that instrumental reciprocity is a mistake for payoff-maximizing individuals irrespective of their beliefs. We find that, despite the fact that instrumental reciprocity is suboptimal, it is one of the most frequently used cooperative strategies. Moreover, although the use of instrumental reciprocity is sensitive to the costs of deviating from the payoff-maximizing strategy, these costs alone cannot explain the high frequency with which subjects choose to reciprocate instrumentally. Full article

We experimentally study how people resolve a tension between favoritism and fairness when allocating a profit in a team production setting. Past research shows that people tend to favor their ingroup at the cost of an outgroup when allocating a given amount of money. However, when the money to be allocated depends on joint production, we find that most players allocate proportionally according to others’ relative contributions, irrespective of their social identity affiliations. We discuss the implications of our findings on how distributive norms could shape team cooperation. Full article

This paper examines a persuasion game between two agents with one-sided asymmetric information, where the informed agent can reveal her private information prior to playing a Battle-of-the-Sexes coordination game. There is a close connection between the extent of information revelation and the possibility of coordination failure; while, in the absence of any coordination failure, there exist equilibria with full disclosure, in the presence of strategic uncertainty in coordination there exists an equilibrium with no information revelation. We provide a purification argument for the non-existence result, as well demonstrate that it is robust to several extensions, including both-sided asymmetric information and imprecise information revelation. Full article

Many anthropological records exist of seemingly worthless tokens exchanged in traditional societies. The most famous instances of such tokens are probably the Kula necklaces and armbands first described by B. Malinowski. In our experiment, each participant can send a token to another participant before each round of a repeated public good game. We use as examples of tokens a bracelet built by the participants in the lab, a simple piece of cardboard provided by the experimenter, and an object brought from home by the participants. Notwithstanding the cheap-talk nature of the decision to send the token, both sending and receiving the token are associated with a significant increase in contributions to the public good. Regression analysis shows that contributions to the public good in the treatments featuring a bracelet and a cardboard piece are higher than in a control study. The home object appears not to have been equally useful in increasing contributions. Full article

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs. Full article

The development of a cancerous tumor requires affected cells to collectively display an assortment of characteristic behaviors that contribute differently to its growth. A heterogeneous population of tumor cells is far more resistant to treatment than a homogeneous one as different cell types respond dissimilarly to treatments; yet, these cell types are also in competition with one another. This paper models heterogeneous cancer cell interactions within the tumor mass through several game theoretic approaches including classical normal form games, replicator dynamics, and spatial games. Our concept model community consists of four cell strategies: an angiogenesis-factor-producing cell, a proliferative cell, a cytotoxin producing cell, and a neutral stromal cell. By comparing pairwise strategic interactions, invasibility and counter-invasibility, we establish conditions for dominance and the existence of both monomorphic and polymorphic equilibria. The spatial game supports co-occurrence among multiple subpopulations in accordance with biological observations of developing tumors. As the tumor progresses from primarily stromal cells to a more malignant state, angiogenic and cytotoxic cells form clusters while proliferative cells are widespread. The clustering of certain subpopulations suggests insight into the behaviors of cancer cells that could influence future treatment strategies. Full article

In this paper, we provide a welfare ranking for the equilibria of the supply function and quantity competitions in a differentiated product duopoly with demand uncertainty. We prove that the expected consumer surplus is always higher under the supply function competition, irrespective of whether the (duopolistic) products are substitutes, complements, or independent. Numerical simulations suggest that if the products are either complements or independent, or if they have an extremely low degree of substitution, then the supply function competition can always be Pareto superior to the quantity competition in terms of the producers’ and consumers’ welfares. Moreover, if the degree of product substitution is not extremely low, then the supply function competition can be Pareto superior to the quantity competition if and only if the size of the demand uncertainty is sufficiently large to exceed a critical level. We find that this critical level of demand uncertainty becomes higher when the duopolistic products are less differentiated. Additionally, this critical level is nonincreasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve when all other parameters are fixed. Our results imply that in electricity markets with differentiated products, the regulators should not intervene to impose the quantity competition in favor of the supply function competition unless the degree of product substitution is sufficiently high and the predicted demand fluctuations are sufficiently small. Full article

Game-theoretic models are a convenient tool to systematically analyze competitive situations. This makes them particularly handy in the field of security where a company or a critical infrastructure wants to defend against an attacker. When the optimal solution of the security game involves several pure strategies (i.e., the equilibrium is mixed), this may induce additional costs. Minimizing these costs can be done simultaneously with the original goal of minimizing the damage due to the attack. Existing models assume that the attacker instantly knows the action chosen by the defender (i.e., the pure strategy he is playing in the i-th round) but in real situations this may take some time. Such adversarial inertia can be exploited to gain security and save cost. To this end, we introduce the concept of information delay, which is defined as the time it takes an attacker to mount an attack. In this period it is assumed that the adversary has no information about the present state of the system, but only knows the last state before commencing the attack. Based on a Markov chain model we construct strategy policies that are cheaper in terms of maintenance (switching costs) when compared to classical approaches. The proposed approach yields slightly larger security risk but overall ensures a better performance. Furthermore, by reinvesting the saved costs in additional security measures it is possible to obtain even more security at the same overall cost. Full article

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first the case with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process: appearing, growing and then disappearing once a culture of cooperation is sufficiently established in the local population. Full article

In this experiment, we test whether subjects’ responses to variations in the action set in a dictator game depends on induced group identities. The action set includes choices in which the dictator can either give money to or take money from the other player. As an extension to the anonymous setting, we introduce induced group identities using the minimal group paradigm. Based on a dictator game conducted with more than 300 students in Indonesia, we implement a full factorial design in order to analyze the framing of the action set in a varied cultural context and to examine varied prevalence of social norms given a group identity context. If group identity is not salient, we find that participants are slightly more generous when they have an opportunity to give to rather than to take from the recipient. However, when participants are matched with in-group members, this result is reversed and highly significant. The result of differing responses to framing effects in within-group interactions compared to a neutral setting are largely ascribed to the varied compliance with existing social norms. Full article

This paper reports results from controlled laboratory experiments on the Laffer curve and explores the productivity differences under the strategy method and the direct method. The data collected in Pakistan show no significant productivity difference across the two methods. The paper argues that the Laffer curve is not the result of a simple leisure—income tradeoff; the disutility of work and perceived unfairness of the tax imposed also influence the work decisions. A behavioral model that incorporates these factors induces a “fairness adjusted” Laffer curve with the negative relationship between tax rate and tax revenue showing up after 54% tax rate. Full article

The multi-dimensional nature of social exclusion requires several perspectives in understanding its causes and consequences. Focus on the topic is largely centred around questions of material deprivation. However, as poverty and inequality are inextricably linked to questions of access and inclusion, a holistic approach is required. Consequently, we explore how imposed relational asymmetries which manifest as differences in the ability to exercise personal agency and in turn, engender wealth inequalities, affect social cooperation in future interactions. To do this, we generate wealth inequalities through two Prisoner’s Dilemma games, where one party is excluded from participating in the determination of the outcomes of the game. The effects of this asymmetry in social participation on ex post cooperation is examined using a Public Goods game. We find that the presence of prior asymmetric influence in social decision-making subsequently reduces contributions to the public good, independent of endowment level. This reduction in social welfare is driven by the under-contribution from players who were excluded in prior social interactions. Simply put, the data shows that a history of social exclusion reduces subsequent public goods provision, independent of material inequality. Full article

We elicit individual-level peer-punishment types in a cooperation (social dilemma) and a coordination (weakest link) problem. In line with previous literature, we find heterogeneity in peer-punishment in both environments. Comparing punishment behavior across the two environments within subject, we observe a high degree of individuals’ punishment type stability. However, the aggregate punishment demand is higher in the weakest-link game. The difference between the two environments is driven by subjects whose behavioral types are inconsistent rather than by a change in the punishment demand of those who punish in both environments. Full article

Arad and Rubinstein (2012, AER) proposed the 11–20 money request game as an alternative to the P beauty contest game for measuring the depth of thinking. In this paper, we show theoretically that in the Nash equilibrium of the 11–20 game players are more likely to choose high numbers if they are risk-averse rather than risk neutral. Hence, the depth of thinking measured in the 11–20 game is biased by risk aversion. Based on a lab experiment, we confirm this hypothesis empirically. Full article

In certain critical infrastructures, correlations between cyber and physical components can be exploited to launch strategic attacks, so that disruptions to one component may affect others and possibly the entire infrastructure. Such correlations must be explicitly taken into account in ensuring the survival of the infrastructure. For large discrete infrastructures characterized by the number of cyber and physical components, we characterize the cyber–physical interactions at two levels: (i) the cyber–physical failure correlation function specifies the conditional survival probability of the cyber sub-infrastructure given that of the physical sub-infrastructure (both specified by their marginal probabilities), and (ii) individual survival probabilities of both sub-infrastructures are characterized by first-order differential conditions expressed in terms of their multiplier functions. We formulate an abstract problem of ensuring the survival probability of a cyber–physical infrastructure with discrete components as a game between the provider and attacker, whose utility functions are composed of infrastructure survival probability terms and cost terms, both expressed in terms of the number of components attacked and reinforced. We derive Nash equilibrium conditions and sensitivity functions that highlight the dependence of infrastructure survival probability on cost terms, correlation functions, multiplier functions, and sub-infrastructure survival probabilities. We apply these analytical results to characterize the defense postures of simplified models of metro systems, cloud computing infrastructures, and smart power grids. Full article

We experimentally investigate variants of the investment game by Berg, Dickhaut, and McCabe (1995), in which one of the two players decides who are first mover and second mover. It has been shown by Kleine, Königstein, and Rozsnyói (2014) that voluntary leadership increases both investment and backtransfer. We interpret voluntary leadership as a signal of cooperation that stimulates reciprocal cooperation. If a relatively rich player takes the lead (putting himself/herself under investment risk) this should be seen as a less strong signal of cooperation than taking the lead among equally endowed players. Indeed, we show that under asymmetric endowments, voluntary leadership has a weaker effect than under symmetric endowments. Full article

We test the empirical content of the assumption of preference dependent beliefs using a behavioral model of strategic decision making in which the rankings of individuals over final outcomes in simple games influence their beliefs over the opponent’s behavior. This approach— by analogy with Psychological Game Theory—allows for interdependence between preferences and beliefs but reverses the order of causality. We use existing evidence from a multi-stage experiment in which we first elicit distributional preferences in a Random Dictator Game, then estimate beliefs in a related $2\times 2$ effort game conditional on these preferences. Our structural estimations confirm our working hypothesis on how social preferences shape beliefs: subjects with higher guilt (envy) expect others to put less (more) effort, which reduces the expected difference in payoffs. Full article

This paper explores the role of cultural transmission in extortion. Extortion is modeled as an asymmetric contest where individuals from one group attempt to take from individuals in another group. Using a model of cultural transmission, this paper finds the existence of a unique asymptotically stable equilibrium where there are a fraction of people who defend against extortion and a fraction of people who take from others. The degree of extortion is decreased when: (1) extortion is less effective; (2) socialization efforts of parents who resist are more effective; and (3) socialization efforts of parents who abstain from extortion are more effective. A key finding is the existence of a complementarity between the effectiveness of socialization. When socialization is more effective for resisting extortion and choosing not to extort, there is a much larger reduction of extortion than either increase could achieve alone. This provides a potential explanation for why some countries like Singapore and Hong Kong were able to greatly reduce corruption and suggests potential policy applications. Full article

In this article, we analyze the stability of couples on the marriage market. Recent developments in cooperative game theory allow a new model that uses team games which make it possible to model the marriage market. Coalition structures can model couples. We analyze two cases: a symmetrical one with only one type of men and one type of women; and one with several types of women and men. Full article

This paper examines the subgame-perfect equilibria in symmetric $2\times 2$ supergames. We solve the smallest discount factor value for which the players obtain all the feasible and individually rational payoffs as equilibrium payoffs. We show that the critical discount factor values are not that high in many games and they generally depend on how large the payoff set is compared to the set of feasible payoffs. We analyze how the stage-game payoffs affect the required level of patience and organize the games into groups based on similar behavior. We study how the different strategies affect the set of equilibria by comparing pure, mixed and correlated strategies. This helps us understand better how discounting affects the set of equilibria and we can identify the games where extreme patience is required and the type of payoffs that are difficult to obtain. We also observe discontinuities in the critical values, which means that small changes in the stage-game payoffs may affect dramatically the equilibrium payoffs. Full article

The evolution of social or biological species can be modeled as an evolutionary game with the equilibrium strategies of the game as prediction for the ultimate distributions of species in population, when some species may survive with positive proportions, while others become extinct. We say a strategy is dense if it contains a large and diverse number of positive species, and is sparse if it has only a few dominant ones. Sparse equilibrium strategies can be found relatively easily, while dense ones are more computationally costly. Here we show that by formulating a “complementary” problem for the computation of equilibrium strategies, we are able to reduce the cost for computing dense equilibrium strategies much more efficiently. We describe the primary and complementary algorithms for computing dense as well as sparse equilibrium strategies, and present test results on randomly generated games as well as a more biologically related one. In particular, we demonstrate that the complementary algorithm is about an order of magnitude faster than the primary algorithm to obtain the dense equilibrium strategies for all our test cases. Full article

In public goods game experiments, designs implementing non-linearities in the production are less common than the standard linear setting, especially so under the assumption that the private goods production and public goods aggregation function are both non-linear. We study a voluntary contribution game (VCM) in which returns from the private project have diminishing marginal benefits and the contributions to the joint project exhibit pairwise strategic complementarities. As a control, we use a public goods game with an identical private production technology, but with the standard linear public goods aggregation. In addition to the aggregation technology, we manipulate the group size variable: In both treatments, the subjects will first play a VCM game in groups of five for 20 rounds, after which the group size is reduced to two, and the game is played for another 20 rounds. A significant over-contribution is observed in both settings when the group size is five. The rate of over-contribution is much higher under the complementary technology, but as predicted by theory, the contributions drop drastically when the group size is reduced from n = 5 to n = 2 within this treatment. Our experiment also provides empirical evidence that the so-called group size effect is present in both treatments, but it is much weaker under the standard aggregation technology. Full article

Whereas game theorists and logicians use formal methods to investigate ideal strategic behavior, many cognitive scientists use computational cognitive models of the human mind to predict and simulate human behavior. In this paper, we aim to bring these fields closer together by creating a generic translation system which, starting from a strategy for a turn-based game represented in formal logic, automatically generates a computational model in the Primitive Information Processing Elements (PRIMs) cognitive architecture, which has been validated on various experiments in cognitive psychology. The PRIMs models can be run and fitted to participants’ data in terms of decisions, response times, and answers to questions. As a proof of concept, we run computational modeling experiments on the basis of a game-theoretic experiment about the turn-based game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We run such models starting from logical representations of several strategies, such as backward induction and extensive-form rationalizability, as well as different player types according to stance towards risk and level of theory of mind. Hereby, response times and decisions for such centipede-like games are generated, which in turn leads to concrete predictions for future experiments with human participants. Such precise predictions about different aspects, including reaction times, eye movements and active brain areas, cannot be derived on the basis of a strategy logic by itself: the computational cognitive models play a vital role and our generic translation system makes their construction more efficient and systematic than before. Full article

Many public projects are funded in a dynamic manner in which contributors are able to make gradual increases in contributions and condition additional contributions on the cooperation of others. This study presents results from experiments in which subjects with an initial fixed endowment make contributions to a public project gradually over a series of rounds. A 2 × 2 experimental design is used to examine the effectiveness of multiple thresholds that once crossed increase the marginal benefit of a contribution to the public project and the existence of a completion benefit upon project completion. Results reveal that when the multiple threshold design is combined with a completion benefit, overall contributions and project completion rates increase relative to other treatments. Without the presence of a completion benefit, contributions in the multiple threshold design are not significantly different from a constant marginal benefit design. In addition, completion benefits are shown to strongly encourage additional cooperation and project completion. Finally, projects are more likely to be completed when substantial contributions occur in the early rounds. Full article