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Games, Vol. 9, Pages 18: Generalized Trust, Need for Cognitive Closure, and the Perceived Acceptability of Personal Data Collection


This vignette-based study examines how generalized trust and the need for cognitive closure relate to the perceived acceptability of contemporary business methods of personal data collection. Subjects are exposed to four scenarios that describe a method of personal data collection, involving either brand-name companies or generic descriptors of companies. After each scenario, subjects rate how acceptable they find the practice of data collection, along with the frequency and quality of experiences that they have had with the company (for brand names) or type of company (for generic descriptors). Judgments of perceived acceptability are analyzed, both across the portfolio of judgments and within each separate scenario. While analyses of each separate scenario point to the context-dependency of the perceived acceptability of data collection, several results stand out when analyzing the subjects’ portfolios of responses in the aggregate. Higher generalized trust is linked to a higher average acceptability rating, and the effect is stronger when companies are described with brand names rather than generic descriptors. Uniformly, however, no relationship is found between need for cognitive closure and perceived acceptability. Additionally, positive experiences are found to be a stronger predictor of perceived acceptability of data collection than frequency of use.

Games, Vol. 9, Pages 17: How to Analyze Models of Nonlinear Public Goods


Public goods games often assume that the effect of the public good is a linear function of the number of contributions. In many cases, however, especially in biology, public goods have nonlinear effects, and nonlinear games are known to have dynamics and equilibria that can differ dramatically from linear games. Here I explain how to analyze nonlinear public goods games using the properties of Bernstein polynomials, and how to approximate the equilibria. I use mainly examples from the evolutionary game theory of cancer, but the approach can be used for a wide range of nonlinear public goods games.

Games, Vol. 9, Pages 16: Theory of Mind and General Intelligence in Dictator and Ultimatum Games


Decreasing social sensitivity (i.e., the ability of a person to perceive, understand, and respect the feelings and viewpoints of others), has been shown to facilitate selfish behavior. This is not only true for exogenous changes in social sensitivity, but also for social sensitivity influenced by someone’s social cognition. In this analysis, we examined one measure of social cognition, namely a person’s Theory of Mind (ToM), to examine differences in decision-making in standard non-strategic and strategic environments (dictator and ultimatum games). We found that participants with higher ToM gave a greater share in the non-strategic environment. In the ultimatum game, however, ToM showed no correlation with the offers of the ultimators. Instead, we found that general intelligence scores—measured by the Wonderlic test—shared a negative, albeit weak, correlation with the amount offered in the ultimatum game. Thus, we find that lower social cognition is an important explanatory variable for selfish behavior in a non-strategic environment, while general intelligence shares some correlation in a strategic environment. Similar to the change in social sensitivity created by a specific game design, social sensitivity influenced by individual personality traits can influence behavior in non-strategic environments.

Games, Vol. 9, Pages 15: Sequential Auctions with Capacity Constraints: An Experimental Investigation


We conduct a laboratory experiment where groups of 4 subjects constrained to obtain at most one good each, sequentially bid for three goods in first and second price auctions. Subjects learn at the beginning of each auction their valuation for the good and exit the auction once they have obtained one good. We show that, contrary to equilibrium predictions, subjects’ bidding behavior is excessively similar across units and across mechanisms at the aggregate level. We provide two (complementary) explanations for these departures. One is bounded rationality. Subjects do not fully comprehend subtle differences between mechanisms. The other is self-selection. Subjects are very heterogeneous and some of them deviate more from equilibrium than others. Since deviations take mostly the form of overbidding, these subjects win the first or second good and exit the auction, leaving those who play closer to theoretical predictions to bid for the third good. Support for this hypothesis comes from the documented higher bidding, lower efficiency and lower profits associated with the first and second unit compared to the third one.

Games, Vol. 9, Pages 14: Does Imperfect Data Privacy Stop People from Collecting Personal Data?


Many companies try to access personal information to discriminate among consumers. We analyse how privacy regulations affect the acquisition and disclosure of information in a simple game of persuasion. Theory predicts that no data will be acquired with Disclosure Duty of collected data whereas Consent Law with perfect privacy results in complete information acquisition. Imperfect privacy, i.e., an environment in which leaks of collected data are possible, gives rise to multiple equilibria. Results from a laboratory experiment confirm the qualitative differences between Consent Law and Disclosure Duty and show that imperfect privacy does not stop people from collecting personal information.

Games, Vol. 9, Pages 13: Creating a Domain of Losses in the Laboratory: Effects of Endowment Size


This study examines the effects of initial endowment size on individual behavior in a binary choice game with no dominant strategy. Subjects make decisions in two, theoretically identical sequences, differing in initial endowment levels only. Each decision involves a choice between an option with a certain loss and an option with a loss that is increasing in the number of individuals who choose it. For the higher endowment level, all subjects are guaranteed a positive payoff. For the lower endowment level, subjects who choose the uncertain loss option could receive a negative payoff. The results indicate that in the first round of play, subjects with the higher endowment level choose the certain loss option significantly more often than subjects with the lower endowment level. There are, however, no significant differences in behavior beyond the first few rounds of play.

Games, Vol. 9, Pages 12: The Optimal Contract under Adverse Selection in a Moral-Hazard Model with a Risk-Averse Agent


This paper studies the optimal contract offered by a risk-neutral principal to a risk-averse agent when the agent’s hidden ability and action both improve the probability of the project being successful. We show that if the agent is sufficiently prudent and able, the principal induces a higher probability of success than under moral hazard, despite the costly informational rent given up. Moreover, there is distortion at the top. Finally, the conditions to avoid pooling are difficult to satisfy because of the different kinds of incentives to be managed and the overall trade-off between rent extraction, insurance, and efficiency involved.

Games, Vol. 9, Pages 11: Imitation of Peers in Children and Adults


Imitation of the successful choices of others is a simple and superficially attractive learning rule. It has been shown to be an important driving force for the strategic behavior of (young) adults. In this study we examine whether imitation is prevalent in the behavior of children aged between 8 and 10. Surprisingly, we find that imitation seems to be cognitively demanding. Most children in this age group ignore information about others, foregoing substantial learning opportunities. While this seems to contradict much of the literature in the field of psychology, we argue that success-based imitation of peers may be harder for children to perform than non-success-based imitation of adults.

Games, Vol. 9, Pages 10: Dynamic Pricing Decisions and Seller-Buyer Interactions under Capacity Constraints


Focusing on sellers’ pricing decisions and the ensuing seller-buyer interactions, we report an experiment on dynamic pricing with scarcity in the form of capacity constraints. Rational expectations equilibrium solutions are constructed and then tested experimentally with subjects assigned the roles of sellers and buyers. We investigate behavior in two between-subject conditions with high and moderate levels of capacity. Our laboratory market exhibits strategic sophistication: the price offers of sellers and the buyers’ aggregate responses largely approximate equilibrium predictions. We also observe systematic deviations from equilibrium benchmarks on both sides of the market. Specifically, in our experiment the sellers are boundedly strategic: their prices often exhibit strategic adjustments to profit from buyers with limited strategic sophistication, but they are also often biased towards equilibrium pricing even when that would not be ex-post optimal.

Games, Vol. 9, Pages 9: Game of Thrones: Accommodating Monetary Policies in a Monetary Union


In this paper, we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyze the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm, we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash equilibrium solution), a fully-cooperative solution with all players following a joint course of action (a Pareto optimal solution) and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully-cooperative solution yields the best results, the noncooperative solution fares worst and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty countries coming closest to the Pareto optimum.

Games, Vol. 9, Pages 8: A Game-Theoretic Approach for Modeling Competitive Diffusion over Social Networks


In this paper, we consider a novel game theory model for the competitive influence maximization problem. We model this problem as a simultaneous non-cooperative game with complete information and rational players, where there are at least two players who are supposed to be out of the network and are trying to institutionalize their options in the social network; that is, the objective of players is to maximize the spread of a desired opinion rather than the number of infected nodes. In the proposed model, we extend both the Linear Threshold model and the Independent Cascade model. We study an influence maximization model in which users’ heterogeneity, information content, and network structure are considered. Contrary to previous studies, in the proposed game, players find not only the most influential initial nodes but also the best information content. The proposed novel game was implemented on a real data set where individuals have different tendencies toward the players’ options that change over time because of gaining influence from their neighbors and the information content they receive. This means that information content, the topology of the graph, and the individual’s initial tendency significantly affect the diffusion process. The proposed game is solved and the Nash equilibrium is determined for a real data set. Lastly, the numerical results obtained from the proposed model were compared with some well-known models previously reported in the literature.

Games, Vol. 9, Pages 7: Linear–Quadratic Mean-Field-Type Games: A Direct Method


In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

Games, Vol. 9, Pages 6: Optimal Incentives in a Principal–Agent Model with Endogenous Technology


One of the standard predictions of the agency theory is that more incentives can be given to agents with lower risk aversion. In this paper, we show that this relationship may be absent or reversed when the technology is endogenous and projects with a higher efficiency are also riskier. Using a modified version of the Holmstrom and Milgrom’s framework, we obtain that lower agent’s risk aversion unambiguously leads to higher incentives when the technology function linking efficiency and riskiness is elastic, while the risk aversion–incentive relationship can be positive when this function is rigid.

Games, Vol. 9, Pages 5: Examining Spillovers between Long and Short Repeated Prisoner’s Dilemma Games Played in the Laboratory


We had participants play two sets of repeated Prisoner’s Dilemma (RPD) games, one with a large continuation probability and the other with a small continuation probability, as well as Dictator Games (DGs) before and after the RPDs. We find that, regardless of which is RPD set is played first, participants typically cooperate when the continuation probability is large and defect when the continuation probability is small. However, there is an asymmetry in behavior when transitioning from one continuation probability to the other. When switching from large to small, transient higher levels of cooperation are observed in the early games of the small continuation set. Conversely, when switching from small to large, cooperation is immediately high in the first game of the large continuation set. We also observe that response times increase when transitioning between sets of RPDs, except for altruistic participants transitioning into the set of RPDs with long continuation probabilities. These asymmetries suggest a bias in favor of cooperation. Finally, we examine the link between altruism and RPD play. We find that small continuation probability RPD play is correlated with giving in DGs played before and after the RPDs, whereas high continuation probability RPD play is not.

Games, Vol. 9, Pages 4: Incentive Magnitude Effects in Experimental Games: Bigger is not Necessarily Better


In experimental games, task-related incentives are payments to experimental subjects that vary according to their strategy choices and the consequent outcomes of the games. Limited evidence exists regarding incentive magnitude effects in experimental games. We examined one-off strategy choices and self-reported reasons for choices in eight 3 × 3 and four 4 × 4 normal-form games under task-related incentives of conventional magnitude and compared them with choices and reasons in the same games under incentives five times as large. Both strategy choices and self-reported reasons for choices were almost indistinguishable between the two conditions. These results are in line with earlier findings on individual decision making and with a parametric model, in which the incentive elasticity of effort is very small when compared with other factors, such as the complexity of the decision problem.

Games, Vol. 9, Pages 2: On the Query Complexity of Black-Peg AB-Mastermind


Mastermind is a two players zero sum game of imperfect information. Starting with Erdős and Rényi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), Chvátal (1983), Goodrich (2009). The first player, called “codemaker”, chooses a secret code and the second player, called “codebreaker”, tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. For variants that allow color repetition, Doerr et al. (2016) showed optimal results. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k ≥ n colors where no repetition of colors is allowed. We present upper and lower bounds on the number of guesses necessary to break the secret code. For the case k = n , the secret code can be algorithmically identified within less than ( n − 3 ) ⌈ log 2 n ⌉ + 5 2 n − 1 queries. This result improves the result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2. For the case k > n , we prove an upper bound of ( n − 2 ) ⌈ log 2 n ⌉ + k + 1 . Furthermore, we prove a new lower bound of n for the case k = n , which improves the recent n − log log ( n ) bound of Berger et al. (2016). We then generalize this lower bound to k queries for the case k ≥ n .

Games, Vol. 9, Pages 1: The Effects of Excluding Coalitions


One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φ E value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

Games, Vol. 8, Pages 52: Public-Goods Games with Endogenous Institution-Formation: Experimental Evidence on the Effect of the Voting Rule


We report experimental results on voluntary contributions to public-goods provision from situations in which parties can create institutions to impose a certain contribution level on its members. We focus on a public-goods game where the joint decisions inside the institution are made based on the plurality voting rule. We show that, comparing to the unanimity voting rule, the plurality rule results in a significant and large decrease in the institution initiation rate, along with a significant and large increase in the institution implementation rate. In the end, as the two effects cancel each other out, the choice of the voting rule does not significantly affect the average contribution level or efficiency.

Games, Vol. 8, Pages 51: Polarization and Segregation through Conformity Pressure and Voluntary Migration: Simulation Analysis of Co-Evolutionary Dynamics


While conformity pressures people to assimilate in a community, an individual occasionally migrates among communities when the individual feels discomfort. These two factors cause segregation and cultural diversity within communities in the society. By embedding a migration dynamic into Kuran and Sandholm’s model (2008) of preference evolution, we build an agent-based model to see how the variance of preferences in the entire society quantitatively changes over time. We find from the Monte-Carlo simulations that, while preferences assimilate within a community, self-selected migrations enlarge the diversity of preferences over communities in the society. We further study how the arrival rate of migration opportunities and the degree of conformity pressures affect the variance of preferences.

Games, Vol. 8, Pages 50: Contribution-Based Grouping under Noise


Many real-world mechanisms are “noisy” or “fuzzy”, that is the institutions in place to implement them operate with non-negligible degrees of imprecision and error. This observation raises the more general question of whether mechanisms that work in theory are also robust to more realistic assumptions such as noise. In this paper, in the context of voluntary contribution games, we focus on a mechanism known as “contribution-based competitive grouping”. First, we analyze how the mechanism works under noise and what happens when other assumptions such as population homogeneity are relaxed. Second, we investigate the welfare properties of the mechanism, interpreting noise as a policy instrument, and we use logit dynamic simulations to formulate mechanism design recommendations.

Games, Vol. 8, Pages 48: Game Theoretic Interaction and Decision: A Quantum Analysis


An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result, cooperation systems, decision systems and quantum systems all become visible as manifestations of special interaction systems. The treatment of the theory is purely mathematical and does not require any special knowledge of physics. It is shown how standard notions in cooperative game theory arise naturally in this context. In particular, states of general interaction systems are seen to arise as linear superpositions of pure quantum states and Fourier transformation to become meaningful. Moreover, quantum games fall into this framework. Finally, a theory of Markov evolution of interaction states is presented that generalizes classical homogeneous Markov chains to the present context.

Games, Vol. 8, Pages 49: Computing Human-Understandable Strategies: Deducing Fundamental Rules of Poker Strategy


Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In many situations, we would like to compute strategies that can actually be implemented by humans, who may have computational limitations and may only be able to remember a small number of features or components of the strategies that have been computed. For example, a human poker player or military leader may not have access to large precomputed tables when making real-time strategic decisions. We study poker games where private information distributions can be arbitrary (i.e., players are dealt cards from different distributions, which depicts the phenomenon in large real poker games where at some points in the hand players have different distribution of hand strength by applying Bayes’ rule given the history of play in the hand thus far). We create a large training set of game instances and solutions, by randomly selecting the information probabilities, and present algorithms that learn from the training instances to perform well in games with unseen distributions. We are able to conclude several new fundamental rules about poker strategy that can be easily implemented by humans.

Games, Vol. 8, Pages 47: Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games


This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring. We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called self-supporting sets, since the set itself provides the continuation payoffs that are required to support the equilibrium strategies. Moreover, the corresponding strategies are simple as the players face the same augmented game on each round but they play different mixed actions after each realized pure-action profile. We find that certain payoffs can be obtained in equilibrium with much lower discount factor values compared to pure strategies. The theory and the concepts are illustrated in 2 × 2 games.

Games, Vol. 8, Pages 46: Representations of Political Power Structures by Strategically Stable Game Forms: A Survey


We survey the results on representations of committees and constitutions by game forms that possess some kind of equilibrium strategies for each profile of preferences of the players. The survey is restricted to discrete models, that is, we deal with finitely many players and alternatives. No prior knowledge of social choice is assumed: As far as definitions are concerned, the paper is self-contained. Section 2 supplies the necessary general tools for the rest of the paper. Each definition is followed by a simple (but nontrivial) example. In Section 3 we give a complete account of representations of committees (proper and monotonic simple games), by exactly and strongly consistent social choice functions. We start with Peleg’s representations of weak games, and then provide a complete and detailed account of Holzman’s solution of the representation problem for simple games without veto players. In Section 4 we deal with representations of constitutions by game forms. Following Gärdenfors we model a constitution by a monotonic and superadditive effectivity function. We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium (Pareto optimal Nash equilibrium); and strong Nash equilibrium. We conclude in Section 5 with a report on two recent works on representations of constitutions under incomplete information.

Games, Vol. 8, Pages 45: Shapley Value-Based Payment Calculation for Energy Exchange between Micro- and Utility Grids


In recent years, microgrids have developed as important parts of power systems and have provided affordable, reliable, and sustainable supplies of electricity. Each microgrid is managed as a single controllable entity with respect to the existing power system but demands for joint operation and sharing the benefits between a microgrid and its hosting utility. This paper is focused on the joint operation of a microgrid and its hosting utility, which cooperatively minimize daily generation costs through energy exchange, and presents a payment calculation scheme for power transactions based on a fair allocation of reduced generation costs. To fairly compensate for energy exchange between the micro- and utility grids, we adopt the cooperative game theoretic solution concept of Shapley value. We design a case study for a fictitious interconnection model between the Mueller microgrid in Austin, Texas and the utility grid in Taiwan. Our case study shows that when compared to standalone generations, both the micro- and utility grids are better off when they collaborate in power exchange regardless of their individual contributions to the power exchange coalition.

Games, Vol. 8, Pages 44: Moral Entitlements and Aspiration Formation in Asymmetric Bargaining: Experimental Evidence from Germany and China


Using a unique experimental data set, we investigate how asymmetric legal rights shape bargainers’ aspiration levels through moral entitlements derived from equity norms and number prominence. Aspiration formation is typically hard to observe in real life. Our study involves 15 negotiations from Germany and China. Over the course of the negotiation, bargainers discuss the distribution of an amount of money by alternating offers until they consent or break off. Legal rights are randomly assigned by asymmetric outside options. We videotape and code the in-group discussions. In total, verbal data from 30 groups, 1100 pages of transcripts, and 65 h of discussions are content-analyzed. Our main finding is that strong groups derive and defend moral entitlements from equity concerns with regard to their outside options. They strive for equitable but unequal distributions (e.g., proportional split and split the difference). Moral entitlements materialize in the recorded aspiration levels and final payoffs, which exceed the equal split. By contrast, weak groups aim at equality. Over the course of the negotiation, equity tends to lose, while the prominence of round numbers gains importance. Similarities between the subject pools are found in that equity and prominence are both decisive for the formation of aspiration levels. Chinese negotiations are characterized by long periods of stagnation, only minimal concessions, and the communication of false goals. By contrast, Germans steadily reduce their goals and make concessions.

Games, Vol. 8, Pages 43: Social Preferences and Context Sensitivity


This paper is a partial review of the literature on ‘social preferences'. There are empirical findings that convincingly demonstrate the existence of social preferences, but there are also studies that indicate their fragility. So how robust are social preferences, and how exactly are they context dependent? One of the most promising insights from the literature, in my view, is an equilibrium explanation of mutually referring conditional social preferences and expectations. I use this concept of equilibrium, summarized by means of a figure, to discuss a range of empirical studies. Where appropriate, I also briefly discuss a couple of insights from the (mostly parallel) evolutionary literature about cooperation. A concrete case of the Orma in Kenya will be used as a motivating example in the beginning.

Games, Vol. 8, Pages 42: Instability of Mixed Nash Equilibria in Generalised Hawk-Dove Game: A Project Conflict Management Scenario


This paper generalises the Hawk-Dove evolutionary game by introducing cost sharing ratios for both players, and applies the generalised Hawk-Dove model to conflict management in projects through investigating the stability of Nash equilibria. A model with clashing interests between a project owner and a contractor is considered to derive their strategy adaptation given the cost sharing ratios. As expected, the pure Nash equilibria are shown to be dominantly stable while the mixed strategy equilibrium is observed to be unstable, across the range of considered cost sharing ratios. In addition, simulations are conducted on the strategy adaptation and stability of the equilibria under noisy and latent conditions. The obtained results can be used by project managers in optimising their strategy in practice.

Games, Vol. 8, Pages 41: Towards a Fair Distribution Mechanism for Asylum


It has been suggested that the distribution of refugees over host countries can be made more fair or efficient if policy makers take into account not only numbers of refugees to be distributed but also the goodness of the matches between refugees and their possible host countries. There are different ways to design distribution mechanisms that incorporate this practice, which opens up a space for normative considerations. In particular, if the mechanism takes countries’ or refugees’ preferences into account, there may be trade-offs between satisfying their preferences and the number of refugees distributed. This article argues that, in such cases, it is not a reasonable policy to satisfy preferences. Moreover, conditions are given which, if satisfied, prevent the trade-off from occurring. Finally, it is argued that countries should not express preferences over refugees, but rather that priorities for refugees should be imposed, and that fairness beats efficiency in the context of distributing asylum. The framework of matching theory is used to make the arguments precise, but the results are general and relevant for other distribution mechanisms such as the relocations currently in effect in the European Union.

Games, Vol. 8, Pages 40: Vector Games with Potential Function


The theory of non cooperative games with potential function was introduced by Monderer and Shapley in 1996. Such games have interesting properties, among which is the existence of equilibria in pure strategies. The paper by Monderer and Shapley has inspired many game theory researchers. In the present paper, many classes of multiobjective games with potential functions are studied. The notions of generalized, best-reply and Pareto potential games are introduced in a multicriteria setting. Some properties and Pareto equilibria are investigated.

Games, Vol. 8, Pages 39: On Adverse Effects of Consumers’ Attaching Greater Importance to Firms’ Ethical Conduct


Consumers increasingly care about firms’ ethical conduct (e.g., labor and environmental practices) when making their consumption choices. This note presents a simple framework to highlight the possibility that this development may induce a less desirable production technology choice and bring about lower market transparency. When faced with consumers’ greater moral concerns, more firms may choose an undesirable mode of production and shroud information about it.

Games, Vol. 8, Pages 38: Strategic Behavior of Moralists and Altruists


Does altruism and morality lead to socially better outcomes in strategic interactions than selfishness? We shed some light on this complex and non-trivial issue by examining a few canonical strategic interactions played by egoists, altruists and moralists. By altruists, we mean people who do not only care about their own material payoffs but also about those to others, and, by a moralist, we mean someone who cares about own material payoff and also about what would be his or her material payoff if others were to act like himself or herself. It turns out that both altruism and morality may improve or worsen equilibrium outcomes, depending on the nature of the game. Not surprisingly, both altruism and morality improve the outcomes in standard public goods games. In infinitely repeated games, however, both altruism and morality may diminish the prospects of cooperation, and to different degrees. In coordination games, morality can eliminate socially inefficient equilibria while altruism cannot.

Games, Vol. 8, Pages 37: Team Incentives under Moral and Altruistic Preferences: Which Team to Choose?


This paper studies incentives provision when agents are characterized either by homo moralis preferences, i.e., their utility is represented by a convex combination of selfish preferences and Kantian morality, or by altruism. In a moral hazard in a team setting with two agents whose efforts affect output stochastically, I demonstrate that the power of extrinsic incentives decreases with the degrees of morality and altruism displayed by the agents, thus leading to increased profits for the principal. I also show that a team of moral agents will only be preferred if the production technology exhibits decreasing returns to efforts; the probability of a high realization of output conditional on both agents exerting effort is sufficiently high; and either the outside option for the agents is zero or the degree of morality is sufficiently low.

Games, Vol. 8, Pages 36: Dual-Process Reasoning in Charitable Giving: Learning from Non-Results


To identify dual-process reasoning in giving, we exposed experimental participants making a charitable donation to vivid images of the charity’s beneficiaries in order to stimulate affect. We hypothesized that the effect of an affective manipulation on giving would be larger when we simultaneously put the subjects under cognitive load using a numerical recall task. Independent treatment checks reveal opposite responses in men and women and cast some doubt on the reliability of our mainstream treatment manipulations and assessment tools. We find no evidence for dual-process decision-making, even among women, whose responses to the manipulations conformed most to our expectations. These results highlight the need for caution in the use of these common manipulations, the importance of independent manipulation checks, and the limitations of dual-process models for understanding altruistic behavior.

Games, Vol. 8, Pages 35: Cooperation in Public Goods Games: Stay, But Not for Too Long


Cooperation in repeated public goods game is hardly achieved, unless contingent behavior is present. Surely, if mechanisms promoting positive assortment between cooperators are present, then cooperators may beat defectors, because cooperators would collect greater payoffs. In the context of evolutionary game theory, individuals that always cooperate cannot win the competition against defectors in well-mixed populations. Here, we study the evolution of a population where fitness is obtained in repeated public goods games and players have a fixed probability of playing the next round. As a result, the group size decreases during the game. The population is well-mixed and there are only two available strategies: always cooperate (ALLC) or always defect (ALLD). Through numerical calculation and analytical approximations we show that cooperation can emerge if the players stay playing the game, but not for too long. The essential mechanism is the interaction between the transition from strong to weak altruism, as the group size decreases, and the existence of an upper limit to the number of rounds representing limited time availability.

Games, Vol. 8, Pages 34: The Impact of Previous Action on Bargaining—An Experiment on the Emergence of Preferences for Fairness Norms


The communication of participants to identify an acceptable bargaining outcome in the Nash bargaining game is all about fairness norms. Participants introduce fairness norms which yield a better outcome for themselves in order to convince the other participant of their bargaining proposal. Typically, these fairness norms are in line with theoretical predictions, which support a wide variety of different but fair outcomes the participants can choose from. In this experiment, we play two treatments of the Nash bargaining game: in one treatment, the participants play a dictator game prior to bargaining, and in the other treatment they do not. We find that participants who have not played the dictator game intensively discuss the outcome of the game and come to solutions closer to the equal split of the pie the longer they chat. This effect vanishes as soon as the participants have previous experience from a dictator game: instead of chatting, they establish the fairness norm introduced in the dictator game. Remarkably, if the dictator is unfair in the dictator game, he also gets a higher share of the pie in the Nash bargaining game.

Games, Vol. 8, Pages 33: A Note on Disbelief in Others regarding Backward Induction


We present experimental results on the role of beliefs in the cognitive ability of others in a problem involving backward induction. Using a modified version of the so-called race game, our design allows the effects of a player’s own inability to perform backward induction to be separated from the effects of her disbelief in the ability of others to do so. We find that behavior is responsive to the dependence on others who might fail in backward induction as well as information regarding their backward induction skills.

Games, Vol. 8, Pages 32: Structural Holes in Social Networks with Exogenous Cliques


It has been empirically shown that structural holes in social networks enable potential large benefits to those individuals who bridge them (Burt, 2004). The work in Goyal and Vega-Redondo (2007) shows that the large payoff differentials caused by structural holes can persist even when agents strategically add and remove ties to smooth those differentials, thereby providing a game-theoretic rationale for the existence of bridge-agents. The present paper ties back to the initial empirical literature by explicitly assuming that agents are exogenously linked forming cliques, as in a firm environment. In this setting, bridge-agents cannot be sustained under the same conditions of Goyal and Vega-Redondo (2007). Instead, they can be sustained when the deviation possibilities are restricted and only when they connect small groups of agents to the rest.

Games, Vol. 8, Pages 31: The Monty Hall Problem as a Bayesian Game


This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty’s motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty and show that, under certain conditions on p, the unique equilibrium is one in which the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. In particular, we show that our formulation can explain the experimental results in Page (1998), that more people gradually choose switch as the number of doors in the problem increases.

Games, Vol. 8, Pages 30: Game Theory of Pollution: National Policies and Their International Effects


In this paper we put forward a simple game-theoretical model of pollution control, where each country is in control of its own pollution, while the environmental effects of policies do not stop at country borders. In our noncooperative differential game, countries as players minimize the present value of their own costs defined as a linear combination of pollution costs and costs of environmentally friendly policies, where the state vector of the system consists of the pollution stock per country. A player’s time-varying decision is her investment into clean policies, while her expected costs include also pollution caused by her neighbors. We analyze three variants of this game: (1) a Nash game in which each player chooses her investment into clean policies such that her expected costs are minimal, (2) a game in which the players imitate the investments into clean policies of their neighbors without taking the neighbor’s success concerning their costs into account and (3) a game in which each player imitates her neighbors’ investments into clean policies if this behavior seems to bring a profit. In each of these scenarios, we show under which conditions the countries have incentives to act environmentally friendly. We argue that the different results of these games can be used to understand and design effective environmental policies.

Games, Vol. 8, Pages 29: Anticipated Communication in the Ultimatum Game


Anticipated verbal feedback in a dictator game has been shown to induce altruistic behavior. However, in the ultimatum game which, apart from generosity, entails a strategic component since a proposer may (rightly) fear that the responder will reject a low offer, it remains an open question whether anticipated verbal communication can be effective in increasing offers. We implement a between-subjects experimental design in the ultimatum game with strategy method manipulating the form of anticipated verbal communication (no communication, one-sided communication from proposers and two-sided communication) and find that offers are significantly higher in the presence of anticipated two-sided communication. However, anticipated one-sided communication from proposers has no effect on offers, suggesting, as found in previous studies, that it is the anticipation of feedback that is relevant.

Games, Vol. 8, Pages 28: Reacting to Unfairness: Group Identity and Dishonest Behavior


We experimentally investigate whether individuals are more likely to engage in dishonest behavior after having experienced unfairness perpetrated by an individual with a salient group identity. Two individuals generate an endowment together, but only one can decide how to share it. They either share the same group identity or have distinct group identities. Then, they approach a task in which they can opportunistically engage in dishonest behavior. Our results show that when individuals share the same group identity, unfair distributive decisions do not trigger a dishonest reaction. In contrast, when different group identities coexist, dishonest behavior is observed as a reaction to unfairness.

Games, Vol. 8, Pages 27: Cycles in Team Tennis and Other Paired-Element Contests


Team Tennis competitions produce aggregate scores for teams, and thus team rankings, based on head-to-head matchups of individual team members. Similar scoring rules can be used to rank any two groups that must be compared on the basis of paired elements. We explore such rules in terms of their strategic and social choice characteristics, with particular emphasis on the role of cycles. We first show that cycles play an important role in promoting competitive balance, and show that cycles allow for a maximum range of competitive balance within a league of competing teams. We also illustrate the impact that strategic behavior can have on the unpredictability of competition outcomes, and show for a general class of team tennis scoring rules that a rule is strategy-proof if and only if it is acyclic (dictatorial) and manipulable otherwise. Given the benefits of cycles and their relationship with manipulability, a league valuing competitive balance may invite such social choice violations when choosing a scoring rule.

Games, Vol. 8, Pages 26: Gender, Emotions, and Tournament Performance in the Laboratory


Individuals face competitive environments daily, and it is important to understand how emotions affect behavior in these environments and resulting economic consequences. Using a two-stage laboratory experiment, I analyze the role of reported emotions in tournament performance and assess how the behavioral response differs across genders. The first stage serves to induce emotions, while the second stage presents the subject with a one-on-one winner-take-all tournament with the individual who generated the feeling, using a real-effort task. Ultimately, I show that women respond to the negative feelings more strongly than men. I find that women increase performance when experiencing negative emotions, while male performance remains unaffected. Remarkably, there is no gender gap in tournament performance when there are negative emotions.

Games, Vol. 8, Pages 25: Multi-Leader Multi-Follower Model with Aggregative Uncertainty


We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated.

Games, Vol. 8, Pages 24: Clusters with Minimum Transportation Cost to Centers: A Case Study in Corn Production Management


In Northern Thailand, the size and topographical structure of farmland makes it necessary for operators of small-scale waste management systems to be able to reach their clients in an effective manner. Over the past decades, corn contract farming has increased, and the chief method for eliminating waste from these farms has chiefly been open burning on the fields, which produces enormous amounts of greenhouse gases (GHG) and Polycyclic Aromatic Hydrocarbons (PAHs). To find a way to reduce GHG emissions in the corn production system, this work focuses on finding clusters with minimum transportation time from waste disposal centers. To solve the clustering problems, four models are created and solved on AIMMS and MATLAB. Simulation results indicate that the number of clients essentially affects the performance of the procedure. The case studies are on corn production management in Chiang Mai, the region’s economic capital, as well as in 9 provinces in Northern Thailand, including Chiang Mai, whose combined corn production comprises 32.73 percent of the national production. With roughly 15% of the corn cobs and husks involved in the study, we found that by changing the waste elimination process, the total CO2 emissions can be reduced by up to 12,008.40 tons per year in Chiang Mai and up to 180,198.14 tons per year in the 9 provinces of Northern Thailand.

Games, Vol. 8, Pages 23: Security Investment, Hacking, and Information Sharing between Firms and between Hackers


A four period game between two firms and two hackers is analyzed. The firms first defend and the hackers thereafter attack and share information. Each hacker seeks financial gain, beneficial information exchange, and reputation gain. The two hackers’ attacks and the firms’ defenses are inverse U-shaped in each other. A hacker shifts from attack to information sharing when attack is costly or the firm’s defense is cheap. The two hackers share information, but a second more disadvantaged hacker receives less information, and mixed motives may exist between information sharing and own reputation gain. The second hacker’s attack is deterred by the first hacker’s reputation gain. Increasing information sharing effectiveness causes firms to substitute from defense to information sharing, which also increases in the firms’ unit defense cost, decreases in each firm’s unit cost of own information leakage, and increases in the unit benefit of joint leakage. Increasing interdependence between firms causes more information sharing between hackers caused by larger aggregate attacks, which firms should be conscious about. We consider three corner solutions. First and second, the firms deter disadvantaged hackers. When the second hacker is deterred, the first hacker does not share information. Third, the first hacker shares a maximum amount of information when certain conditions are met. Policy and managerial implications are provided for how firms should defend against hackers with various characteristics.

Games, Vol. 8, Pages 22: Emotions and Behavior Regulation in Decision Dilemmas


We introduce a dynamic model of emotional behavior regulation that can generalize to a wide range of decision dilemmas. Dilemmas are characterized by availability of mutually exclusive goals that a decision maker is dually motivated to pursue. In our model, previous goal pursuant decisions produce negative emotions that regulate an individual’s propensity to further pursue those goals at future times. This emotional regulation of behavior helps explain the non-stationarity and switching observed between so-called “preferences” revealed in repeated decision dilemmas (e.g., by choosing A over B at time 1, then choosing B over A at time 2). We also explain how behavior regulation under dilemma conditions is affected by the set of available options and how the strength and decay rate of emotions affect the tendency to choose behaviors pursuant of extremely (rather than moderately) different options over time. We discuss how emotional behavior regulation insights provided by our model can extend to a variety of topics including approach and avoidance, temptation and self-control, moral balancing, impulse buying and shopping momentum, dieting and exercise, work and leisure, sleep regulation, cooperation, and competition.

Games, Vol. 8, Pages 21: A Study of the Triggers of Conflict and Emotional Reactions


We study three triggers of conflict and explore their resultant emotional reactions in a laboratory experiment. Economists suggest that the primary trigger of conflict is monetary incentives. Social psychologists suggest that conflicts are often triggered by fear. Finally, evolutionary biologists suggest that a third trigger is uncertainty about an opponent’s desire to cause harm. Consistent with the predictions from economics, social psychology, and evolutionary biology, we find that conflict originates from all three triggers. The three triggers differently impact the frequency of conflict, but not the intensity. Also, we find that the frequency and intensity of conflict decrease positive emotions and increase negative emotions and that conflict impacts negative emotions more than positive emotions.

Games, Vol. 8, Pages 20: Watching Eyes and Living up to Expectations: Unkind, Not Kind, Eyes Increase First Mover Cooperation in a Sequential Prisoner’s Dilemma


(1) Background: Why and when images of watching eyes encourage prosocial behavior is still subject to discussion, and two recent meta-analyses show no effect of watching eyes on generosity. This study aims to discern the effect of watching eyes of different valence on two separate aspects of prosocial behavior, and additionally investigates whether individuals’ social value orientation moderates the effect of eyes. (2) Methods: Individuals take on the role of either a first or second mover in an incentivized, anonymous sequential prisoner’s dilemma (n = 247), a two-person game which separates the need to form expectations about the other player (first mover cooperation, trust) from the motive of greed (second mover cooperation, reciprocity). During decision-making, a picture of either kind eyes, unkind eyes, or a control picture is presented above each decision matrix. (3) Results: The results indicate that unkind eyes, and not kind eyes, significantly boost first mover cooperation. In contrast, neither type of eye cues increase second mover cooperation. Social value orientation does not moderate these effects. (4) Conclusions: Thus, the data suggest that the valence of eye cues matters, and we propose that unkind eyes urge first movers to live up to the interaction partner’s expectations.

Games, Vol. 8, Pages 19: Epistemic Game Theory and Logic: Introduction


Epistemic game theory and the systems of logic that support it are crucial for understanding rational behavior in interactive situations in which the outcome for an agent depends, not just on her own behavior, but also on the behavior of those with whom she is interacting. Scholars in many fields study such interactive situations, that is, games of strategy. [...]

Games, Vol. 8, Pages 18: The Emotional Moves of a Rational Actor: Smiles, Scowls, and Other Credible Messages


Many scholars turn to emotions to understand irrational behavior. We do the opposite: we turn to rationality and game theory to understand people’s emotions. We discuss a striking theory of emotions that began with the game theory of credible threats and promises, then was enriched by evolutionary biology and psychology, and now is being tested in psychological experiments. We review some of these experiments which use economic games to set up strategic situations with real payoffs. The experiments test whether a player’s emotional expressions lend credibility to promises, threats, and claims of danger or hardship. The results offer insights into the hidden strategies behind a warm smile, an angry scowl, a look of terror, and eyes of despair.

Games, Vol. 8, Pages 17: Emotion at Stake—The Role of Stake Size and Emotions in a Power-to-Take Game Experiment in China with a Comparison to Europe


This paper experimentally investigates how monetary incentives and emotions influence behavior in a two-player power-to-take game (PTTG). In this game, one player can claim any part of the other's endowment (take rate), and the second player can respond by destroying any part of his or her own endowment. The experiment is run in China. We further compare our findings with the behavior of two European subject pools. Our results give new insights regarding emotion regulation. Even though stake size does not appear to matter for take rates and destruction rates, it does matter for the reaction function of the responder regarding the take rate. When stakes are high, there is less destruction for low and intermediate take rates, and more destruction for high take rates, compared to relatively low stakes. Under low incentives, ‘hot’ anger-type emotions are important for destruction, while ‘cool’ contempt becomes prominent under high monetary incentives. These results suggest emotion regulation in the high-stake condition. Moreover, emotions are found to fully mediate the impact of the take rate on destruction when stakes are low, whereas they only partially do so if stakes are high. Comparing the low-stakes data for China with existing European data, we find similarities in behavior, emotions and emotion intensities, as well as the full mediation of the take rate by emotions. We find some differences related to the type of emotions that are important for destruction. Whereas anger and joy are important in both, in addition, irritation and fear play a role in China, while this holds for contempt in the EU.

Games, Vol. 8, Pages 16: The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm


We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus—if nonempty—of such a game is composed of the images of a particular payoff vector under all symmetries of the game. This payoff vector belongs to the set of integer imputations that weakly preserve the desirability relation between the players. We propose an algorithm for finding the integer nucleolus of any directed simple game with a nonempty integer imputation set. The algorithm supports the parallel execution of multiple threads in a computer application. We also consider the integer prenucleolus and the class of directed generalized simple games.

Games, Vol. 8, Pages 15: On Information Aggregation and Interim Efficiency in Networks


This paper considers a population of agents that are engaged in a listening network. The agents wish to match their actions to the true value of some uncertain (exogenous) parameter and to the actions of the other agents. Each agent begins with some initial information about the parameter and, in addition, is able to receive further information from their neighbors in the network. I derive a closed expression for the (interim) social welfare loss that depends on the initial information structure and on the possible pieces of information that can be gathered under the network. Then, I explore how changes in the network may affect social welfare for extreme levels of complementarity in the agents’ actions. When the level of complementarity is very high, efficiency is achieved regardless of the network structure. For very low levels of complementarity in actions, efficiency can be either associated to more sparse or denser networks, depending on the size of the induced informative gains. The implications of this paper are relevant in security environments where agents are naturally interpreted as analysts who try to forecast the value of a parameter that describes a threat to security.

Games, Vol. 8, Pages 14: Swap Equilibria under Link and Vertex Destruction


We initiate the study of the destruction or adversary model (Kliemann 2010) using the swap equilibrium (SE) stability concept (Alon et al., 2010). The destruction model is a network formation game incorporating the robustness of a network under a more or less targeted attack. In addition to bringing in the SE concept, we extend the model from an attack on the edges to an attack on the vertices of the network. We prove structural results and linear upper bounds or super-linear lower bounds on the social cost of SE under different attack scenarios. For the case that the vertex to be destroyed is chosen uniformly at random from the set of max-sep vertices (i.e., where each causes a maximum number of separated player pairs), we show that there is no tree SE with only one max-sep vertex. We conjecture that there is no tree SE at all. On the other hand, we show that for the uniform measure, all SE are trees (unless two-connected). This opens a new research direction asking where the transition from “no cycle” to “at least one cycle” occurs when gradually concentrating the measure on the max-sep vertices.

Games, Vol. 8, Pages 13: Interdependent Defense Games with Applications to Internet Security at the Level of Autonomous Systems


We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon interdependent security (IDS) games, a model by Heal and Kunreuther that considers the source of the risk to be the result of a fixed randomized-strategy. We adapt IDS games to model the attacker’s deliberate behavior. We define the attacker’s pure-strategy space and utility function and derive appropriate cost functions for the defenders. We provide a complete characterization of mixed-strategy Nash equilibria (MSNE), and design a simple polynomial-time algorithm for computing all of them for an important subclass of IDD games. We also show that an efficient algorithm to determine whether some attacker’s strategy can be a part of an MSNE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming (DP) algorithm to compute an approximate MSNE when the graph/network structure of the game is a directed tree with a single source. We also show that the DP algorithm is a fully polynomial-time approximation scheme. In addition, we propose a generator of random instances of IDD games based on the real-world Internet-derived graph at the level of autonomous systems (≈27 K nodes and ≈100 K edges as measured in March 2010 by the DIMES project). We call such games Internet games. We introduce and empirically evaluate two heuristics from the literature on learning-in-games, best-response gradient dynamics (BRGD) and smooth best-response dynamics (SBRD), to compute an approximate MSNE in IDD games with arbitrary graph structures, such as randomly-generated instances of Internet games. In general, preliminary experiments applying our proposed heuristics are promising. Our experiments show that, while BRGD is a useful technique for the case of Internet games up to certain approximation level, SBRD is more efficient and provides better approximations than BRGD. Finally, we discuss several extensions, future work, and open problems.

Games, Vol. 8, Pages 12: Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks


The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm.

Games, Vol. 8, Pages 11: The Welfare Cost of Signaling


Might the resource costliness of making signals credible be low or negligible? Using a job market as an example, we build a signaling model to determine the extent to which a transfer from an applicant might replace a resource cost as an equilibrium method of achieving signal credibility. Should a firm’s announcement of hiring for an open position be believed, the firm has an incentive to use a properly-calibrated fee to implement a separating equilibrium. The result is robust to institutional changes, outside options, many firms or many applicants and applicant risk aversion, though a sufficiently risk-averse applicant who is sufficiently likely to be a high type may lead to a preference for a pooling equilibrium.

Games, Vol. 8, Pages 10: Cyclic Competition and Percolation in Grouping Predator-Prey Populations


We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically,without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games.

Games, Vol. 8, Pages 9: Assessing Others’ Risk‐Taking Behavior from Their Affective States: Experimental Evidence Using a Stag Hunt Game


Researchers are increasingly exploring the role of emotions in interactive decision‐making. Recent theories have focused on the interpersonal effects of emotions—the influence of the decisionmaker’s expressed emotions on observers’ decisions and judgments. In this paper, we examine whether people assess others’ risk preferences on the basis of their emotional states, whether this affects their own behavior, and how this assessment matches others’ actual behavior. To test these ideas, we used an experimental Stag Hunt game (n = 98), and included non‐trivial financial consequences. Participants were told (truthfully) that their counterparts’ previous task had left them happy, fearful, or emotionally neutral. People who were told their counterparts were fearful reported that they expected less risky decisions from these counterparts than people told their counterparts were neutral or happy. As a result, given that the Stag Hunt is a coordination game, these participants were themselves less risky. Interestingly, these participants’ expectations were not accurate; thus, coordination failed, and payoffs were low. This raises the possibility of a “curse of knowledge” whereby one player’s erroneous beliefs about the effects of the counterpart’s emotional state leads the first player to make poor action choices.

Games, Vol. 8, Pages 5: Anger Management: Aggression and Punishment in the Provision of Public Goods


The ability to punish free-riders can increase the provision of public goods. However, sometimes, the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is that punishment can express anger about free-riding. If this is the case, then tools that regulate emotions could decrease the use of punishments while keeping welfare high, possibly depending on pre-existing levels of aggression. In this lab experiment, we find that adopting an objective attitude (objective), through a form of emotion regulation called cognitive reappraisal, decreases the use of punishments and makes a statistically insignificant improvement to both net earnings and self-reported emotions compared to a control condition (natural). Although the interaction between the emotion regulation treatment and level of aggression is not significant, only low aggression types reduce their punishments; the results are of the same direction, but statistically insignificant for high aggression types. Overall, our findings suggest that pairing emotion regulation with punishments can decrease the use of punishments without harming monetary and mental welfare.

Games, Vol. 8, Pages 8: The Evolution of Reputation-Based Cooperation in Regular Networks


Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study of the interplay between both mechanisms remains almost uncharted. Here, we present a new individual-based model for the evolution of reciprocal cooperation between reputation and networks. We comparatively analyze four of the leading moral assessment rules—shunning, image scoring, stern judging, and simple standing—and base the model on the giving game in regular networks for Cooperators, Defectors, and Discriminators. Discriminators rely on a proper moral assessment rule. By using individual-based models, we show that the four assessment rules are differently characterized in terms of how cooperation evolves, depending on the benefit-to-cost ratio, the network-node degree, and the observation and error conditions. Our findings show that the most tolerant rule—simple standing—is the most robust among the four assessment rules in promoting cooperation in regular networks.

Games, Vol. 8, Pages 7: Social Pressure and Environmental Effects on Networks: A Path to Cooperation


In this paper, we study how the pro-social impact due to the vigilance by other individuals is conditioned by both environmental and evolutionary effects. To this aim, we consider a known model where agents play a Prisoner’s Dilemma Game (PDG) among themselves and the pay-off matrix of an individual changes according to the number of neighbors that are “vigilant”, i.e., how many neighbors watch out for her behavior. In particular, the temptation to defect decreases linearly with the number of vigilant neighbors. This model proved to support cooperation in specific conditions, and here we check its robustness with different topologies, microscopical update rules and initial conditions. By means of many numerical simulations and few theoretical considerations, we find in which situations the vigilance by the others is more effective in favoring cooperative behaviors and when its influence is weaker.

Games, Vol. 8, Pages 6: Acknowledgement to Reviewers of Games in 2016


The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]

Games, Vol. 8, Pages 4: A Nobel Prize for Property Rights Theory


This article provides a brief overview of the Property-Rights Theory of the firm, pioneered by Grossman and Hart (1986) and Hart and Moore (1990), and situates the theory in other literatures.

Games, Vol. 8, Pages 3: Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies


Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of belief-revision policies are beliefs, not strategies and acts. Thus, the rationality of belief-revision policies is subject to Bayesian epistemology. The components of any belief-revision policy are credences constrained by the probability axioms, by conditionalization, and by the principles of indifference and of regularity. The principle of indifference states that an agent updates his credences proportionally to the evidence, and no more. The principle of regularity states that an agent assigns contingent propositions a positive (but uncertain) credence. The result is rational constraints on real people’s credences that account for their uncertainty. Nonetheless, there is the open problem of non-evidential components that affect people’s credence distributions, despite the rational constraint on those credences. One non-evidential component is people’s temperaments, which affect people’s evaluation of evidence. The result is there might not be a proper recommendation of a strategy profile for a game (in terms of a solution concept), despite agents’ beliefs and corresponding acts being rational.

Games, Vol. 8, Pages 1: Cognitive Hierarchy Theory and Two-Person Games


The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory.

Games, Vol. 8, Pages 2: Economic Harmony: An Epistemic Theory of Economic Interactions


We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We show that the aforementioned minor epistemic modification of the concept of utility is quite powerful in generating plausible and successful predictions of experimental results, obtained in the standard ultimatum game, and the sequential common pool resource dilemma (CPR) game. Notably, the cooperation and fairness observed in the studied games are accounted for without adding an other-regarding component in the players’ utility functions. For the standard ultimatum game, the theory predicts a division of φ and 1 − φ, for the proposer and responder, respectively, where φ is the famous Golden Ratio (≈0.618), most known for its aesthetically pleasing properties. We discuss possible extensions of the proposed theory to repeated and evolutionary ultimatum games.

Games, Vol. 7, Pages 40: Network Formation with Endogenous Link Strength and Decreasing Returns to Investment


We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the direct link between any pair of agents is a concave function of their investments towards each other. In comparison with some existing models of network formation where the strength technology is a convex function of investment, we find that (i) the symmetric complete network can dominate the star architecture in terms of total utility; (ii) a dominating symmetric complete network needs not be stable; and, (iii) star and complete networks can be dominated by small-world networks.

Games, Vol. 7, Pages 39: Modeling Poker Challenges by Evolutionary Game Theory


We introduce a model for studying the evolutionary dynamics of Poker. Notably, despite its wide diffusion and the raised scientific interest around it, Poker still represents an open challenge. Recent attempts for uncovering its real nature, based on statistical physics, showed that Poker in some conditions can be considered as a skill game. In addition, preliminary investigations reported a neat difference between tournaments and ‘cash game’ challenges, i.e., between the two main configurations for playing Poker. Notably, these previous models analyzed populations composed of rational and irrational agents, identifying in the former those that play Poker by using a mathematical strategy, while in the latter those playing randomly. Remarkably, tournaments require very few rational agents to make Poker a skill game, while ‘cash game’ may require several rational agents for not being classified as gambling. In addition, when the agent interactions are based on the ‘cash game’ configuration, the population shows an interesting bistable behavior that deserves further attention. In the proposed model, we aim to study the evolutionary dynamics of Poker by using the framework of Evolutionary Game Theory, in order to get further insights on its nature, and for better clarifying those points that remained open in the previous works (as the mentioned bistable behavior). In particular, we analyze the dynamics of an agent population composed of rational and irrational agents, that modify their behavior driven by two possible mechanisms: self-evaluation of the gained payoff, and social imitation. Results allow to identify a relation between the mechanisms for updating the agents’ behavior and the final equilibrium of the population. Moreover, the proposed model provides further details on the bistable behavior observed in the ‘cash game’ configuration.

Games, Vol. 7, Pages 38: Probabilistic Unawareness


The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands—modal and probabilistic—of doxastic logic.

Games, Vol. 7, Pages 37: Epistemically Robust Strategy Subsets


We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set Y i contains all player types that believe with sufficient probability that the others are of types in Y − i and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability.

Games, Vol. 7, Pages 36: Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals


This paper develops a game-theoretic and epistemic account of a peculiar mode of practical reasoning that sustains focal points but also more general forms of rule-following behavior which I call community-based reasoning (CBR). It emphasizes the importance of counterfactuals in strategic interactions. In particular, the existence of rules does not reduce to observable behavioral patterns but also encompasses a range of counterfactual beliefs and behaviors. This feature was already at the core of Wittgenstein’s philosophical account of rule-following. On this basis, I consider the possibility that CBR may provide a rational basis for cooperation in the prisoner’s dilemma.

Games, Vol. 7, Pages 35: Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium


In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno, 2016), the notion of PBE was used to provide a characterization of SE in terms of a strengthening of the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of “conservative” belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE.

Games, Vol. 7, Pages 34: Coevolution of Cooperation and Layer Selection Strategy in Multiplex Networks


Recently, the emergent dynamics in multiplex networks, composed of layers of multiple networks, has been discussed extensively in network sciences. However, little is still known about whether and how the evolution of strategy for selecting a layer to participate in can contribute to the emergence of cooperative behaviors in multiplex networks of social interactions. To investigate these issues, we constructed a coevolutionary model of cooperation and layer selection strategies in which each an individual selects one layer from multiple layers of social networks and plays the Prisoner’s Dilemma with neighbors in the selected layer. We found that the proportion of cooperative strategies increased with increasing the number of layers regardless of the degree of dilemma, and this increase occurred due to a cyclic coevolution process of game strategies and layer selection strategies. We also showed that the heterogeneity of links among layers is a key factor for multiplex networks to facilitate the evolution of cooperation, and such positive effects on cooperation were observed regardless of the difference in the stochastic properties of network topologies.

Games, Vol. 7, Pages 33: Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation


Who benefits from the ignorance of others? We address this question from the point of view of a policy maker who can induce some ignorance into a system of agents competing for resources. Evolutionary game theory shows that when unconditional cooperators or ignorant agents compete with defectors in two-strategy settings, unconditional cooperators get exploited and are rendered extinct. In contrast, conditional cooperators, by utilizing some kind of reciprocity, are able to survive and sustain cooperation when competing with defectors. We study how cooperation thrives in a three-strategy setting where there are unconditional cooperators, conditional cooperators and defectors. By means of simulation on various kinds of graphs, we show that conditional cooperators benefit from the existence of unconditional cooperators in the majority of cases. However, in worlds that make cooperation hard to evolve, defectors benefit.

Games, Vol. 7, Pages 32: Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions


In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the “best informed player” would be sure to obtain if he/she were to sell the goods to his/her opponents via take-it-or-leave-it offers. Our mechanism is probabilistic and of an extensive form. It relies on a new solution concept, for analyzing extensive-form games of incomplete information, which assumes only mutual belief of rationality. Moreover, our mechanism enjoys several novel properties with respect to privacy, computation and collusion.

Games, Vol. 7, Pages 31: Evolutionary Inspection and Corruption Games


We extend a standard two-person, non-cooperative, non-zero sum, imperfect inspection game, considering a large population of interacting inspectees and a single inspector. Each inspectee adopts one strategy, within a finite/infinite bounded set of strategies returning increasingly illegal profits, including compliance. The inspectees may periodically update their strategies after randomly inter-comparing the obtained payoffs, setting their collective behaviour subject to evolutionary pressure. The inspector decides, at each update period, the optimum fraction of his/her renewable budget to invest on his/her interference with the inspectees’ collective effect. To deter the inspectees from violating, he/she assigns a fine to each illegal strategy. We formulate the game mathematically, study its dynamics and predict its evolution subject to two key controls, the inspection budget and the punishment fine. Introducing a simple linguistic twist, we also capture the corresponding version of a corruption game.

Games, Vol. 7, Pages 30: Simulating the Impact of Crossover Kidney Transplantation on the Nord Italia Transplant Program


The increasing number of patients affected by chronic kidney disease makes it necessary to rely on living donors. However, a patient often cannot exploit her potential donor, due to blood or tissue incompatibility. Therefore, crossover transplantation programs have been developed in several countriesin order to increase the number of people receiving a kidney from a living donor. After reviewing the essential medical facts needed for the subsequent results, we quickly introduce two known algorithms for crossover transplantation. Next, we consider a dataset provided by the Nord Italia Transplant program, and we apply the above algorithms in order to highlight the benefits of these efficient procedures.

Games, Vol. 7, Pages 29: What Goes Around, Comes Around: Experimental Evidence on Exposed Lies


We experimentally investigate the optimal way to handle the uncovering of a noble lie, that is, a lie that supposedly is in the best interest of a given community. For this purpose, we analyze a public good game with feedback to group members on the average contributions of the other group members. The computer program inflates the feedback and shows higher than real average contributions to the high contributors. As shown by earlier studies, the partial feedback inflation increases the total payoff of the public good as it avoids the feeling of being a sucker for above average contributors. The lie is then uncovered and we continue with different feedback modes on contributions, some inflated, some true. We find that players respond similarly to both feedback modes. However, with true feedback, initial contributions in the second stage are significantly higher than with inflated feedback.

Games, Vol. 7, Pages 28: When Do Types Induce the Same Belief Hierarchy?


Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.

Games, Vol. 7, Pages 27: Evolution of Mindsight and Psychological Commitment among Strategically Interacting Agents


We study the evolution of strategic psychological capabilities in a population of interacting agents. Specifically, we consider agents which are either blind or with mindsight, and either transparent or opaque. An agent with mindsight can observe the psychological makeup of a transparent agent, i.e., its logic, emotions, commitments and other elements that determine how it chooses actions. A blind agent cannot observe and opaque agents cannot be observed. Our assumption that mindsight and transparency are costly and optional exposes a middle ground between standard game theory without mindsight and evolution of preferences theory with obligatory and costless mindsight. We show that the only evolutionarily stable monomorphic population is one in which all agents are blind, opaque, and act-rational. We find that mindsight, transparency, and rule-rational commitments may evolve, albeit only in a portion of the population that fluctuates in size over generations. We reexamine the Ultimatum and Trust games in light of our findings and demonstrate that an evolved population of agents can differ significantly from a population of simplistic payoff-maximizers in terms of psychological traits and economic outcomes.

Games, Vol. 7, Pages 26: Evolutionary Game between Commensal and Pathogenic Microbes in Intestinal Microbiota


The human intestinal microbiota plays a fundamental role in host health and is associated with many diseases when the homeostasis is disturbed. Although recent achievements in metagenomic sequencing have begun to reveal the variety of microbial composition associated with healthy and disease states, species-specific interactions and systematic dynamics still pose a great challenge to resolve the complexity of human microbiota. Using Clostridium difficile infection in human intestinal microbiota as an example, we apply evolutionary game theory to gain a fundamental understanding of the phenotypic variability and dynamic progression of microbiota. Here, microbiota dynamics are determined by the frequency-dependent fitness of each phenotypic population in the presence of the others. More specifically, the fitness is a function of phenotypic composition of the microbiota. We show how the phenotypic variability of microbiota can be explained by game theoretical approach. Knowledge of this study provides a new perspective in administrating antibiotic when dealing with pathogenic invasion. Instead of solely targeting to pathogens, therapies should aim at the whole ecosystem by reducing the fitness of pathogens compared to that of commensal microbes. In this case, the system will eradicate the pathogens by itself.

Games, Vol. 7, Pages 25: Payoff Shares in Two-Player Contests


In imperfectly discriminating contests with symmetric valuations, equilibrium payoffs are positive shares of the value of the prize. In contrast to a bargaining situation, players’ shares sum to less than one because a residual share of the value is lost due to rent dissipation. In this paper, we consider contests with two players and investigate the relationship between these equilibrium shares and the parameters of a class of asymmetric Tullock contest success functions. Our main finding is that any players’ shares that sum up to less than one can arise as the unique outcome of a pure-strategy Nash equilibrium for appropriate parameters.

Games, Vol. 7, Pages 24: The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games


We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system’s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.

Games, Vol. 7, Pages 23: Trait Emotional Intelligence Is Related to Risk Taking when Adolescents Make Deliberative Decisions


Most forms of risky behavior reach their peak during adolescence. A prominent line of research is exploring the relationship between people’s emotional self-efficacy and risk taking, but little is known about this relationship in the cognitive-deliberative domain among adolescents. The main aim of the present study consists in investigating whether trait EI (Emotional Intelligence) is positively related to risk taking under predominantly cognitive-deliberative conditions among adolescents. Ninety-four adolescents played the cold version of the Columbia Card Task one month following an assessment of their trait EI. Results showed that trait EI is associated with risk taking under cognitive-deliberative conditions among adolescents. Moreover, the present research showed that trait EI is related to risk taking through the decision makers’ self-motivation. These results provide novel insights into research investigating the connections between emotional intelligence, decision science and adolescence research.

Games, Vol. 7, Pages 22: Auctions Versus Private Negotiations in Buyer-Seller Networks


Buyer-seller networks where price is determined by an ascending-bid auction are important in many economic examples such as certain real estate markets, radio spectrum sharing, and buyer-supplier networks. However, it may be that some sellers are better off not participating in the auction. We consider what happens if sellers can make a take it or leave it offer to one of their linked buyers before the auction takes place and thus such a seller can choose not to participate in the auction. We give conditions on the graph and buyers valuations under which the buyer and seller will both agree to such a take it or leave it offer. Specifically, the buyer-seller pair will choose private negotiation over the auction if the seller acts as a network bridge with power over the buyer and if there are enough buyers with low valuations so that the seller does not expect to receive a high price in the auction.

Games, Vol. 7, Pages 21: Promoting Residential Recycling: An Alternative Policy Based on a Recycling Reward System


This paper analyzes a reward system that uses a club good to promote recycling. In particular, we examine a context of incomplete information in which the administrator is unable to observe the resident’s attitude towards recycling. The results suggest that despite the lack of information, the administrator is able to induce all types of residents to recycle when the reward is sufficiently high. Furthermore, we show that education programs, technologies that help to reduce the residential recycling cost and penalties for garbage dumping are complementary tools that could also promote recycling.

Games, Vol. 7, Pages 20: Space Debris Removal: A Game Theoretic Analysis


We analyse active space debris removal efforts from a strategic, game-theoretical perspective. Space debris is non-manoeuvrable, human-made objects orbiting Earth, which pose a significant threat to operational spacecraft. Active debris removal missions have been considered and investigated by different space agencies with the goal to protect valuable assets present in strategic orbital environments. An active debris removal mission is costly, but has a positive effect for all satellites in the same orbital band. This leads to a dilemma: each agency is faced with the choice between the individually costly action of debris removal, which has a positive impact on all players; or wait and hope that others jump in and do the ‘dirty’ work. The risk of the latter action is that, if everyone waits, the joint outcome will be catastrophic, leading to what in game theory is referred to as the ‘tragedy of the commons’. We introduce and thoroughly analyse this dilemma using empirical game theory and a space debris simulator. We consider two- and three-player settings, investigate the strategic properties and equilibria of the game and find that the cost/benefit ratio of debris removal strongly affects the game dynamics.

Games, Vol. 7, Pages 19: Optimal Decision Rules in Repeated Games Where Players Infer an Opponent’s Mind via Simplified Belief Calculation


In strategic situations, humans infer the state of mind of others, e.g., emotions or intentions, adapting their behavior appropriately. Nonetheless, evolutionary studies of cooperation typically focus only on reaction norms, e.g., tit for tat, whereby individuals make their next decisions by only considering the observed outcome rather than focusing on their opponent’s state of mind. In this paper, we analyze repeated two-player games in which players explicitly infer their opponent’s unobservable state of mind. Using Markov decision processes, we investigate optimal decision rules and their performance in cooperation. The state-of-mind inference requires Bayesian belief calculations, which is computationally intensive. We therefore study two models in which players simplify these belief calculations. In Model 1, players adopt a heuristic to approximately infer their opponent’s state of mind, whereas in Model 2, players use information regarding their opponent’s previous state of mind, obtained from external evidence, e.g., emotional signals. We show that players in both models reach almost optimal behavior through commitment-like decision rules by which players are committed to selecting the same action regardless of their opponent’s behavior. These commitment-like decision rules can enhance or reduce cooperation depending on the opponent’s strategy.

Games, Vol. 7, Pages 18: Sharing the Costs of Complex Water Projects: Application to the West Delta Water Conservation and Irrigation Rehabilitation Project, Egypt


Effective sharing mechanisms of joint costs among beneficiaries of a project are a fundamental requirement for the sustainability of the project. Projects that are heterogeneous both in terms of the landscape of the area under development or the participants (users) lead to a more complicated set of allocation mechanisms than homogeneous projects. The analysis presented in this paper uses cooperative game theory to develop schemes for sharing costs and revenues from a project involving various beneficiaries in an equitable and fair way. The proposed approach is applied to the West Delta irrigation project. It sketches a differential two-part tariff that reproduces the allocation of total project costs using the Shapley Value, a well-known cooperative game allocation solution. The proposed differential tariff, applied to each land section in the project reflecting their landscape-related costs, contrasts the unified tariff that was proposed using the traditional methods in the project planning documents.

Games, Vol. 7, Pages 17: Vertical Relationships within Platform Marketplaces


In two-sided markets a platform allows consumers and sellers to interact by creating sub-markets within the platform marketplace. For example, Amazon has sub-markets for all of the different product categories available on its site, and smartphones have sub-markets for different types of applications (gaming apps, weather apps, map apps, ridesharing apps, etc.). The network benefits between consumers and sellers depend on the mode of competition within the sub-markets: more competition between sellers lowers product prices, increases the surplus consumers receive from a sub-market, and makes platform membership more desirable for consumers. However, more competition also lowers profits for a seller which makes platform membership less desirable for a seller and reduces seller entry and the number of sub-markets available on the platform marketplace. This dynamic between seller competition within a sub-market and agents’ network benefits leads to platform pricing strategies, participation decisions by consumers and sellers, and welfare results that depend on the mode of competition. Thus, the sub-market structure is important when investigating platform marketplaces.

Games, Vol. 7, Pages 16: Can We Predict the Winner in a Market with Network Effects? Competition in Cryptocurrency Market


We analyze how network effects affect competition in the nascent cryptocurrency market. We do so by examining early dynamics of exchange rates among different cryptocurrencies. While Bitcoin essentially dominates this market, our data suggest no evidence of a winner-take-all effect early in the market. Indeed, for a relatively long period, a few other cryptocurrencies competing with Bitcoin (the early industry leader) appreciated much more quickly than Bitcoin. The data in this period are consistent with the use of cryptocurrencies as financial assets (popularized by Bitcoin), and not consistent with winner-take-all dynamics. Toward the end of our sample, however, things change dramatically. Bitcoin appreciates against the USD, while other currencies depreciate against the USD. The data in this period are consistent with strong network effects and winner-take-all dynamics. This trend continues at the time of writing.

Games, Vol. 7, Pages 15: Keeping Pace with Criminals: An Extended Study of Designing Patrol Allocation against Adaptive Opportunistic Criminals


Game theoretic approaches have recently been used to model the deterrence effect of patrol officers’ assignments on opportunistic crimes in urban areas. One major challenge in this domain is modeling the behavior of opportunistic criminals. Compared to strategic attackers (such as terrorists) who execute a well-laid out plan, opportunistic criminals are less strategic in planning attacks and more flexible in executing well-laid plans based on their knowledge of patrol officers’ assignments. In this paper, we aim to design an optimal police patrolling strategy against opportunistic criminals in urban areas. Our approach is comprised by two major parts: learning a model of the opportunistic criminal (and how he or she responds to patrols) and then planning optimal patrols against this learned model. The planning part, by using information about how criminals responds to patrols, takes into account the strategic game interaction between the police and criminals. In more detail, first, we propose two categories of models for modeling opportunistic crimes. The first category of models learns the relationship between defender strategy and crime distribution as a Markov chain. The second category of models represents the interaction of criminals and patrol officers as a Dynamic Bayesian Network (DBN) with the number of criminals as the unobserved hidden states. To this end, we: (i) apply standard algorithms, such as Expectation Maximization (EM), to learn the parameters of the DB[...]

Games, Vol. 7, Pages 14: Ergodic Inequality


Weak conditions are provided under which society’s long-run distribution of wealth is independent of initial asset holdings.

Games, Vol. 7, Pages 13: The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence


We investigate the role of framing, inequity in initial endowments and history in shaping behavior in a corrupt transaction by extending the one-shot bribery game introduced by Cameron et al. (2009) to a repeated game setting. We find that the use of loaded language significantly reduces the incidence of bribery and increases the level of punishment. Punishment of bribery leads to reduced bribery in future. The evidence suggests that this game captures essential features of a corrupt transaction, over and above any sentiments of inequity aversion or negative reciprocity However, showing subjects the history of past play has little effect on the level of corruption.

Games, Vol. 7, Pages 12: Time-Preference Heterogeneity and Multiplicity of Equilibria in Two-Group Bargaining


We consider a multilateral bargaining game in which the agents can be classified into two groups according to their instantaneous preferences. In one of these groups there is one agent with a different discount factor. We analyze how this time-preference heterogeneity may generate multiplicity of equilibria. When such an agent is sufficiently more patient than the rest, there is an equilibrium in which her group-mates make the same proposal as the members of the other group. Thus, in heterogeneous groups the presence of more patient members may reduce the utility of its members.

Games, Vol. 7, Pages 11: Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games


Social motives are frequently used to explain deviations from selfishness in non-strategic settings such as the Dictator Game. Previous research has mainly focused on two-player games; the workings of social motives in multiplayer Dictator Games are less well understood. A core feature of multiplayer games is that players can consider inequalities between others, in addition to outcomes that have two-player analogues, such as social efficiency and the inequality between self and others. We expect that existing models of social motives can be improved if players are allowed to consider the inequality between others. Results from two laboratory experiments confirm this: motives for the inequality between others were found, and these motives could not be reduced to motives with dyadic analogues. Explorative analyses show that our findings are robust to a number of potential misspecifications: motives for the inequality between others were also found when utility included non-linear evaluations of inequality, and when alternative types of self-other comparison mechanisms were modeled. Thus, to adequately capture social motives in multiplayer games, models should account for the complexities of the multiplayer setting. We speculate that our findings also hold for strategic games; but further research is needed to elucidate this.