http://www.mdpi.com/journal/games Latest open access articles published in Games at http://www.mdpi.com/journal/games http://www.mdpi.com/2073-4336/4/2/182 William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games. Games 2013-05-06 4 2 Article 10.3390/g4020182 182 199 2073-4336 2013-05-06 doi: 10.3390/g4020182 Bin Wu Arne Traulsen Chaitanya Gokhale http://www.mdpi.com/2073-4336/4/2/163 Costly signaling is a mechanism through which the honesty of signals can be secured in equilibrium, even in interactions where communicators have conflicting interests. This paper explores the dynamics of one such signaling game: Spence’s model of education. It is found that separating equilibria are unlikely to emerge under either the replicator or best response dynamics, but that partially communicative mixed equilibria are quite important dynamically. These mixtures are Lyapunov stable in the replicator dynamic and asymptotically stable in the best response dynamic. Moreover, they have large basins of attraction, in fact larger than those of either pooling or separating equilibria. This suggests that these mixtures may play significant, and underappreciated, roles in the explanation of the emergence and stability of information transfer. Games 2013-04-26 4 2 Article 10.3390/g4020163 163 181 2073-4336 2013-04-26 doi: 10.3390/g4020163 Elliott Wagner http://www.mdpi.com/2073-4336/4/2/144 In repeated public good experiments, reciprocity helps to sustain high levels of cooperation. Can this be achieved by location choices in addition to making contributions? It is more realistic to rely on an intuitive neighborhood model for community members who interact repeatedly. In our experiments, participants can locate their contribution, yielding a small benefit for the participant, who receives the contribution and a small disadvantage for the participant, at the opposite location. This mechanism of individually targeted sanctions helps to foster initial cooperation. It decreases over time, however. Location choices are used to reciprocate, but may not suffice to stabilize voluntary cooperation as an effect observed in the field. Games 2013-04-26 4 2 Article 10.3390/g4020144 144 162 2073-4336 2013-04-26 doi: 10.3390/g4020144 Siegfried Berninghaus Werner Güth Stephan Schosser http://www.mdpi.com/2073-4336/4/1/125 Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP. Games 2013-03-20 4 1 Article 10.3390/g4010125 125 143 2073-4336 2013-03-20 doi: 10.3390/g4010125 Wei Yang Youyi Feng Baichun Xiao http://www.mdpi.com/2073-4336/4/1/106 In this paper, we use a two-period one-to-one matching model with incomplete information to examine the effect of changes in divorce costs on marital dissolution. Each individual who has a nontransferable expected utility about the quality of each potential marriage decides whether to marry or to remain single at the beginning of the first period. Individuals married in the first period learn the qualities of their marriages at the beginning of the second period and then decide whether to stay married or to unilaterally divorce. We show that, for any society, there exist matching environments where the probability of the marital dissolution does not reduce divorce costs under gender-optimal matching rules. In such environments, an allocation effect of divorce costs with an ambiguous sign outweighs an incentive effect that is always negative. We also show that these results may also arise under stable matching rules that are not gender optimal. Games 2013-03-20 4 1 Article 10.3390/g4010106 106 124 2073-4336 2013-03-20 doi: 10.3390/g4010106 Ismail Saglam http://www.mdpi.com/2073-4336/4/1/89 We examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the marginal per capita return (MPCR), i.e. the return to each participant from each dollar that is contributed, is held constant. Moreover, the efficiency gains from the punishment mechanism are significantly higher in the 40-participant than in the four-participant treatment. This is true despite the coordination problems inherent in an institution relying on decentralized individual punishment decisions in the context of a larger group. It reflects increased per capita expenditures on punishment that offset the greater coordination difficulties in the larger group. However, if the marginal group return (MGR), i.e. the return to the entire group of participants, stays constant, resulting in an MPCR that shrinks with group size, no such offset occurs and punishment loses much but not all of its effectiveness at encouraging voluntary contributions to a public good. Efficiency is not significantly different from the small-group treatment. Games 2013-02-19 4 1 Article 10.3390/g4010089 89 105 2073-4336 2013-02-19 doi: 10.3390/g4010089 Bin Xu C. Cadsby Liangcong Fan Fei Song http://www.mdpi.com/2073-4336/4/1/66 This study investigates the relationship between an actor’s beliefs about others’ other-regarding (social) preferences and her own other-regarding preferences, using an “avant-garde” hierarchical Bayesian method. We estimate two distributional other-regarding preference parameters, α and β, of actors using incentivized choice data in binary Dictator Games. Simultaneously, we estimate the distribution of actors’ beliefs about others α and β, conditional on actors’ own α and β, with incentivized belief elicitation. We demonstrate the benefits of the Bayesian method compared to it’s hierarchical frequentist counterparts. Results show a positive association between an actor’s own (α; β ) and her beliefs about average(α; β) in the population. The association between own preferences and the variance in beliefs about others’ preferences in the population, however, is curvilinear for α and insignificant for β. These results are partially consistent with the cone effect [1,2] which is described in detail below. Because in the Bayesian-Nash equilibrium concept, beliefs and own preferences are assumed to be independent, these results cast doubt on the application of the Bayesian-Nash equilibrium concept to experimental data. Games 2013-02-19 4 1 Article 10.3390/g4010066 66 88 2073-4336 2013-02-19 doi: 10.3390/g4010066 Ozan Aksoy Jeroen Weesie http://www.mdpi.com/2073-4336/4/1/50 This paper departs from the standard profit-maximizing model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards their competitors. A reciprocal firm responds to unkind behavior of rivals with unkind actions (negative reciprocity), while at the same time, it responds to kind behavior of rivals with kind actions (positive reciprocity). We find that collusion is easier to sustain when firms have a concern for reciprocity towards competing firms provided that they consider collusive prices to be kind and punishment prices to be unkind. Thus, reciprocity concerns among firms can have adverse welfare consequences for consumers. Games 2013-02-07 4 1 Article 10.3390/g4010050 50 65 2073-4336 2013-02-07 doi: 10.3390/g4010050 Doruk İriş Luís Santos-Pinto http://www.mdpi.com/2073-4336/4/1/38 In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable. Games 2013-01-30 4 1 Article 10.3390/g4010038 38 49 2073-4336 2013-01-30 doi: 10.3390/g4010038 Ahmed Doghmi http://www.mdpi.com/2073-4336/4/1/21 In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, ex-post, the equilibrium allocation is still efficient but may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully—i.e., the mechanism is ex-ante fair. Games 2013-01-18 4 1 Article 10.3390/g4010021 21 37 2073-4336 2013-01-18 doi: 10.3390/g4010021 Matt Van Essen http://www.mdpi.com/2073-4336/4/1/1 The finitely repeated Prisoners’ Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A game-theoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicator-mutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The ”Convincer” strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the ”Follower” strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicator-mutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate. Games 2013-01-04 4 1 Article 10.3390/g4010001 1 20 2073-4336 2013-01-04 doi: 10.3390/g4010001 Kristian Lindgren Vilhelm Verendel http://www.mdpi.com/2073-4336/3/4/150 We numerically solve the classical "Game of Pure Strategy" using linear programming. We notice an intricate even-odd behaviour in the results of our computations that seems to encourage odd or maximal bids. Games 2012-11-08 3 4 Article 10.3390/g3040150 150 156 2073-4336 2012-11-08 doi: 10.3390/g3040150 Glenn C. Rhoads Laurent Bartholdi http://www.mdpi.com/2073-4336/3/4/138 We expand upon the previous models of inequity aversion of Fehr and Schmidt [1], and Frohlich et al. [2], which assume that dictators get disutility if the final allocation of surplus deviates from the equal split (egalitarian principle) or from the subjects' production (libertarian principle). In our model, dictators may also account for the way in which the surplus was generated. More precisely, our model incorporates the idea of liberal egalitarian ethics into the analysis, making it possible for dictators to divide the surplus according to the accountability principle, which states that subjects should only be rewarded for factors under their control. This fairness ideal does not hold subjects responsible for factors beyond their control in the production of the surplus, an idea that is absent in the models of inequity aversion cited above (JEL Codes: D3, D6, D63). Games 2012-10-23 3 4 Letter 10.3390/g3040138 138 149 2073-4336 2012-10-23 doi: 10.3390/g3040138 Ismael Rodriguez-Lara Luis Moreno-Garrido http://www.mdpi.com/2073-4336/3/3/119 Two deviations of alternating-offer bargaining behavior from economic theory are observed together, yet have been studied separately. Players who could secure themselves a large surplus share if bargainers were purely self-interested incompletely exploit their advantage. Delay in agreement occurs even if all experimentally controlled information is common knowledge. This paper rationalizes both regularities coherently by modeling heterogeneous social preferences, either self-interest or envy, of one bargaining party as private information in a three period game of bargaining and preference screening and signaling. Games 2012-09-13 3 3 Article 10.3390/g3030119 119 137 2073-4336 2012-09-13 doi: 10.3390/g3030119 Stefan Kohler http://www.mdpi.com/2073-4336/3/2/97 The Type Indeterminacy model is a theoretical framework that uses some elements of quantum formalism to model the constructive preference perspective suggested by Kahneman and Tversky. In a dynamic decision context, type indeterminacy induces a game with multiple selves associated with a state transition process. We define a Markov perfect equilibrium among the selves with individual identity (preferences) as the state variable. The approach allows to characterize generic personality types and derive some comparative static results. Games 2012-05-15 3 2 Article 10.3390/g3020097 97 118 2073-4336 2012-05-15 doi: 10.3390/g3020097 Ariane Lambert-Mogiliansky Jerome Busemeyer http://www.mdpi.com/2073-4336/3/2/78 The literature on social norms has often stressed that social disapproval is crucial to foster compliance with norms and promote fair and cooperative behavior. With this in mind, we explore the disapproval of allocation decisions using experimental data from five dictator games with a feedback stage. Our data suggests that subjects are heterogeneous in their disapproval patterns, distinguishing two main groups: (1) Subjects who only disapprove choices that harm them, and (2) subjects who disapprove socially inefficient choices. Games 2012-04-23 3 2 Article 10.3390/g3020078 78 96 2073-4336 2012-04-23 doi: 10.3390/g3020078 Raúl López-Pérez Marc Vorsatz http://www.mdpi.com/2073-4336/3/1/56 This paper investigates how the introduction of social preferences affects players’ equilibrium behavior in both the one-shot and the infinitely repeated version of the Prisoner’s Dilemma game. We show that fairness concerns operate as a ”substitute” for time discounting in the infinitely repeated game, as fairness helps sustain cooperation for lower discount factors. In addition, such cooperation can be supported under larger parameter values if players are informed about each others’ social preferences than if they are uninformed. Finally, our results help to identify conditions under which cooperative behavior observed in recent experimental repeated games can be rationalized using time preferences alone (patience) or a combination of time and social preferences (fairness). Games 2012-03-21 3 1 Article 10.3390/g3010056 56 77 2073-4336 2012-03-21 doi: 10.3390/g3010056 John Duffy Félix Muñoz-García http://www.mdpi.com/2073-4336/3/1/41 Players in economic situations often have preferences not only over their own outcome but also over what happens to fellow players, entirely apart from any strategic considerations. While this can be modeled directly by simply writing down final preferences, these are commonly unknown a priori. In many cases it is therefore both helpful and instructive to explicitly model these interactions. This paper presents a simple structure in the context of game theory, building on a model due to Bergstrom, that incorporates these ‘synergisms’ between players. It is powerful enough to cover a wide range of such interactions and model many disparate experimental and empirical results, yet straightforward enough to be used in many applied situations where altruism, or a baser motive, is implied. Games 2012-03-15 3 1 Article 10.3390/g3010041 41 55 2073-4336 2012-03-15 doi: 10.3390/g3010041 Julian Jamison http://www.mdpi.com/2073-4336/3/1/30 In a recent paper, we analyzed the self-assembly of a complex cooperation network. The network was shown to approach a state where every agent invests the same amount of resources. Nevertheless, highly-connected agents arise that extract extraordinarily high payoffs while contributing comparably little to any of their cooperations. Here, we investigate a variant of the model, in which highly-connected agents have access to additional resources. We study analytically and numerically whether these resources are invested in existing collaborations, leading to a fairer load distribution, or in establishing new collaborations, leading to an even less fair distribution of loads and payoffs. Games 2012-03-05 3 1 Article 10.3390/g3010030 30 40 2073-4336 2012-03-05 doi: 10.3390/g3010030 Anne-Ly Do Lars Rudolf Thilo Gross http://www.mdpi.com/2073-4336/3/1/1 This paper addresses the role of affect and emotions in shaping the behavior of responders in the ultimatum game. A huge amount of research shows that players do not behave in an economically rational way in the ultimatum game, and emotional mechanisms have been proposed as a possible explanation. In particular, feelings of fairness, anger and envy are likely candidates as affective determinants. We introduce a three-player ultimatum game with three-options, which permits the responder to either penalize the proposer or to penalize a third party by rejecting offers. This allows for partially distinguishing rejections due to a retaliation motive driven by anger towards the proposer from rejections due to inequity aversion driven by feelings of envy towards a third party. Results from two experiments suggest that responders experience feelings of dissatisfaction and unfairness if their share is small in comparison to the proposer’s share; anger, then, may trigger rejections towards the proposer. Responders also experience dissatisfaction and envy when third party shares exceed their own shares; however, in contrast to anger, envy does not trigger rejections and is dissociated from the decision to accept or reject an offer. We conclude that acting upon anger is socially acceptable, whereas envy is not acceptable as a reason for action. Furthermore, we find that responders generally feel better after rejections, suggesting that rejections serve to regulate one’s affective state. Games 2012-02-13 3 1 Article 10.3390/g3010001 1 29 2073-4336 2012-02-13 doi: 10.3390/g3010001 Hans-Rüdiger Pfister Gisela Böhm http://www.mdpi.com/2073-4336/2/4/463 Games has received help from many individuals since its inaugural issue in 2009. We are especially grateful to the following 146 referees for their great support of Games during the past two years. Games 2011-12-20 2 4 Editorial 10.3390/g2040463 463 464 2073-4336 2011-12-20 doi: 10.3390/g2040463 Games Editorial Office http://www.mdpi.com/2073-4336/2/4/452 This article explains the emergence of an unique equilibrium resolution as the result of a compromise between two selves with different preferences. The stronger this difference is, the more generous the resolution gets. This result is in contrast to predictions of other models in which sinful consumption is distributed bimodally. Therefore, our result fits better with our daily observations concerning a lot of ambivalent goods where we often form nonrigid resolutions. The normative analysis uses the device of a hypothetical impartial self that regards both conflicting motives as equally legitimate. The result of this analysis is dilemmatic. It demonstrates that the resolution is broken too often to be welfare maximal. However, the introduction of external self-commitment devices results in their overuse and is welfare decreasing. Games 2011-12-09 2 4 Article 10.3390/g2040452 452 462 2073-4336 2011-12-09 doi: 10.3390/g2040452 Dimitri Migrow Matthias Uhl http://www.mdpi.com/2073-4336/2/4/434 This paper provides experimental evidence on how players predict end-game effects in a linear public good game. Our regression analysis yields a measure of the relative importance of priors and signals on subjects’ beliefs on contributions and allows us to conclude that, first, the weight of the signal is relatively unimportant, while priors have a large weight and, second, priors are the same for all periods. Hence, subjects do not expect end-game effects and there is very little updating of beliefs. We argue that the sustainability of cooperation is related to this pattern of belief formation. Games 2011-11-21 2 4 Article 10.3390/g2040434 434 451 2073-4336 2011-11-21 doi: 10.3390/g2040434 Pablo Brañas-Garza Maria Paz Espinosa http://www.mdpi.com/2073-4336/2/4/412 This paper reports an experiment evaluating the effect of gift giving on building trust. We have nested our explorations in the standard version of the investment game. Our gift treatment includes a dictator stage in which the trustee decides whether to give a gift to the trustor before both of them proceed to play the investment game. We observe that in such case the majority of trustees offer their endowment to trustors. Consequently, receiving a gift significantly increases the amounts sent by trustors when controlling for the differences in payoffs created by it. Trustees are, however, not better off by giving a gift as the increase in the amount sent by trustors is not large enough to offset the trustees’ loss associated with the cost of giving a gift. Games 2011-09-27 2 4 Article 10.3390/g2040412 412 433 2073-4336 2011-09-27 doi: 10.3390/g2040412 Maroš Servátka Steven Tucker Radovan Vadovič http://www.mdpi.com/2073-4336/2/3/365 The paper presents a complete information model of bidding in second price sealed-bid and ascending-bid (English) auctions, in which potential buyers know the unit valuation of other bidders and may spitefully prefer that their rivals earn a lower surplus. Bidders with spiteful preferences should overbid in equilibrium when they know their rival has a higher value than their own, and bidders with a higher value underbid to reciprocate the spiteful overbidding of the lower value bidders. The model also predicts different bidding behavior in second price as compared to ascending-bid auctions. The paper also presents experimental evidence broadly consistent with the model. In the complete information environment, lower value bidders overbid more than higher value bidders, and they overbid more frequently in the second price auction than in the ascending price auction. Overall, the lower value bidder submits bids that exceed value about half the time. These patterns are not found in the incomplete information environment, consistent with the model. Games 2011-09-16 2 3 Article 10.3390/g2030365 365 411 2073-4336 2011-09-16 doi: 10.3390/g2030365 Naoko Nishimura Timothy N. Cason Tatsuyoshi Saijo Yoshikazu Ikeda http://www.mdpi.com/2073-4336/2/3/355 The replicator-mutator dynamics is a set of differential equations frequently used in biological and socioeconomic contexts to model evolutionary processes subject to mutation, error or experimentation. The replicator-mutator dynamics generalizes the widely used replicator dynamics, which appears in this framework as the extreme case where replication is perfectly precise. This paper studies the influence of strictly dominated strategies on the location of the rest points of the replicator-mutator dynamics, at the limit where the mutation terms become arbitrarily small. It can be proved that such limit rest points for small mutation are Nash equilibria, so strictly dominated strategies do not occur at limit stationary points. However, we show through a simple case how strictly dominated strategies can have an influence on the location of the limit rest points for small mutation. Consequently, the characterization of the limit rest points of the replicator-mutator dynamics cannot in general proceed safely by readily eliminating strictly dominated strategies. Games 2011-09-14 2 3 Article 10.3390/g2030355 355 364 2073-4336 2011-09-14 doi: 10.3390/g2030355 Segismundo S. Izquierdo Luis R. Izquierdo http://www.mdpi.com/2073-4336/2/3/333 We report experimental results on the minority of three-game, where three players choose one of two alternatives and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non-strict and payoff-asymmetric and a unique symmetric mixed strategy equilibrium in which each player’s behavior is based on the toss of a fair coin. This straightforward behavior is predicted by equilibrium selection, impulse-balance equilibrium, and payoff-sampling equilibrium. Experimental participants rely on various decision rules, and only a quarter of them perfectly randomize. Games 2011-09-09 2 3 Article 10.3390/g2030333 333 354 2073-4336 2011-09-09 doi: 10.3390/g2030333 Thorsten Chmura Werner Güth http://www.mdpi.com/2073-4336/2/3/302 We study network formation with n players and link cost α > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player ν incorporates the expected number of players to which ν will become disconnected. We focus on unilateral link formation and Nash equilibrium. We show existence of Nash equilibria and a price of stability of 1 + ο(1) under moderate assumptions on the adversary and n ≥ 9. We prove bounds on the price of anarchy for two special adversaries: one removes a link chosen uniformly at random, while the other removes a link that causes a maximum number of player pairs to be separated. We show an Ο(1) bound on the price of anarchy for both adversaries, the constant being bounded by 15 + ο(1) and 9 + ο(1), respectively. Games 2011-08-23 2 3 Article 10.3390/g2030302 302 332 2073-4336 2011-08-23 doi: 10.3390/g2030302 Lasse Kliemann http://www.mdpi.com/2073-4336/2/3/277 We present a model where each of two players chooses between remuneration based on either private or team effort. Although at least one of the players has the equilibrium strategy to choose private remuneration, we frequently observe both players to choose team remuneration in a series of laboratory experiments. This allows for high cooperation payoffs but also provides individual free-riding incentives. Due to significant cooperation, we observe that, in team remuneration, participants make higher profits than in private remuneration. We also observe that, when participants are not given the option of private remuneration, they cooperate significantly less. Games 2011-08-19 2 3 Article 10.3390/g2030277 277 301 2073-4336 2011-08-19 doi: 10.3390/g2030277 Claudia Keser Claude Montmarquette http://www.mdpi.com/2073-4336/2/3/257 Two independent, but related, choice prediction competitions are organized that focus on behavior in simple two-person extensive form games (http://sites.google.com/site/extformpredcomp/): one focuses on predicting the choices of the first mover and the other on predicting the choices of the second mover. The competitions are based on an estimation experiment and a competition experiment. The two experiments use the same methods and subject pool, and examine games randomly selected from the same distribution. The current introductory paper presents the results of the estimation experiment, and clarifies the descriptive value of some baseline models. The best baseline model assumes that each choice is made based on one of several rules. The rules include: rational choice, level-1 reasoning, an attempt to maximize joint payoff, and an attempt to increase fairness. The probability of using the different rules is assumed to be stable over games. The estimated parameters imply that the most popular rule is rational choice; it is used in about half the cases. To participate in the competitions, researchers are asked to email the organizers models (implemented in computer programs) that read the incentive structure as input, and derive the predicted behavior as an output. The submission deadline is 1 December 2011, the results of the competition experiment will not be revealed until that date. The submitted models will be ranked based on their prediction error. The winners of the competitions will be invited to write a paper that describes their model. Games 2011-07-25 2 3 Article 10.3390/g2030257 257 276 2073-4336 2011-07-25 doi: 10.3390/g2030257 Eyal Ert Ido Erev Alvin E. Roth http://www.mdpi.com/2073-4336/2/3/235 We prove the existence of a trembling-hand perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games. Games 2011-07-15 2 3 Article 10.3390/g2030235 235 256 2073-4336 2011-07-15 doi: 10.3390/g2030235 Oriol Carbonell-Nicolau http://www.mdpi.com/2073-4336/2/2/209 We characterize the structure of Nash equilibria for a certain class of asset market games. In equilibrium, different assets have different returns, and (risk neutral) investors with different wealth hold portfolios with different structures. In equilibrium, an asset’s return is inversely related to the elasticity of its supply. The larger an investor, the more diversified is his portfolio. Smaller investors do not hold all the assets, but achieve higher percentage returns. More generally, our results can be applied also to other “multi-market games” in which several players compete in several arenas simultaneously, like multi-market Cournot oligopolies, or multiple rent-seeking games. Games 2011-04-12 2 2 Article 10.3390/g2020209 209 234 2073-4336 2011-04-12 doi: 10.3390/g2020209 Manfred Nermuth http://www.mdpi.com/2073-4336/2/2/200 We submitted three models to the competition which were based on the I-SAW model. The models introduced four new assumptions. In the first model an adjustment process was introduced through which the tendency for exploration was higher at the beginning and decreased over time in the exploration stage. Another new assumption was that surprise as a factor influencing the weight of a trial in the sampling procedure was added. In the second model we added the possibility of an exclusion of unreliable experiences gained in the early trials of a game and the possibility of a revision of a reasonable alternative which was responsible for a very bad outcome in the previous trial. Three of the four added assumptions were combined in the third model. Because each of our models contains at least two new assumptions, we estimated the relative effect of each assumption on the estimation and prediction scores and carried out a test of robustness. In this way, we were able to clarify the usefulness of each added assumption. Games 2011-04-12 2 2 Commentary 10.3390/g2020200 200 208 2073-4336 2011-04-12 doi: 10.3390/g2020200 Wasilios Hariskos Johannes Leder Kinneret Teodorescu http://www.mdpi.com/2073-4336/2/1/187 This paper describes the “Bounded Memory, Inertia, Sampling and Weighting” (BI-SAW) model, which won the http://sites.google.com/site/gpredcomp/Market Entry Prediction Competition in 2010. The BI-SAW model refines the I-SAW Model (Erev et al. [1]) by adding the assumption of limited memory span. In particular, we assume when players draw a small sample to weight against the average payoff of all past experience, they can only recall 6 trials of past experience. On the other hand, we keep all other key features of the I-SAW model: (1) Reliance on a small sample of past experiences, (2) Strong inertia and recency effects, and (3) Surprise triggers change. We estimate this model using the first set of experimental results run by the competition organizers, and use it to predict results of a second set of similar experiments later ran by the organizers. We find significant improvement in out-of-sample predictability (against the I-SAW model) in terms of smaller mean normalized MSD, and such result is robust to resampling the predicted game set and reversing the role of the sets of experimental results. Our model’s performance is the best among all the participants. Games 2011-03-21 2 1 Article 10.3390/g2010187 187 199 2073-4336 2011-03-21 doi: 10.3390/g2010187 Wei Chen Shu-Yu Liu Chih-Han Chen Yi-Shan Lee http://www.mdpi.com/2073-4336/2/1/163 We consider a market for lemons in which the seller is a monopolistic price setter and the buyer receives a private noisy signal of the product’s quality. We model this as a game and analyze perfect Bayesian equilibrium prices, trading probabilities and gains of trade. In particular, we vary the buyer’s signal precision, from being completely uninformative, as in standard models of lemons markets, to being perfectly informative. We show that high quality units are sold with positive probability even in the limit of uninformative signals, and we identify some discontinuities in the equilibrium predictions at the boundaries of completely uninformative and completely informative signals, respectively. Games 2011-03-18 2 1 Article 10.3390/g2010163 163 186 2073-4336 2011-03-18 doi: 10.3390/g2010163 Mark Voorneveld Jörgen W. Weibull http://www.mdpi.com/2073-4336/2/1/136 This paper presents a case of parsimony and generalization in model comparisons. We submitted two versions of the same cognitive model to the Market Entry Competition (MEC), which involved four-person and two-alternative (enter or stay out) games. Our model was designed according to the Instance-Based Learning Theory (IBLT). The two versions of the model assumed the same cognitive principles of decision making and learning in the MEC. The only difference between the two models was the assumption of homogeneity among the four participants: one model assumed homogeneous participants (IBL-same) while the other model assumed heterogeneous participants (IBL-different). The IBL-same model involved three free parameters in total while the IBL-different involved 12 free parameters, i.e., three free parameters for each of the four participants. The IBL-different model outperformed the IBL-same model in the competition, but after exposing the models to a more challenging generalization test (the Technion Prediction Tournament), the IBL-same model outperformed the IBL-different model. Thus, a loser can be a winner depending on the generalization conditions used to compare models. We describe the models and the process by which we reach these conclusions. Games 2011-03-16 2 1 Article 10.3390/g2010136 136 162 2073-4336 2011-03-16 doi: 10.3390/g2010136 Cleotilde Gonzalez Varun Dutt Tomás Lejarraga http://www.mdpi.com/2073-4336/2/1/114 We investigate to what extent genuine social preferences can explain observed other-regarding behavior. In a dictator game variant subjects can choose whether to learn about the consequences of their choice for the receiver. We find that a majority of subjects showing other-regarding behavior when the payoffs of the receiver are known, choose to ignore these consequences if possible. This behavior is inconsistent with preferences about outcomes. Other-regarding behavior may also be explained by avoiding cognitive dissonance as in Konow (2000). Our experiment’s choice data is in line with this approach. In addition, we successfully relate individual behavior to proxies for cognitive dissonance. Games 2011-02-18 2 1 Article 10.3390/g2010114 114 135 2073-4336 2011-02-18 doi: 10.3390/g2010114 Astrid Matthey Tobias Regner http://www.mdpi.com/2073-4336/2/1/87 A new model of strategic networking is developed and analyzed, where an agent’s investment in links is nonspecific. The model comprises a large class of games which are both potential and super- or submodular games. We obtain comparative statics results for Nash equilibria with respect to investment costs for supermodular as well as submodular networking games. We also study supermodular games with potentials. We find that the set of potential maximizers forms a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest potential maximizer. Finally, we provide a broad spectrum of applications from social interaction to industrial organization. Games 2011-02-17 2 1 Article 10.3390/g2010087 87 113 2073-4336 2011-02-17 doi: 10.3390/g2010087 Jacques Durieu Hans Haller Philippe Solal http://www.mdpi.com/2073-4336/2/1/52 Logic and game theory have had a few decades of contacts by now, with the classical results of epistemic game theory as major high-lights. In this paper, we emphasize a recent new perspective toward “logical dynamics”, designing logical systems that focus on the actions that change information, preference, and other driving forces of agency. We show how this dynamic turn works out for games, drawing on some recent advances in the literature. Our key examples are the long-term dynamics of information exchange, as well as the much-discussed issue of extensive game rationality. Our paper also proposes a new broader interpretation of what is happening here. The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, and we are witnessing the birth of something new which is not just logic, nor just game theory, but rather a Theory of Play. Games 2011-02-16 2 1 Article 10.3390/g2010052 52 86 2073-4336 2011-02-16 doi: 10.3390/g2010052 Johan Van Benthem Eric Pacuit Olivier Roy http://www.mdpi.com/2073-4336/2/1/21 The Intergroup Prisoner’s Dilemma with Intragroup Power Dynamics (IPD^2) is a new game paradigm for studying human behavior in conflict situations. IPD^2 adds the concept of intragroup power to an intergroup version of the standard Repeated Prisoner’s Dilemma game. We conducted a laboratory study in which individual human participants played the game against computer strategies of various complexities. The results show that participants tend to cooperate more when they have greater power status within their groups. IPD^2 yields increasing levels of mutual cooperation and decreasing levels of mutual defection, in contrast to a variant of Intergroup Prisoner’s Dilemma without intragroup power dynamics where mutual cooperation and mutual defection are equally likely. We developed a cognitive model of human decision making in this game inspired by the Instance-Based Learning Theory (IBLT) and implemented within the ACT-R cognitive architecture. This model was run in place of a human participant using the same paradigm as the human study. The results from the model show a pattern of behavior similar to that of human data. We conclude with a discussion of the ways in which the IPD^2 paradigm can be applied to studying human behavior in conflict situations. In particular, we present the current study as a possible contribution to corroborating the conjecture that democracy reduces the risk of wars. Games 2011-02-08 2 1 Article 10.3390/g2010021 21 51 2073-4336 2011-02-08 doi: 10.3390/g2010021 Ion Juvina Christian Lebiere Jolie M. Martin Cleotilde Gonzalez http://www.mdpi.com/2073-4336/2/1/16 This note briefly summarizes the consequences of adding correlated individual differences to the best baseline model in the Games competition, I-SAW. I find evidence that the traits of an individual are correlated, but refining I-SAW to capture these correlations does not significantly improve the model’s accuracy when predicting average behavior. Games 2011-02-07 2 1 Short Note 10.3390/g2010016 16 20 2073-4336 2011-02-07 doi: 10.3390/g2010016 Luke Lindsay http://www.mdpi.com/2073-4336/2/1/1 This paper provides a new way to identify conditional cooperation in a real-time version of the standard voluntary contribution mechanism. We define contribution cycles as the number of contributors a player waits for before committing to a further contribution, and use a permutation test on contribution cycles to assign a measure of conditional cooperation to each group play. The validity of the measures is tested in an experiment. We find that roughly 20% of the plays exhibit dynamics of conditional cooperation. Moreover, notwithstanding a decline in contributions, conditional cooperation is found to be stable over time. Games 2011-01-14 2 1 Article 10.3390/g2010001 1 15 2073-4336 2011-01-14 doi: 10.3390/g2010001 M. Vittoria Levati Ro’i Zultan http://www.mdpi.com/2073-4336/1/4/551 We survey the recent literature on coordination games, where there is a conflictbetween risk dominance and payoff dominance. Our main focus is on models of local interactions, where players only interact with small subsets of the overall population rather than with society as a whole. We use Ellison’s [1] Radius-Coradius Theorem to present prominent results on local interactions. Amongst others, we discuss best reply learning in a global- and in a local- interaction framework and best reply learning in multiple location models and in a network formation context. Further, we discuss imitation learning in a localandin a global- interactions setting. Games 2010-11-15 1 4 Article 10.3390/g1040551 551 585 2073-4336 2010-11-15 doi: 10.3390/g1040551 Simon Weidenholzer http://www.mdpi.com/2073-4336/1/4/527 Is mutually beneficial cooperation in trust games more prevalent with private property or common property? Does the strength of property right entitlement affect the answer? Cox, Ostrom, Walker, et al. [1] report little difference between cooperation in private and common property trust games. We assign stronger property right entitlements by requiring subjects to meet a performance quota in a real effort task to earn their endowments. We report experiment treatments with sequential choice and strategy responses. We find that cooperation is lower in common property trust games than in private property trust games, which is an idiosyncratic prediction of revealed altruism theory [2]. Demonstrable differences and similarities between our strategy response and sequential choice data provide insight into the how these protocols can yield different results from hypothesis tests even when they are eliciting the same behavioral patterns across treatments. Games 2010-11-10 1 4 Article 10.3390/g1040527 527 550 2073-4336 2010-11-10 doi: 10.3390/g1040527 James C. Cox Daniel T. Hall http://www.mdpi.com/2073-4336/1/4/478 We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems in the area of interactive epistemology that specify some sufficient epistemic conditions of equilibrium notions such as Nash equilibrium and Iterated Deletion of Strictly Dominated Strategies (IDSDS). Then, we present a variant of the logic extended with dynamic operators of Dynamic Epistemic Logic (DEL). We show that it allows to express the notion IDSDS in a more compact way. The second part of the paper deals with games with weaker forms of complete information. We first discuss several assumptions on different aspects of perfect information about the game structure (e.g., the assumption that a player has perfect knowledge about the players’ strategy sets or about the preference orderings over strategy profiles), and show that every assumption is expressed by a corresponding logical axiom of our logic. Then we provide a proof of Harsanyi’s claim that all uncertainty about the structure of a game can be reduced to uncertainty about payoffs. Sound and complete axiomatizations of the logics are given, as well as some complexity results for the satisfiability problem. Games 2010-11-02 1 4 Article 10.3390/g1040478 478 526 2073-4336 2010-11-02 doi: 10.3390/g1040478 Emiliano Lorini François Schwarzentruber http://www.mdpi.com/2073-4336/1/4/459 We study behavior in a moonlighting game with unequal initial endowments. In this game, predictions for second-mover behavior based on inequality aversion are in contrast to reciprocity. We find that inequality aversion explains only few observations. The comparison to a treatment with equal endowments supports the conclusion that behavior is better captured by intuitive notions of reciprocity than by inequality aversion. Extending the model by allowing for alternative reference points promises better performance, but leads to other problems. We conclude that the fact that inequality aversion often works as a good short-hand for reciprocity is driven by biased design choices. Games 2010-10-21 1 4 Article 10.3390/g1040459 459 477 2073-4336 2010-10-21 doi: 10.3390/g1040459 Dirk Engelmann Martin Strobel http://www.mdpi.com/2073-4336/1/4/422 In this note we introduce different levels of decay in the Goyal, Galeotti and Kamphorst (GGK) insider-outsider model of network formation. First, we deal with situations where the amount of decay is sufficiently low to avoid superfluous connections in strict Nash networks and we examine the architectures of strict Nash networks. We show that centrality and small diameter are robust features of strict Nash networks. Then, we study the Nash and efficient networks when the decay vanishes. Games 2010-10-20 1 4 Article 10.3390/g1040422 422 437 2073-4336 2010-10-20 doi: 10.3390/g1040422 Pascal Billand Christophe Bravard Sudipta Sarangi http://www.mdpi.com/2073-4336/1/4/438 We study social learning in a large population of agents who only observe the actions taken by their neighbours. Agents have to choose one, out of two, reversible actions, each optimal in one, out of two, unknown states of the world. Each agent chooses rationally, on the basis of private information and of the observation of his neighbours’ actions. Agents can repeatedly update their choices at revision opportunities that they receive in a random sequential order. We show that if agents receive equally informative signals and observe both neighbours, then actions converge exponentially fast to a configuration where some agents are permanently wrong. In contrast, if agents are unequally informed (in that some agents receive a perfectly informative signal and others are uninformed) and observe one neighbour only, then everyone will eventually choose the correct action. Convergence, however, obtains very slowly, at rate √t. Games 2010-10-20 1 4 Article 10.3390/g1040438 438 458 2073-4336 2010-10-20 doi: 10.3390/g1040438 Antonio Guarino Antonella Ianni http://www.mdpi.com/2073-4336/1/4/415 We introduce consistency of beliefs in the space of hierarchies of conditional beliefs (Battigalli and Siniscalchi) and use it to provide epistemic conditions for equilibria in finite multi-stage games with observed actions. Games 2010-10-20 1 4 Article 10.3390/g1040415 415 421 2073-4336 2010-10-20 doi: 10.3390/g1040415 Paulo Barelli http://www.mdpi.com/2073-4336/1/4/395 This paper focuses on the dynamic aspects of individual behavior affected by its social embedding, either at large (society-wide norms or averages) or at a local neighborhood. The emphasis is on how initial conditions can affect the long run outcome and to derive, discuss and apply the conditions for such thresholds. For this purpose, intertemporal social pressure (from peers, from norms, or from fashions) is modelled in two different ways: (i) individual benefit is influenced by the possession of a stock (in the application: weight) and the society wide average, and (ii) individual benefits depend on a norm that follows its own motion, of course driven by agents’ behavior. The topical issue of obesity serves as motivation and corresponding models and examples are presented and analyzed. Games 2010-10-13 1 4 Article 10.3390/g1040395 395 414 2073-4336 2010-10-13 doi: 10.3390/g1040395 Franz Wirl Gustav Feichtinger http://www.mdpi.com/2073-4336/1/4/381 It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski’s Fixpoint Theorem. Games 2010-10-08 1 4 Article 10.3390/g1040381 381 394 2073-4336 2010-10-08 doi: 10.3390/g1040381 Krzysztof R. Apt Jonathan A. Zvesper http://www.mdpi.com/2073-4336/1/4/357 If actors want to reach a particular goal, they are often better off forming collaborative relations and investing together rather than investing separately. We study the coordination and cooperation problems that might hinder successful collaboration in a dynamic network setting. We develop an experiment in which coordination problems are mainly due to finding partners for collaboration, while cooperation problems arise at the investment levels of partners who have already agreed to collaborate. The results show that as costs of forming links increase, groups succeed less often in solving the coordination problem. Still, if subjects are able to solve the coordination problem, they invest in a suboptimal way in the network good. It is mostly found that if cooperation is successful in terms of investment, it is due to subjects being able to monitor how much their partners invest. Moreover, subjects deal better with the coordination and cooperation problems as they gain experience. Games 2010-09-28 1 4 Article 10.3390/g1040357 357 380 2073-4336 2010-09-28 doi: 10.3390/g1040357 Antonie Knigge Vincent Buskens http://www.mdpi.com/2073-4336/1/3/338 We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful. Games 2010-09-21 1 3 Article 10.3390/g1030338 338 356 2073-4336 2010-09-21 doi: 10.3390/g1030338 Sylvain Béal Subhadip Chakrabarti Amandine Ghintran Philippe Solal http://www.mdpi.com/2073-4336/1/3/317 Human social networks reshape continuously, as individuals forge new contacts while abandoning existing ones. Simultaneously, individuals adapt their behavior, leading to an intricate interplay been network evolution and behavior evolution. Here, we review a framework, called Active Linking, which allows an analytical treatment of such a co-evolutionary dynamics. Using this framework we showed that an increase in the number of ways of responding to adverse interactions leads an overall increase of cooperation, which is here extended to all two-player social dilemmas. In addition, we discuss the role of the selection pressure in these results. Games 2010-09-17 1 3 Article 10.3390/g1030317 317 337 2073-4336 2010-09-17 doi: 10.3390/g1030317 Sven Van Segbroeck Francisco C. Santos Jorge M. Pacheco Tom Lenaerts http://www.mdpi.com/2073-4336/1/3/299 This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivisibility. We are interested in the classes of games that guarantee a non-empty core no matter what are the admissible values assigned to the parameters defining these programs. We call such classes universally balanced. We present characterization and complexity results on the universally balancedness property for some classes of interesting combinatorial optimization games. In particular, we focus on the algorithmic properties for identifying universally balancedness for the games under discussion. Games 2010-09-13 1 3 Article 10.3390/g1030299 299 316 2073-4336 2010-09-13 doi: 10.3390/g1030299 Gabrielle Demange Xiaotie Deng http://www.mdpi.com/2073-4336/1/3/286 A set of coalition structures P is farsightedly stable (i) if all possible deviations from any coalition structure p belonging to P to a coalition structure outside P are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improvingpath from any coalition structure outside the set leading to some coalition structure in the set, and (iii) if there is no proper subset of P satisfying the first two conditions. A non-empty farsightedly stable set always exists. We provide a characterization of unique farsightedly stable sets of coalition structures and we study the relationship between farsighted stability and other concepts such as the largest consistent set and the von Neumann-Morgenstern farsightedly stable set. Finally, we illustrate our results by means of coalition formation games with positive spillovers. Games 2010-09-02 1 3 Article 10.3390/g1030286 286 298 2073-4336 2010-09-02 doi: 10.3390/g1030286 P. Jean-Jacques Herings Ana Mauleon Vincent Vannetelbosch http://www.mdpi.com/2073-4336/1/3/262 We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time. Games 2010-08-10 1 3 Article 10.3390/g1030262 262 285 2073-4336 2010-08-10 doi: 10.3390/g1030262 Siegfried Berninghaus Hans Haller http://www.mdpi.com/2073-4336/1/3/242 We propose a model in which agents of a population interacting according to a network of contacts play games of coordination with each other and can also dynamically break and redirect links to neighbors if they are unsatisfied. As a result, there is co-evolution of strategies in the population and of the graph that represents the network of contacts. We apply the model to the class of pure and general coordination games. For pure coordination games, the networks co-evolve towards the polarization of different strategies. In the case of general coordination games our results show that the possibility of refusing neighbors and choosing different partners increases the success rate of the Pareto-dominant equilibrium. Games 2010-07-29 1 3 Article 10.3390/g1030242 242 261 2073-4336 2010-07-29 doi: 10.3390/g1030242 Marco Tomassini Enea Pestelacci http://www.mdpi.com/2073-4336/1/3/226 We study the stability of social and economic networks when players are farsighted. We first provide an algorithm that characterizes the unique pairwise and groupwise farsightedly stable set of networks under the componentwise egalitarian allocation rule. We then show that this set coincides with the unique groupwise myopically stable set of networks but not with the unique pairwise myopically stable set of networks. We conclude that, if groupwise deviations are allowed then whether players are farsighted or myopic does not matter; if players are farsighted then whether players are allowed to deviate in pairs only or in groups does not matter. Games 2010-07-22 1 3 Article 10.3390/g1030226 226 241 2073-4336 2010-07-22 doi: 10.3390/g1030226 Gilles Grandjean Ana Mauleon Vincent Vannetelbosch http://www.mdpi.com/2073-4336/1/3/221 Ion Juvina found an error in our manuscript published in Games. [...] Games 2010-07-21 1 3 Correction 10.3390/g1030221 221 225 2073-4336 2010-07-21 doi: 10.3390/g1030221 Ido Erev Eyal Ert Alvin E. Roth http://www.mdpi.com/2073-4336/1/3/189 We study 4 x 4 games for which the best response dynamics contain a cycle. We give examples in which multiple Shapley polygons occur for these kinds of games. We derive conditions under which Shapley polygons exist and conditions for the stability of these polygons. It turns out that there is a very strong connection between the stability of heteroclinic cycles for the replicator equation and Shapley polygons for the best response dynamics. It is also shown that chaotic behaviour can not occur in this kind of game. Games 2010-07-15 1 3 Article 10.3390/g1030189 189 220 2073-4336 2010-07-15 doi: 10.3390/g1030189 Hahn http://www.mdpi.com/2073-4336/1/3/168 In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [2], Battigalli [3], Battigalli and Siniscalchi [4]) as possible representatives for backward induction and forward induction reasoning. We compare both concepts on a conceptual, epistemic and an algorithm level, thereby highlighting some of the crucial differences between backward and forward induction reasoning in dynamic games. Games 2010-07-02 1 3 Article 10.3390/g1030168 168 188 2073-4336 2010-07-02 doi: 10.3390/g1030168 Perea http://www.mdpi.com/2073-4336/1/2/159 We consider three-sided coalition formation problems when each agent is concerned about his local status as measured by his relative rank position within the group of his own type and about his global status as measured by the weighted sum of the average rankings of the other types of groups. We show that a core stable coalition structure always exists, provided that the corresponding weights are balanced and each agent perceives the two types of status as being substitutable. Games 2010-06-25 1 2 Article 10.3390/g1020159 159 167 2073-4336 2010-06-25 doi: 10.3390/g1020159 Lazarova Dimitrov http://www.mdpi.com/2073-4336/1/2/137 The literature on International Environmental Agreements (IEAs) predicts a rather low number of signatories to an IEA. This is in sharp contrast to empirical evidence. As experimental economics provides some evidence for more complex human behavior, extending the theory of IEAs to a broader class of preferences is clearly promising. The present paper shows that where countries’ preferences incorporate justice and fairness there will be a strong incentive for them to choose similar abatement policies within and outside an IEA. Consequently, free-riding at the expense of the signatory states diminishes and participation in an IEA becomes a more successful strategy, so that the size of stable IEAs increases. Games 2010-06-24 1 2 Article 10.3390/g1020137 137 158 2073-4336 2010-06-24 doi: 10.3390/g1020137 Grüning Peters http://www.mdpi.com/2073-4336/1/2/117 A choice prediction competition is organized that focuses on decisions from experience in market entry games (http://sites.google.com/site/gpredcomp/ and http://www.mdpi.com/si/games/predict-behavior/). The competition is based on two experiments: An estimation experiment, and a competition experiment. The two experiments use the same methods and subject pool, and examine games randomly selected from the same distribution. The current introductory paper presents the results of the estimation experiment, and clarifies the descriptive value of several baseline models. The experimental results reveal the robustness of eight behavioral tendencies that were documented in previous studies of market entry games and individual decisions from experience. The best baseline model (I-SAW) assumes reliance on small samples of experiences, and strong inertia when the recent results are not surprising. The competition experiment will be run in May 2010 (after the completion of this introduction), but they will not be revealed until September. To participate in the competition, researchers are asked to E-mail the organizers models (implemented in computer programs) that read the incentive structure as input, and derive the predicted behavior as an output. The submitted models will be ranked based on their prediction error. The winners of the competition will be invited to publish a paper that describes their model. Games 2010-05-14 1 2 Article 10.3390/g1020117 117 136 2073-4336 2010-05-14 doi: 10.3390/g1020117 Erev Ert Roth http://www.mdpi.com/2073-4336/1/2/103 I study the speed of the evolutionary process on small heterogeneous graphs using the Hawk-Dove game. The graphs are based on empirical observation data of grooming interactions in 81 primate groups. Analytic results for the star graph have revealed that irregular graphs can slow down the evolutionary process by increasing the mean time to absorption. Here I show that the same effects can be found for graphs representing natural animal populations which are much less heterogeneous than star graphs. Degree variance has proven to be a good predictor for the mean time to absorption also for these graphs. Games 2010-05-06 1 2 Article 10.3390/g1020103 103 116 2073-4336 2010-05-06 doi: 10.3390/g1020103 Voelkl http://www.mdpi.com/2073-4336/1/2/89 In two-person generosity games, the proposer’s agreement payoff is exogenously given, whereas that of the responder is endogenously determined by the proposer’s choice of the pie size. In three-person generosity games, equal agreement payoffs for two of the players are either exogenously excluded or imposed. We predict that the latter crowds out - or at least weakens - efficiency seeking. Our treatments rely on a 2x3 factorial design, differing in whether the responder or the third (dummy) player is the residual claimant and whether the proposer’s agreement payoff is larger, equal, or smaller than the other exogenously given agreement payoff. Games 2010-04-22 1 2 Article 10.3390/g1020089 89 102 2073-4336 2010-04-22 doi: 10.3390/g1020089 Güth Pull Stadler Stribeck http://www.mdpi.com/2073-4336/1/2/66 We study the recursive core introduced in Huang and Sjöström [8]. In general partition function form games, the recursive core coalition structure may be either coarser or finer than the one that maximizes the social surplus. Moreover, the recursive core structure is typically different from the one predicted by the α-core. We fully implement the recursive core for general games, including non-superadditive games where the grand coalition does not form in equilibrium. We do not put any restrictions, such as stationarity, on strategies. Games 2010-04-15 1 2 Article 10.3390/g1020066 66 88 2073-4336 2010-04-15 doi: 10.3390/g1020066 Huang Sjöström http://www.mdpi.com/2073-4336/1/1/53 Game and decision theory start from rather strong premises. Preferences, represented by utilities, beliefs represented by probabilities, common knowledge and symmetric rationality as background assumptions are treated as “given.” A richer language enabling us to capture the process leading to what is “given” seems superior to the stenography of decision making in terms of utility cum probability. However, similar to traditional rational choice modeling, boundedly rational choice modeling, as outlined here, is far from being a “global” theory with empirical content; rather it serves as a tool to formulate “local” theories with empirical content. Games 2010-03-23 1 1 Article 10.3390/g1010053 53 65 2073-4336 2010-03-23 doi: 10.3390/g1010053 Güth Kliemt http://www.mdpi.com/2073-4336/1/1/34 Experimental and empirical evidence shows that the utility an individual derives from a certain state depends on the reference state she compares it to. According to economic theory, the reference state is determined by past, present and future outcomes of either the individual herself or her reference group. The experiment described in this paper suggests that, in addition, reference states depend to a significant degree on environmental factors not relevant for outcomes. It indicates that reference states - and hence utility - can relatively easily be influenced without changing people’s outcomes, e.g., through priming. Games 2010-03-16 1 1 Article 10.3390/g1010034 34 52 2073-4336 2010-03-16 doi: 10.3390/g1010034 Matthey http://www.mdpi.com/2073-4336/1/1/18 Explaining human cooperation in large groups of non-kin is a major challenge to both rational choice theory and the theory of evolution. Recent research suggests that group cooperation can be explained by positing that cooperators can punish non-cooperators or cheaters. The experimental evidence comes from public goods games in which group members are fully informed about the behavior of all others and cheating occurs in full view. We demonstrate that under more realistic information conditions, where cheating is less obvious, punishment is much less effective in enforcing cooperation. Evidently, the explanatory power of punishment is constrained by the visibility of cheating. Games 2010-03-15 1 1 Article 10.3390/g1010018 18 33 2073-4336 2010-03-15 doi: 10.3390/g1010018 Bornstein Weisel http://www.mdpi.com/2073-4336/1/1/3 We introduce a class of evolutionary game dynamics — pairwise comparison dynamics — under which revising agents choose a candidate strategy at random, switching to it with positive probability if and only if its payoff is higher than the agent’s current strategy. We prove that all such dynamics satisfy Nash stationarity: the set of rest points of these dynamics is always identical to the set of Nash equilibria of the underlying game. We also show how one can modify the replicator dynamic and other imitative dynamics to ensure Nash stationarity without increasing the informational demands placed on the agents. These results provide an interpretation of Nash equilibrium that relies on large numbers arguments and weak requirements on payoff observations rather than on strong equilibrium knowledge assumptions. Games 2009-12-01 1 1 Article 10.3390/g1010003 3 17 2073-4336 2009-12-01 doi: 10.3390/g1010003 William H. Sandholm http://www.mdpi.com/2073-4336/1/1/1 Over the last fifty years, game theory has evolved from a mathematical theory of optimal behaviour in stylized situations (“games”) to a general theory of human behaviour, be it actually observed or normatively desirable. Its scope includes both the mathematical modelling and analysis of competition and conflict and the study of human behaviour in strategic contexts and its determinants. Nowadays, game theory has become the language of economics and is increasingly becoming one of the main methods of analysis in several social sciences. Its theoretical underpinnings can be viewed as a mathematical subdiscipline, while its more behavioural offshoots benefit from cross-fertilization with psychology. Game theory has grown within economics but is, by its very nature, interdisciplinary, to the extent that no game theorist can or should define him or herself in disciplinary terms anymore. [...] Games 2009-09-30 1 1 Editorial 10.3390/g1010001 1 2 2073-4336 2009-09-30 doi: 10.3390/g1010001 Carlos Alós-Ferrer