Games
http://mdpi.com/journal/games
Latest open access articles published in Games at http://mdpi.com/journal/games<![CDATA[Games, Vol. 6, Pages 299-317: Stable Sampling Equilibrium in Common Pool Resource Games]]>
http://mdpi.com/2073-4336/6/3/299
This paper reconsiders evidence from experimental common pool resource games from the perspective of a model of payoff sampling. Despite being parameter-free, the model is able to replicate some striking features of the data, including single-peaked frequency distributions, the persistent use of strictly dominated actionsand stable heterogeneity in choices. These properties can also be accurately replicated using logit quantal response equilibrium (QRE), but only by tuning the free parameter separately for separate games. When the QRE parameter is constrained to be the same across games, sampling equilibrium provides a superior fit to the data. We argue that these findings are likely to generalize to other complex games with multiple players and strategies.Games2015-08-3163Article10.3390/g60302992993172073-43362015-08-31doi: 10.3390/g6030299Juan CárdenasCésar MantillaRajiv Sethi<![CDATA[Games, Vol. 6, Pages 273-298: Bargaining over Strategies of Non-Cooperative Games]]>
http://mdpi.com/2073-4336/6/3/273
We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.Games2015-08-3163Article10.3390/g60302732732982073-43362015-08-31doi: 10.3390/g6030273Giuseppe AttanasiAurora García-GallegoNikolaos GeorgantzísAldo Montesano<![CDATA[Games, Vol. 6, Pages 262-272: Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation]]>
http://mdpi.com/2073-4336/6/3/262
Reciprocal cooperation can be studied in the Centipede game, in which two players alternate in choosing between a cooperative GO move and a non-cooperative STOP move. GO sustains the interaction and increases the player pair’s total payoff while incurring a small personal cost; STOP terminates the interaction with a favorable payoff to the defector. We investigated cooperation in four Centipede games differing in their payoffs at the game’s end (positive versus zero) and payoff difference between players (moderate versus high difference). The games shared the same game-theoretic solution, therefore they should have elicited identical decision patterns, according to orthodox game theory. Nevertheless, both zero-end payoffs and high payoff inequality were found to reduce cooperation significantly. Contrary to previous predictions, combining these two factors in one game resulted in a slight weakening of their independent deterrent effects. These findings show that small changes in the payoff function have large and significant effects on cooperation, and that the effects do not combine synergistically.Games2015-08-1863Article10.3390/g60302622622722073-43362015-08-18doi: 10.3390/g6030262Eva KrockowBriony PulfordAndrew Colman<![CDATA[Games, Vol. 6, Pages 251-261: Unfazed by Both the Bull and Bear: Strategic Exploration in Dynamic Environments]]>
http://mdpi.com/2073-4336/6/3/251
People in a changing environment must decide between exploiting options they currently favor and exploring alternative options that provide additional information about the state of the environment. For example, drivers must decide between purchasing gas at their currently favored station (i.e., exploit) or risk a fruitless trip to another station to evaluate whether the price has been lowered since the last visit. Previous laboratory studies on exploratory choice have found that people choose strategically and explore alternative options when it is more likely that the relative value of competing options has changed. Our study extends this work by considering how global trends (which affect all options equally) influence exploratory choice. For example, during an economic crisis, global gas prices may increase or decrease at all stations, yet consumers should still explore strategically to find the best option. Our research question is whether people can maintain effective exploration strategies in the presence of global trends that are irrelevant in that they do not affect the relative value of choice options. We find that people explore effectively irrespective of global trends.Games2015-08-1863Article10.3390/g60302512512612073-43362015-08-18doi: 10.3390/g6030251Peter RieferBradley Love<![CDATA[Games, Vol. 6, Pages 231-250: The Evolvability of Cooperation under Local and Non-Local Mutations]]>
http://mdpi.com/2073-4336/6/3/231
We study evolutionary dynamics in a population of individuals engaged in pairwise social interactions, encoded as iterated games. We consider evolution within the space of memory-1strategies, and we characterize all evolutionary robust outcomes, as well as their tendency to evolve under the evolutionary dynamics of the system. When mutations are restricted to be local, as opposed to non-local, then a wider range of evolutionary robust outcomes tend to emerge, but mutual cooperation is more difficult to evolve. When we further allow heritable mutations to the player’s investment level in each cooperative interaction, then co-evolution leads to changes in the payoff structure of the game itself and to specific pairings of robust games and strategies in the population. We discuss the implications of these results in the context of the genetic architectures that encode how an individual expresses its strategy or investment.Games2015-07-2363Article10.3390/g60302312312502073-43362015-07-23doi: 10.3390/g6030231Alexander StewartJoshua Plotkin<![CDATA[Games, Vol. 6, Pages 214-230: Fairness and Trust in Structured Populations]]>
http://mdpi.com/2073-4336/6/3/214
Classical economic theory assumes that people are rational and selfish, but behavioral experiments often point to inconsistent behavior, typically attributed to “other regarding preferences.” The Ultimatum Game, used to study fairness, and the Trust Game, used to study trust and trustworthiness, have been two of the most influential and well-studied examples of inconsistent behavior. Recently, evolutionary biologists have attempted to explain the evolution of such preferences using evolutionary game theoretic models. While deterministic evolutionary game theoretic models agree with the classical economics predictions, recent stochastic approaches that include uncertainty and the possibility of mistakes have been successful in accounting for both the evolution of fairness and the evolution of trust. Here I explore the role of population structure by generalizing and expanding these existing results to the case of non-random interactions. This is a natural extension since such interactions do not occur randomly in the daily lives of individuals. I find that, in the limit of weak selection, population structure increases the space of fair strategies that are selected for but it has little-to-no effect on the optimum strategy played in the Ultimatum Game. In the Trust Game, in the limit of weak selection, I find that some amount of trust and trustworthiness can evolve even in a well-mixed population; however, the optimal strategy, although trusting if the return on investment is sufficiently high, is never trustworthy. Population structure biases selection towards strategies that are both trusting and trustworthy trustworthy and reduces the critical return threshold, but, much like in the case of fairness, it does not affect the winning strategy. Further considering the effects of reputation and structure, I find that they act synergistically to promote the evolution of trustworthiness.Games2015-07-2063Article10.3390/g60302142142302073-43362015-07-20doi: 10.3390/g6030214Corina Tarnita<![CDATA[Games, Vol. 6, Pages 191-213: The Loser’s Bliss in Auctions with Price Externality]]>
http://mdpi.com/2073-4336/6/3/191
We consider auctions with price externality where all bidders derive utility from the winning price, such as charity auctions. In addition to the benefit to the winning bidder, all bidders obtain a benefit that is increasing in the winning price. Theory makes two predictions in such settings: First, individual bids will be increasing in the multiplier on the winning price. Second, individual bids will not depend on the number of other bidders. Empirically, we find no evidence that increasing the multiplier increases individual bids in a systematic way, but we find that increasing the number of bidders does. An analysis of individual bidding functions reveals that bidders underweight the incentives to win and overweight the incentives to lose.Games2015-07-0363Article10.3390/g60301911912132073-43362015-07-03doi: 10.3390/g6030191Ernan HaruvyPeter Popkowski Leszczyc<![CDATA[Games, Vol. 6, Pages 175-190: What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma]]>
http://mdpi.com/2073-4336/6/3/175
For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies.Games2015-06-2563Article10.3390/g60301751751902073-43362015-06-25doi: 10.3390/g6030175Ethan Akin<![CDATA[Games, Vol. 6, Pages 161-174: A Tale of Two Bargaining Solutions]]>
http://mdpi.com/2073-4336/6/2/161
We set up a rich bilateral bargaining model with four salient points (disagreement point, ideal point, reference point, and tempered aspirations point), where the disagreement point and the utility possibilities frontier are endogenously determined. This model allows us to compare two bargaining solutions that use reference points, the Gupta-Livne solution and the tempered aspirations solution, in terms of Pareto efficiency in a strategic framework. Our main result shows that the weights solutions place on the disagreement point do not directly imply a unique efficiency ranking in this bargaining problem with a reference point. In particular, the introduction of a reference point brings one more degree of freedom to the model which requires also the difference in the weights placed on the reference point to be considered in reaching an efficiency ranking.Games2015-06-1962Article10.3390/g60201611611742073-43362015-06-19doi: 10.3390/g6020161Emin KaragözoğluKerim Keskin<![CDATA[Games, Vol. 6, Pages 150-160: How Moral Codes Evolve in a Trust Game]]>
http://mdpi.com/2073-4336/6/2/150
This paper analyzes the dynamic stability of moral codes in a two population trust game. Guided by a moral code, members of one population, the Trustors, are willing to punish members of the other population, the Trustees, who defect. Under replicator dynamics, adherence to the moral code has unstable oscillations around an interior Nash Equilibrium (NE), but under smoothed best response dynamics we obtain convergence to Quantal Response Equilibrium (QRE).Games2015-06-0362Article10.3390/g60201501501602073-43362015-06-03doi: 10.3390/g6020150Jean RabanalDaniel Friedman<![CDATA[Games, Vol. 6, Pages 124-149: Should Law Keep Pace with Society? Relative Update Rates Determine the Co-Evolution of Institutional Punishment and Citizen Contributions to Public Goods]]>
http://mdpi.com/2073-4336/6/2/124
Until recently, theorists considering the evolution of human cooperation have paid little attention to institutional punishment, a defining feature of large-scale human societies. Compared to individually-administered punishment, institutional punishment offers a unique potential advantage: the ability to control how quickly legal rules of punishment evolve relative to social behavior that legal punishment regulates. However, at what rate should legal rules evolve relative to society to maximize compliance? We investigate this question by modeling the co-evolution of law and cooperation in a public goods game with centralized punishment. We vary the rate at which States update their legal punishment strategy relative to Citizens’ updating of their contribution strategy and observe the effect on Citizen cooperation. We find that when States have unlimited resources, slower State updating lead to more Citizen cooperation: by updating more slowly, States force Citizens to adapt to the legal punishment rules. When States depend on Citizens to finance their punishment activities, however, we find evidence of a ‘Goldilocks’ effect: optimal compliance is achieved when legal rules evolve at a critical evolutionary rate that is slow enough to force citizens to adapt, but fast enough to enable states to quickly respond to outbreaks of citizen lawlessness.Games2015-06-0362Article10.3390/g60201241241492073-43362015-06-03doi: 10.3390/g6020124Daria RoithmayrAlexander IsakovDavid Rand<![CDATA[Games, Vol. 6, Pages 79-123: Students, Temporary Workers and Co-Op Workers: An Experimental Investigation on Social Preferences]]>
http://mdpi.com/2073-4336/6/2/79
We conduct an artefactual field experiment to compare the individual preferences and propensity to cooperate of three pools of subjects: Undergraduate students, temporary workers and permanent workers. We find that students are more selfish and contribute less than workers. Temporary and permanent contract workers have similar other-regarding preferences and display analogous contribution patterns in an anonymous Public Good Game.Games2015-05-1862Article10.3390/g6020079791232073-43362015-05-18doi: 10.3390/g6020079Davide DragoneFabio GaleottiRaimondello Orsini<![CDATA[Games, Vol. 6, Pages 57-78: On the Three-Person Game Baccara Banque]]>
http://mdpi.com/2073-4336/6/2/57
Baccara banque is a three-person zero-sum game parameterized by \(\theta\in(0,1)\). A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium. However, this solution exists only for certain \(\theta\). A third solution, which we call the correlated cooperative equilibrium, always exists. Under a ''with replacement'' assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all \(\theta\).Games2015-05-0862Article10.3390/g602005757782073-43362015-05-08doi: 10.3390/g6020057Stewart EthierJiyeon Lee<![CDATA[Games, Vol. 6, Pages 39-56: A Model of Protocoalition Bargaining with Breakdown Probability]]>
http://mdpi.com/2073-4336/6/2/39
This paper analyses a model of legislative bargaining in which parties form tentative coalitions (protocoalitions) before deciding on the allocation of a resource. Protocoalitions may fail to reach an agreement, in which case they may be dissolved (breakdown) and a new protocoalition may form. We show that agreement is immediate in equilibrium, and the proposer advantage disappears as the breakdown probability goes to zero. We then turn to the special case of apex games and explore the consequences of varying the probabilities that govern the selection of formateurs and proposers. Letting the breakdown probability go to zero, most of the probabilities considered lead to the same ex post pay-off division. Ex ante expected pay-offs may follow a counterintuitive pattern: as the bargaining power of weak players within a protocoalition increases, the weak players may expect a lower pay-off ex ante.Games2015-04-2262Article10.3390/g602003939562073-43362015-04-22doi: 10.3390/g6020039Maria Montero<![CDATA[Games, Vol. 6, Pages 32-38: From Bargaining Solutions to Claims Rules: A Proportional Approach]]>
http://mdpi.com/2073-4336/6/1/32
Agents involved in a conflicting claims problem may be concerned with the proportion of their claims that is satisfied, or with the total amount they get. In order to relate both perspectives, we associate to each conflicting claims problem a bargaining-in-proportions set. Then, we obtain a correspondence between classical bargaining solutions and usual claims rules. In particular, we show that the constrained equal losses, the truncated constrained equal losses and the contested garment (Babylonian Talmud) rules can be obtained throughout the Nash bargaining solution.Games2015-03-0561Article10.3390/g601003232382073-43362015-03-05doi: 10.3390/g6010032José-Manuel Giménez-GómezAntónio OsórioJosep Peris<![CDATA[Games, Vol. 6, Pages 2-31: Selection-Mutation Dynamics of Signaling Games]]>
http://mdpi.com/2073-4336/6/1/2
We study the structure of the rest points of signaling games and their dynamic behavior under selection-mutation dynamics by taking the case of three signals as our canonical example. Many rest points of the replicator dynamics of signaling games are not isolated and, therefore, not robust under perturbations. However, some of them attract open sets of initial conditions. We prove the existence of certain rest points of the selection-mutation dynamics close to Nash equilibria of the signaling game and show that all but the perturbed rest points close to strict Nash equilibria are dynamically unstable. This is an important result for the evolution of signaling behavior, since it shows that the second-order forces that are governed by mutation can increase the chances of successful signaling.Games2015-01-0961Article10.3390/g60100022312073-43362015-01-09doi: 10.3390/g6010002Josef HofbauerSimon Huttegger<![CDATA[Games, Vol. 6, Pages 1: Acknowledgement to Reviewers of Games in 2014]]>
http://mdpi.com/2073-4336/6/1/1
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2014:[...]Games2015-01-0761Editorial10.3390/g6010001112073-43362015-01-07doi: 10.3390/g6010001 Games Editorial Office<![CDATA[Games, Vol. 5, Pages 234-256: Conditional Cooperation and the Marginal per Capita Return in Public Good Games]]>
http://mdpi.com/2073-4336/5/4/234
We investigate experimentally whether the extent of conditional cooperation in public good games depends on the marginal per capita return (MPCR) to the public good and type of game. The MPCR is varied from 0.2 to 0.4 to 0.8. The ‘standard’ game, in which three players contribute before a follower, is compared with a leader-follower game, in which one player leads and three follow. Even though we observe less conditional cooperation for an MPCR of 0.2, the prevalence of conditional cooperation remains relatively stable to changes in the MPCR and game timing. In contrast, the level of MPCR has a strong effect on unconditional contributions. Our results highlight the critical role played by leaders in a public good game.Games2014-11-1454Article10.3390/g50402342342562073-43362014-11-14doi: 10.3390/g5040234Edward CartwrightDenise Lovett<![CDATA[Games, Vol. 5, Pages 204-233: Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences]]>
http://mdpi.com/2073-4336/5/4/204
This paper attacks a problem like the one addressed in an earlier work (Potthoff, 2013) but is more mathematical. The setting is one where an election is to choose a single winner from m (&gt; 2) candidates, it is postulated that voters have knowledge of the preference profile of the electorate, and preference cycles are limited. Both papers devise voting systems whose two key goals are to select a Condorcet winner (if one exists) and to resist manipulation. These systems entail equilibrium strategies where everyone votes sincerely, no group of voters sharing the same preference ordering can gain by deviating given that no one else deviates, and the Condorcet candidate wins. The present paper uses two unusual ballot types. One asks voters to rank the candidates with respect both to their own preferences and to their discerned order of preference of the entire electorate. The other just asks voters for their own preference ranks plus approval votes. Novel mathematical elements distinguish this paper. Its Condorcet completion methods examine all candidate triples, sometimes analyze loop(s) of some of those triples, and order candidates in a set by first determining the last-place candidate. Its non-manipulability proofs involve mathematical induction on m.Games2014-10-3054Article10.3390/g50402042042332073-43362014-10-30doi: 10.3390/g5040204Richard Potthoff<![CDATA[Games, Vol. 5, Pages 191-203: A Note on the Core of TU-cooperative Games with Multiple Membership Externalities]]>
http://mdpi.com/2073-4336/5/4/191
A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.Games2014-10-2154Article10.3390/g50401911912032073-43362014-10-21doi: 10.3390/g5040191Heinrich Nax<![CDATA[Games, Vol. 5, Pages 188-190: Special Issue: Aspects of Game Theory and Institutional Economics]]>
http://mdpi.com/2073-4336/5/3/188
Classical economists from Adam Smith to Thomas Malthus and to Karl Marx have considered the importance of direct interdependence and direct interactions for the economy. This was even more the case for original institutionalist thinkers such as Thorstein Veblen, John Commons, and Clarence Ayres. In their writings, direct interdependence, interactions (or transactions) among agents, with all beneficial and with all problematic consequences, took center stage in economic analysis. Why, for instance, do people adhere to a particular new fashion or trend? Because others do, after eminent people, wealthy people, the “leisure class” (T. Veblen), have made it a symbol for status. The new fashion, however, ceases to serve as such a symbol once too many people follow it. The constant effort put into following trends and adopting fashion turns out to be a social dilemma, driven by Veblenian instincts, such as invidious distinction in predatory societies, conspicuous consumption and emulation. [...]Games2014-09-0453Editorial10.3390/g50301881881902073-43362014-09-04doi: 10.3390/g5030188Wolfram ElsnerTorsten HeinrichHenning SchwardtClaudius Gräbner<![CDATA[Games, Vol. 5, Pages 160-187: An Agent-Based Model of Institutional Life-Cycles]]>
http://mdpi.com/2073-4336/5/3/160
We use an agent-based model to investigate the interdependent dynamics between individual agency and emergent socioeconomic structure, leading to institutional change in a generic way. Our model simulates the emergence and exit of institutional units, understood as generic governed social structures. We show how endogenized trust and exogenously given leader authority influences institutional change, i.e., diversity in institutional life-cycles. It turns out that these governed institutions (de)structure in cyclical patterns dependent on the overall evolution of trust in the artificial society, while at the same time, influencing this evolution by supporting social learning. Simulation results indicate three scenarios of institutional life-cycles. Institutions may, (1) build up very fast and freeze the artificial society in a stable but fearful pattern (ordered system); (2) exist only for a short time, leading to a very trusty society (highly fluctuating system); and (3) structure in cyclical patterns over time and support social learning due to cumulative causation of societal trust (complex system).Games2014-08-1853Article10.3390/g50301601601872073-43362014-08-18doi: 10.3390/g5030160Manuel WäckerleBernhard RengsWolfgang Radax<![CDATA[Games, Vol. 5, Pages 140-159: Learning in Networks—An Experimental Study Using Stationary Concepts]]>
http://mdpi.com/2073-4336/5/3/140
Our study analyzes theories of learning for strategic interactions in networks. Participants played two of the 2 × 2 games used by Selten and Chmura [1]. Every participant played against four neighbors. As a distinct aspect our experimental design allows players to choose different strategies against each different neighbor. The games were played in two network structures: a lattice and a circle. We analyze our results with respect to three aspects. We first compare our results with the predictions of five different equilibrium concepts (Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium) which represent the long-run equilibrium of a learning process. Secondly, we relate our results to four different learning models (impulse-matching learning, action-sampling learning, self-tuning EWA, and reinforcement learning) which are based on the (behavioral) round-by-round learning process. At last, we compare the data with the experimental results of Selten and Chmura [1]. One main result is that the majority of players choose the same strategy against each neighbor. As other results, we observe an order of predictive success for the equilibrium concepts that is different from the order shown by Selten and Chmura and an order of predictive success for the learning models that is only slightly different from the order shown in a recent paper by Chmura, Goerg and Selten [2].Games2014-07-3153Article10.3390/g50301401401592073-43362014-07-31doi: 10.3390/g5030140Siegfried BerninghausThomas NeumannBodo Vogt<![CDATA[Games, Vol. 5, Pages 127-139: The Seawall Bargaining Game]]>
http://mdpi.com/2073-4336/5/2/127
Agents located from downstream to upstream along an estuary and exposed to a flooding risk have to invest in facilities like a seawall (or dike). As the benefits of that local public good increase along the estuary, upstream agents have to bargain for monetary compensation with the most downstream agent in exchange for more protection effort. The paper analyses different bargaining protocols and determines the conditions under which agents are better off. The results show that upstream agents are involved in a chicken game when they have to bargain with the most downstream agent.Games2014-06-2452Article10.3390/g50201271271392073-43362014-06-24doi: 10.3390/g5020127Rémy DelilleJean-Christophe Pereau<![CDATA[Games, Vol. 5, Pages 116-126: Two-Dimensional Effort in Patent-Race Games and Rent-Seeking Contests: The Case of Telephony]]>
http://mdpi.com/2073-4336/5/2/116
Using the political-economic history of the development of telephony during the 1870s as a backdrop, this paper studies a two-player Tullock contest that includes both research effort (R&amp;D) and legal effort (i.e., rent-seeking effort). The two types of efforts complement each other and positively influence the payoff of the contest. We assume that legal effort affects the prize value, increasing the winner’s prospective rents, and research effort impacts the probability of winning the contest. The results of the model break new ground in showing that research effort is a function of legal effort, wherein research effort increases with rent-seeking effort. The model also shows the existence of a strategic equivalence between rent seeking and patent races.Games2014-05-2052Article10.3390/g50201161161262073-43362014-05-20doi: 10.3390/g5020116João FariaFranklin Mixon, Jr.Steven CaudillSamantha Wineke<![CDATA[Games, Vol. 5, Pages 97-115: Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities]]>
http://mdpi.com/2073-4336/5/2/97
We characterize the efficiency space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto-optimal combinatorial auctions in a model with two players and k nonidentical items. We examine a model with multidimensional types, private values and quasilinear preferences for the players with one relaxation: one of the players is subject to a publicly known budget constraint. We show that if it is publicly known that the valuation for the largest bundle is less than the budget for at least one of the players, then Vickrey-Clarke-Groves (VCG) uniquely fulfills the basic properties of being deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal. Our characterization of the efficient space for deterministic budget constrained combinatorial auctions is similar in spirit to that of Maskin 2000 for Bayesian single-item constrained efficiency auctions and comparable with Ausubel and Milgrom 2002 for non-constrained combinatorial auctions.Games2014-04-3052Article10.3390/g5020097971152073-43362014-04-30doi: 10.3390/g5020097Anat LernerRica Gonen<![CDATA[Games, Vol. 5, Pages 92-96: Sequential Rationality in Continuous No-Limit Poker]]>
http://mdpi.com/2073-4336/5/2/92
Newman’s (1959, Operations Research, 7, 557–560) solution for a variant of poker with continuous hand spaces and an unlimited bet size is modified to incorporate sequential rationality.Games2014-04-1452Short Note10.3390/g502009292962073-43362014-04-14doi: 10.3390/g5020092Thomas Norman<![CDATA[Games, Vol. 5, Pages 90-91: Acknowledgement to Reviewers of Games in 2013]]>
http://mdpi.com/2073-4336/5/1/90
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013. [...]Games2014-02-2551Editorial10.3390/g501009090912073-43362014-02-25doi: 10.3390/g5010090 Games Editorial Office<![CDATA[Games, Vol. 5, Pages 53-89: Schelling, von Neumann, and the Event that Didn’t Occur]]>
http://mdpi.com/2073-4336/5/1/53
Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper.Games2014-02-2551Article10.3390/g501005353892073-43362014-02-25doi: 10.3390/g5010053Alexander Field<![CDATA[Games, Vol. 5, Pages 26-52: Examining Monotonicity and Saliency Using Level-k Reasoning in a Voting Game]]>
http://mdpi.com/2073-4336/5/1/26
This paper presents an experiment that evaluates the effect of financial incentives and complexity in political science voting experiments. To evaluate the effect of complexity we adopt a level-k reasoning model concept. This model by Nagel [1] postulates that players might be of different types, each corresponding to the level of reasoning in which they engage. Furthermore, to postulate the effect of financial incentives on subjects’ choice, we used the Quantal Response Equilibrium (QRE) concept. In a QRE, players’ decisions are noisy, with the probability of playing a given strategy increasing in its expected payoff. Hence, the choice probability is a function of the magnitude of the financial incentives. Our results show that low complexity promotes the highest degree of level-k strategic reasoning in every payment treatment. Standard financial incentives are enough to induce equilibrium behavior, and the marginal effect of extra incentives on equilibrium behavior seems to be negligible. High complexity, instead, decreases the rate of convergence to equilibrium play. With a sufficiently high complexity, increasing payoff amounts does promote more strategic behavior in a significant manner. Our results show with complex voting games, higher financial incentives are required for the subjects to exert the effort needed to complete the task.Games2014-02-1451Article10.3390/g501002626522073-43362014-02-14doi: 10.3390/g5010026Anna BassiKenneth Williams<![CDATA[Games, Vol. 5, Pages 1-25: Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results]]>
http://mdpi.com/2073-4336/5/1/1
The paper presents an evolutionary model, based on the assumption that agents may revise their current strategies if they previously failed to attain the maximum level of potential payoffs. We offer three versions of this reflexive mechanism, each one of which describes a distinct type: spontaneous agents, rigid players, and ‘satisficers’. We use simulations to examine the performance of these types. Agents who change their strategies relatively easily tend to perform better in coordination games, but antagonistic games generally lead to more favorable outcomes if the individuals only change their strategies when disappointment from previous rounds surpasses some predefined threshold.Games2014-01-3051Article10.3390/g50100011252073-43362014-01-30doi: 10.3390/g5010001Tassos Patokos<![CDATA[Games, Vol. 4, Pages 776-794: Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study]]>
http://mdpi.com/2073-4336/4/4/776
In this paper, we claim that agents confronting with new interactive situations apply behavioral heuristics that drastically reduce the problem complexity either by neglecting the other players’ incentives, or by restricting attention to subsets of “salient” outcomes. We postulate that these heuristics are sensitive to the manipulation of those features that can be modified without altering the (Nash) equilibrium structure of the game. We call these features “descriptive”. We test experimentally the effect of these descriptive features on both choice behavior and cross-game similarity perception. Analysis of individual choices confirms our hypotheses, and suggests that non-equilibrium choices may derive from simplified mental models of the game structure, rather than from heterogeneous beliefs or limited iterative thinking. In addition, subjects tend to behave similarly in games sharing similar descriptive features, regardless of their strategic structure.Games2013-12-1844Article10.3390/g40407767767942073-43362013-12-18doi: 10.3390/g4040776Sibilla Di GuidaGiovanna Devetag<![CDATA[Games, Vol. 4, Pages 754-775: External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal?]]>
http://mdpi.com/2073-4336/4/4/754
Prompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival’s competition, either with the alliance or with the individual partners. We show that, while strong external pressure on both partners can cause Ally-Ally to become a Nash equilibrium for the two-player Prisoners’ Dilemma, weak or asymmetric pressure that plays on the partners’ differing objectives can undermine the alliance. As well as providing new insights into how allies should respond if the alliance is to continue, this also illustrates how a third party can most effectively cause the alliance to become unsustainable. We create a new game theoretic framework, adding value to existing theory and the practice of alliance formation and sustainability.Games2013-12-1044Article10.3390/g40407547547752073-43362013-12-10doi: 10.3390/g4040754Jane BinnerLeslie FletcherVassili KolokoltsovFrancesco Ciardiello<![CDATA[Games, Vol. 4, Pages 738-753: Auctioning the Right to Play Ultimatum Games and the Impact on Equilibrium Selection]]>
http://mdpi.com/2073-4336/4/4/738
We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equilibrium, and auction prices emerge supporting this equilibrium by the principle of forward induction. With random assignment, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. While Nash equilibria with low offers are observed, the subgame perfect Nash equilibrium never is.Games2013-11-2744Article10.3390/g40407387387532073-43362013-11-27doi: 10.3390/g4040738Jason ShachatJ. Swarthout<![CDATA[Games, Vol. 4, Pages 711-737: A Game-Theoretic Analysis of Baccara Chemin de Fer]]>
http://mdpi.com/2073-4336/4/4/711
Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 x 288 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only his own total, baccara is a 2 x 2484 matrix game, which was solved by Downton and Lockwood in 1975 for d = 1, 2, . . . , 8. Assuming that cards are dealt without replacement from a d-deck shoe and that each of Player and Banker sees the composition of his own two-card hand, baccara is a 25 x 2484 matrix game, which is solved herein for every positive integer d.Games2013-11-1844Article10.3390/g40407117117372073-43362013-11-18doi: 10.3390/g4040711Stewart EthierCarlos Gámez<![CDATA[Games, Vol. 4, Pages 690-710: The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings]]>
http://mdpi.com/2073-4336/4/4/690
We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices.Games2013-11-1844Article10.3390/g40406906907102073-43362013-11-18doi: 10.3390/g4040690Rica GonenAnat Lerner<![CDATA[Games, Vol. 4, Pages 670-689: The Optimality of Team Contracts]]>
http://mdpi.com/2073-4336/4/4/670
This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others’ effort levels and draft enforceable side-contracts on effort levels and realized returns. Standard constraints, resulting in incentive contracts, fail to ensure implementability, and we examine centralized collusion-proof contracts and decentralized team contracts, as well. We prove that the principal may restrict attention to team contracts whenever returns from the project satisfy a mild monotonicity condition.Games2013-11-1844Article10.3390/g40406706706892073-43362013-11-18doi: 10.3390/g4040670Mehmet BarloAyça Özdoğan<![CDATA[Games, Vol. 4, Pages 648-669: An Adaptive Learning Model in Coordination Games]]>
http://mdpi.com/2073-4336/4/4/648
In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in normal form games with strict Nash equilibria. In the model, each player assigns subjective payoff assessments to his own actions, where the assessment of each action is a weighted average of its past payoffs, and chooses the action which has the highest assessment. After receiving a payoff, each player updates the assessment of his chosen action in an adaptive manner. We show almost sure convergence to a Nash equilibrium under one of the following conditions: (i) that, at any non-Nash equilibrium action profile, there exists a player who receives a payoff, which is less than his maximin payoff; (ii) that all non-Nash equilibrium action profiles give the same payoff. In particular, the convergence is shown in the following games: the battle of the sexes game, the stag hunt game and the first order statistic game. In the game of chicken and market entry games, players may end up playing the action profile, which consists of each player’s unique maximin action.Games2013-11-1544Article10.3390/g40406486486692073-43362013-11-15doi: 10.3390/g4040648Naoki Funai<![CDATA[Games, Vol. 4, Pages 624-647: Strategic Voting in Heterogeneous Electorates: An Experimental Study]]>
http://mdpi.com/2073-4336/4/4/624
We study strategic voting in a setting where voters choose from three options and Condorcet cycles may occur. We introduce in the electorate heterogeneity in preference intensity by allowing voters to differ in the extent to which they value the three options. Three information conditions are tested: uninformed, in which voters know only their own preference ordering and the own benefits from each option; aggregate information, in which in addition they know the aggregate realized distribution of the preference orderings and full information, in which they also know how the relative importance attributed to the options are distributed within the electorate. As a general result, heterogeneity seems to decrease the level of strategic voting in our experiment compared to the homogenous preference case that we study in a companion paper. Both theoretically and empirically (with data collected in a laboratory experiment), the main comparative static results obtained for the homogenous case carry over to the present setting with preference heterogeneity. Moreover, information about the realized aggregate distribution of preferences seems to be the element that best explains observed differences in voting behavior. Additional information about the realized distribution of preference intensity does not yield significant further changes.Games2013-11-1144Article10.3390/g40406246246472073-43362013-11-11doi: 10.3390/g4040624Marcelo TyszlerArthur Schram<![CDATA[Games, Vol. 4, Pages 608-623: Bimodal Bidding in Experimental All-Pay Auctions]]>
http://mdpi.com/2073-4336/4/4/608
We report results from experimental first-price, sealed-bid, all-pay auctions for a good with a common and known value. We observe bidding strategies in groups of two and three bidders and under two extreme information conditions. As predicted by the Nash equilibrium, subjects use mixed strategies. In contrast to the prediction under standard assumptions, bids are drawn from a bimodal distribution: very high and very low bids are much more frequent than intermediate bids. Standard risk preferences cannot account for our results. Bidding behavior is, however, consistent with the predictions of a model with reference dependent preferences as proposed by the prospect theory.Games2013-10-1144Article10.3390/g40406086086232073-43362013-10-11doi: 10.3390/g4040608Christiane ErnstChristian Thöni<![CDATA[Games, Vol. 4, Pages 584-607: Of Coordinators and Dictators: A Public Goods Experiment]]>
http://mdpi.com/2073-4336/4/4/584
We experimentally investigate whether human subjects are willing to give up individual freedom in return for the benefits of improved coordination. We conduct a modified iterated public goods game in which subjects in each period first decide which of two groups to join. One group employs a voluntary contribution mechanism, the other group an allocator contribution mechanism. The setup of the allocator mechanism differs between two treatments. In the coordinator treatment, the randomly selected allocator can set a uniform contribution for all group members, including herself. In the dictator treatment, the allocator can choose different contributions for herself and all other group members. We find that subjects willingly submit to authority in both treatments, even when competing with a voluntary contribution mechanism. The allocator groups achieve high contribution levels in both treatments.Games2013-10-1044Article10.3390/g40405845846072073-43362013-10-10doi: 10.3390/g4040584Jürgen FleißStefan Palan<![CDATA[Games, Vol. 4, Pages 561-583: Population Games, Stable Games, and Passivity]]>
http://mdpi.com/2073-4336/4/4/561
The class of “stable games”, introduced by Hofbauer and Sandholm in 2009, has the attractive property of admitting global convergence to equilibria under many evolutionary dynamics. We show that stable games can be identified as a special case of the feedback-system-theoretic notion of a “passive” dynamical system. Motivated by this observation, we develop a notion of passivity for evolutionary dynamics that complements the definition of the class of stable games. Since interconnections of passive dynamical systems exhibit stable behavior, we can make conclusions about passive evolutionary dynamics coupled with stable games. We show how established evolutionary dynamics qualify as passive dynamical systems. Moreover, we exploit the flexibility of the definition of passive dynamical systems to analyze generalizations of stable games and evolutionary dynamics that include forecasting heuristics as well as certain games with memory.Games2013-10-0744Article10.3390/g40405615615832073-43362013-10-07doi: 10.3390/g4040561Michael FoxJeff Shamma<![CDATA[Games, Vol. 4, Pages 532-560: Multidimensional Screening with Complementary Activities: Regulating a Monopolist with Unknown Cost and Unknown Preference for Empire Building]]>
http://mdpi.com/2073-4336/4/3/532
We study the optimal regulation of a monopolist when intrinsic efficiency (intrinsic cost) and empire building tendency (marginal utility of output) are private information, but actual cost (the difference between intrinsic cost and effort level) is observable. This is a problem of multidimensional screening with complementary activities. Results are not only driven by the prior probabilities of the four possible types, but also by the relative magnitude of the uncertainty along the two dimensions of private information. If the marginal utility of output varies much more (less) across managers than the intrinsic marginal cost, there is empire building (efficiency) dominance. In that case, an inefficient empire builder produces more (less) and at lower (higher) marginal cost than an efficient money-seeker. It is only when variabilities are similar that there may be the natural ranking of activities (empire builders produce more, while efficient managers produce at a lower cost).Games2013-09-1643Article10.3390/g40305325325602073-43362013-09-16doi: 10.3390/g4030532Ana BorgesDidier LausselJoão Correia-da-Silva<![CDATA[Games, Vol. 4, Pages 508-531: Solution Concepts of Principal-Agent Models with Unawareness of Actions]]>
http://mdpi.com/2073-4336/4/3/508
In numerous economic scenarios, contracting parties may not have a clear picture of all the relevant aspects. A contracting party may be unaware of what she and/or others are entitled to determine. Therefore, she may reject a contract that is too good to be true. Further, a contracting party may actively exert cognitive effort before signing a contract, so as to avoid being trapped into the contractual agreement ex post. In this paper, we propose a general framework to investigate these strategic interactions with unawareness, reasoning and cognition and intend to unify the solution concepts in the contracting context with unawareness. We build our conceptual framework upon the classical principal-agent relationship and compare the behaviors under various degrees of the unaware agent’s sophistication.Games2013-08-3043Article10.3390/g40305085085312073-43362013-08-30doi: 10.3390/g4030508Ying-Ju ChenXiaojian Zhao<![CDATA[Games, Vol. 4, Pages 497-507: Speech Is Silver, Silence Is Golden]]>
http://mdpi.com/2073-4336/4/3/497
This paper experimentally investigates free-riding behavior on communication cost in a coordination game and finds strong indications of such free-riding. Firstly, the subjects wait for others to send a message when communication is costly, which does not happen when communication is costless. Secondly, the proportion of games where no communication or one-way communication takes place is much higher when communication is costly compared to when it is free.Games2013-08-3043Short Note10.3390/g40304974975072073-43362013-08-30doi: 10.3390/g4030497Ola AnderssonHakan Holm<![CDATA[Games, Vol. 4, Pages 457-496: Contract and Game Theory: Basic Concepts for Settings with Finite Horizons]]>
http://mdpi.com/2073-4336/4/3/457
This paper examines a general model of contract in multi-period settings with both external and self-enforcement. In the model, players alternately engage in contract negotiation and take individual actions. A notion of contractual equilibrium, which combines a bargaining solution and individual incentive constraints, is proposed and analyzed. The modeling framework helps identify the relation between the manner in which players negotiate and the outcome of the long-term contractual relationship. In particular, the model shows the importance of accounting for the self-enforced component of contract in the negotiation process. Examples and guidance for applications are provided, along with existence results and a result on a monotone relation between “activeness of contracting” and contractual equilibrium values.Games2013-08-2143Article10.3390/g40304574574962073-43362013-08-21doi: 10.3390/g4030457Joel Watson<![CDATA[Games, Vol. 4, Pages 437-456: Noncontractible Investments and Reference Points]]>
http://mdpi.com/2073-4336/4/3/437
We analyze noncontractible investments in a model with shading. A seller can make an investment that affects a buyer’s value. The parties have outside options that depend on asset ownership. When shading is not possible and there is no contract renegotiation, an optimum can be achieved by giving the seller the right to make a take-it-or-leave-it offer. However, with shading, such a contract creates deadweight losses. We show that an optimal contract will limit the seller’s offers, and possibly create ex post inefficiency. Asset ownership can improve matters even if revelation mechanisms are allowed.Games2013-08-1443Article10.3390/g40304374374562073-43362013-08-14doi: 10.3390/g4030437Oliver Hart<![CDATA[Games, Vol. 4, Pages 426-436: An Evolutionary Theory of Suicide]]>
http://mdpi.com/2073-4336/4/3/426
We analyze a model in which individuals have hereditary reproductive types. The reproductive value of an individual is determined by her reproductive type and the amount of resources she can access. We introduce the possibility of suicide and assume it is also a genetic trait that interacts with the reproductive type of an individual. The main result of the paper is that populations where suicide is possible grow faster than other populations.Games2013-08-1343Article10.3390/g40304264264362073-43362013-08-13doi: 10.3390/g4030426Balázs SzentesCaroline Thomas<![CDATA[Games, Vol. 4, Pages 398-425: Institutional Inertia and Institutional Change in an Expanding Normal-Form Game]]>
http://mdpi.com/2073-4336/4/3/398
We investigate aspects of institutional change in an evolutionary game-theoretic framework, in principle focusing on problems of coordination in groups when new solutions to a problem become available. In an evolutionary game with an underlying dilemma structure, we let a number of new strategies become gradually available to the agents. The dilemma structure of the situation is not changed by these. Older strategies offer a lesser payoff than newly available ones. The problem that agents have to solve for realizing improved results is, therefore, to coordinate on newly available strategies. Strategies are taken to represent institutions; the coordination on a new strategy by agents, hence, represents a change in the institutional framework of a group. The simulations we run show a stable pattern regarding such institutional changes. A number of institutions are found to coexist, with the specific number depending on the relation of payoffs achievable through the coordination of different strategies. Usually, the strategies leading to the highest possible payoff are not among these. This can be taken to reflect the heterogeneity of rules in larger groups, with different subgroups showing different behavior patterns.Games2013-08-1243Article10.3390/g40303983984252073-43362013-08-12doi: 10.3390/g4030398Torsten HeinrichHenning Schwardt<![CDATA[Games, Vol. 4, Pages 375-397: An Experimental Analysis of Asymmetric Power in Conflict Bargaining]]>
http://mdpi.com/2073-4336/4/3/375
Demands and concessions in a multi-stage bargaining process are shaped by the probabilities that each side will prevail in an impasse. Standard game-theoretic predictions are quite sharp: demands are pushed to the precipice with nothing left on the table, but there is no conflict regardless of the degree of power asymmetry. Indeed, there is no delay in reaching an agreement that incorporates the (unrealized) costs of delay and conflict. A laboratory experiment has been used to investigate the effects of power asymmetries on conflict rates in a two-stage bargaining game that is (if necessary) followed by conflict with a random outcome. Observed demands at each stage are significantly correlated with power, as measured by the probability of winning in the event of disagreement. Demand patterns, however, are flatter than theoretical predictions, and conflict occurs in a significant proportion of the interactions, regardless of the degree of the power asymmetry. To address these deviations from the standard game-theoretic predictions, we also estimated a logit quantal response model, which generated the qualitative patterns that are observed in the data. This one-parameter generalization of the Nash equilibrium permits a deconstruction of the strategic incentives that cause demands to be less responsive to power asymmetries than Nash predictions.Games2013-08-0243Article10.3390/g40303753753972073-43362013-08-02doi: 10.3390/g4030375Katri SiebergDavid ClarkCharles HoltTimothy NordstromWilliam Reed<![CDATA[Games, Vol. 4, Pages 367-374: Reciprocity Effects in the Trust Game]]>
http://mdpi.com/2073-4336/4/3/367
I use data from a previous experiment for classifying subjects based on their behavior in the trust game. Prior literature defines a “reciprocity effect” as the tendency for Second Movers to return proportions increasing in the amounts that they receive. In the data that I use, 31% of Second Movers show reciprocity effects, 31% are neutral, and 25% consistently free-ride, indicating that the aggregate reciprocity effect for the sample as a whole is attributable to a minority of the subjects.Games2013-07-3143Letter10.3390/g40303673673742073-43362013-07-31doi: 10.3390/g4030367Alexander Smith<![CDATA[Games, Vol. 4, Pages 347-366: The Renegotiation-Proofness Principle and Costly Renegotiation]]>
http://mdpi.com/2073-4336/4/3/347
We study contracting and costly renegotiation in settings of complete, but unverifiable information, using the mechanism-design approach. We show how renegotiation activity is best modeled in the fundamentals of the mechanism-design framework, so that noncontractibility of renegotiation amounts to a constraint on the problem. We formalize and clarify the Renegotiation-Proofness Principle (RPP), which states that any state-contingent payoff vector that is implementable in an environment with renegotiation can also be implemented by a mechanism in which renegotiation does not occur in equilibrium. We observe that the RPP is not valid in some settings. However, we prove a general monotonicity result that confirms the RPP’s message about renegotiation opportunities having negative consequences. Our monotonicity theorem states that, as the costs of renegotiation increase, the set of implementable state-contingent payoffs becomes larger.Games2013-07-2543Article10.3390/g40303473473662073-43362013-07-25doi: 10.3390/g4030347James BrennanJoel Watson<![CDATA[Games, Vol. 4, Pages 339-346: Repeated Play of Families of Games by Resource-Constrained Players]]>
http://mdpi.com/2073-4336/4/3/339
This paper studies a repeated play of a family of games by resource-constrained players. To economize on reasoning resources, the family of games is partitioned into subsets of games which players do not distinguish. An example is constructed to show that when games are played a finite number of times, partitioning of the game set according to a coarse exogenously given partition might introduce new symmetric equilibrium payoffs which Pareto dominate best equilibrium outcomes with distinguished games. Moreover, these new equilibrium payoffs are also immune to evolutionary pressure at the partition selection stage.Games2013-07-1143Article10.3390/g40303393393462073-43362013-07-11doi: 10.3390/g4030339Arina Nikandrova<![CDATA[Games, Vol. 4, Pages 329-338: Relative Concerns and Delays in Bargaining with Private Information]]>
http://mdpi.com/2073-4336/4/3/329
We consider Rubinstein’s two-person alternating-offer bargaining model with two-sided incomplete information. We investigate the effects of one party having relative concerns about the bargaining outcome and the delay in reaching an agreement. We find that facing an opponent with stronger relative concerns only hurts the bargainer when she is stronger than her opponent. In addition, we show that an increase of one party’s relative concerns will decrease the maximum delay in reaching an agreement.Games2013-06-2743Article10.3390/g40303293293382073-43362013-06-27doi: 10.3390/g4030329Ana MauleonVincent Vannetelbosch<![CDATA[Games, Vol. 4, Pages 304-328: The Hitchhiker’s Guide to Adaptive Dynamics]]>
http://mdpi.com/2073-4336/4/3/304
Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.Games2013-06-2443Article10.3390/g40303043043282073-43362013-06-24doi: 10.3390/g4030304Åke BrännströmJacob JohanssonNiels von Festenberg<![CDATA[Games, Vol. 4, Pages 283-303: The Effects of Entry in Bilateral Oligopoly]]>
http://mdpi.com/2073-4336/4/3/283
The purpose of this paper is to study the effects of entry into the market for a single commodity in which both sellers and buyers are permitted to interact strategically. With the inclusion of an additional seller, the market is quasi-competitive: the price falls and volume of trade increases, as expected. However, contrary to the conventional wisdom, existing sellers’ payoffs may increase. The conditions under which entry by new sellers raises the equilibrium payoffs of existing sellers are derived. These depend in an intuitive way on the elasticity of a strategic analog of demand and the market share of existing sellers, and encompass entirely standard economic environments. Similar results are derived relating to the entry of additional buyers and the effects of entry on both sides of the market are investigated.Games2013-06-2443Article10.3390/g40302832833032073-43362013-06-24doi: 10.3390/g4030283Alex Dickson<![CDATA[Games, Vol. 4, Pages 243-282: Unraveling Results from Comparable Demand and Supply: An Experimental Investigation]]>
http://mdpi.com/2073-4336/4/2/243
Markets sometimes unravel, with offers becoming inefficiently early. Often this is attributed to competition arising from an imbalance of demand and supply, typically excess demand for workers. However this presents a puzzle, since unraveling can only occur when firms are willing to make early offers and workers are willing to accept them. We present a model and experiment in which workers’ quality becomes known only in the late part of the market. However, in equilibrium, matching can occur (inefficiently) early only when there is comparable demand and supply: a surplus of applicants, but a shortage of high quality applicants.Games2013-06-1942Article10.3390/g40202432432822073-43362013-06-19doi: 10.3390/g4020243Muriel NiederleAlvin RothM. Ünver<![CDATA[Games, Vol. 4, Pages 208-242: Fairness in Risky Environments: Theory and Evidence]]>
http://mdpi.com/2073-4336/4/2/208
The relationship between risk in the environment, risk aversion and inequality aversion is not well understood. Theories of fairness have typically assumed that pie sizes are known ex-ante. Pie sizes are, however, rarely known ex ante. Using two simple allocation problems—the Dictator and Ultimatum game—we explore whether, and how exactly, unknown pie sizes with varying degrees of risk (“endowment risk”) influence individual behavior. We derive theoretical predictions for these games using utility functions that capture additively separable constant relative risk aversion and inequity aversion. We experimentally test the theoretical predictions using two subject pools: students of Czech Technical University and employees of Prague City Hall. We find that: (1) Those who are more risk-averse are also more inequality-averse in the Dictator game (and also in the Ultimatum game but there not statistically significantly so) in that they give more; (2) Using the within-subject feature of our design, and in line with our theoretical prediction, varying risk does not influence behavior in the Dictator game, but does so in the Ultimatum game (contradicting our theoretical prediction for that game); (3) Using the within-subject feature of our design, subjects tend to make inconsistent decisions across games; this is true on the level of individuals as well as in the aggregate. This latter finding contradicts the evidence in Blanco et al. (2011); (4) There are no subject-pool differences once we control for the elicited risk attitude and demographic variables that we collect.Games2013-05-3042Article10.3390/g40202082082422073-43362013-05-30doi: 10.3390/g4020208Silvester Van KotenAndreas OrtmannVitezslav Babicky<![CDATA[Games, Vol. 4, Pages 200-207: A Note on Cooperative Strategies in Gladiators’ Games]]>
http://mdpi.com/2073-4336/4/2/200
Gladiatorial combat was in reality a lot less lethal than it is depicted in the cinema. This short paper highlights how cooperative strategies could have prevailed in the arenas, which is generally what happened during the Games. Cooperation in the arena corresponded to a situation of the professionalization of gladiators, who been trained in gladiatorial schools. This case provides an analogy of the conditions under which cooperation occurs in a context of competition between rival companies.Games2013-05-2242Article10.3390/g40202002002072073-43362013-05-22doi: 10.3390/g4020200Jérôme BalletDamien BazinRadu Vranceanu<![CDATA[Games, Vol. 4, Pages 182-199: Dynamic Properties of Evolutionary Multi-player Games in Finite Populations]]>
http://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.Games2013-05-0642Article10.3390/g40201821821992073-43362013-05-06doi: 10.3390/g4020182Bin WuArne TraulsenChaitanya Gokhale<![CDATA[Games, Vol. 4, Pages 163-181: The Dynamics of Costly Signaling]]>
http://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.Games2013-04-2642Article10.3390/g40201631631812073-43362013-04-26doi: 10.3390/g4020163Elliott Wagner<![CDATA[Games, Vol. 4, Pages 144-162: Reciprocity in Locating Contributions: Experiments on the Neighborhood Public Good Game]]>
http://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.Games2013-04-2642Article10.3390/g40201441441622073-43362013-04-26doi: 10.3390/g4020144Siegfried BerninghausWerner GüthStephan Schosser<![CDATA[Games, Vol. 4, Pages 125-143: Two Pricing Mechanisms in Sponsored Search Advertising]]>
http://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.Games2013-03-2041Article10.3390/g40101251251432073-43362013-03-20doi: 10.3390/g4010125Wei YangYouyi FengBaichun Xiao<![CDATA[Games, Vol. 4, Pages 106-124: Divorce Costs and Marital Dissolution in a One-to-One Matching Framework With Nontransferable Utilities]]>
http://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.Games2013-03-2041Article10.3390/g40101061061242073-43362013-03-20doi: 10.3390/g4010106Ismail Saglam<![CDATA[Games, Vol. 4, Pages 89-105: Group Size, Coordination, and the Effectiveness of Punishment in the Voluntary Contributions Mechanism: An Experimental Investigation]]>
http://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.Games2013-02-1941Article10.3390/g4010089891052073-43362013-02-19doi: 10.3390/g4010089Bin XuC. CadsbyLiangcong FanFei Song<![CDATA[Games, Vol. 4, Pages 66-88: Hierarchical Bayesian Analysis of Biased Beliefs and Distributional Other-Regarding Preferences]]>
http://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.Games2013-02-1941Article10.3390/g401006666882073-43362013-02-19doi: 10.3390/g4010066Ozan AksoyJeroen Weesie<![CDATA[Games, Vol. 4, Pages 50-65: Tacit Collusion under Fairness and Reciprocity]]>
http://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.Games2013-02-0741Article10.3390/g401005050652073-43362013-02-07doi: 10.3390/g4010050Doruk İrişLuís Santos-Pinto<![CDATA[Games, Vol. 4, Pages 38-49: Nash Implementation in an Allocation Problem with Single-Dipped Preferences]]>
http://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.Games2013-01-3041Article10.3390/g401003838492073-43362013-01-30doi: 10.3390/g4010038Ahmed Doghmi<![CDATA[Games, Vol. 4, Pages 21-37: An Equilibrium Analysis of Knaster’s Fair Division Procedure]]>
http://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.Games2013-01-1841Article10.3390/g401002121372073-43362013-01-18doi: 10.3390/g4010021Matt Van Essen<![CDATA[Games, Vol. 4, Pages 1-20: Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play]]>
http://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.Games2013-01-0441Article10.3390/g40100011202073-43362013-01-04doi: 10.3390/g4010001Kristian LindgrenVilhelm Verendel<![CDATA[Games, Vol. 3, Pages 150-156: Computer Solution to the Game of Pure Strategy]]>
http://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.Games2012-11-0834Article10.3390/g30401501501562073-43362012-11-08doi: 10.3390/g3040150Glenn C. RhoadsLaurent Bartholdi<![CDATA[Games, Vol. 3, Pages 138-149: Modeling Inequity Aversion in a Dictator Game with Production]]>
http://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).Games2012-10-2334Letter10.3390/g30401381381492073-43362012-10-23doi: 10.3390/g3040138Ismael Rodriguez-LaraLuis Moreno-Garrido<![CDATA[Games, Vol. 3, Pages 119-137: Incomplete Information about Social Preferences Explains Equal Division and Delay in Bargaining]]>
http://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.Games2012-09-1333Article10.3390/g30301191191372073-43362012-09-13doi: 10.3390/g3030119Stefan Kohler<![CDATA[Games, Vol. 3, Pages 97-118: Quantum Type Indeterminacy in Dynamic Decision-Making: Self-Control through Identity Management]]>
http://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.Games2012-05-1532Article10.3390/g3020097971182073-43362012-05-15doi: 10.3390/g3020097Ariane Lambert-MogilianskyJerome Busemeyer<![CDATA[Games, Vol. 3, Pages 78-96: What Behaviors are Disapproved? Experimental Evidence from Five Dictator Games]]>
http://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.Games2012-04-2332Article10.3390/g302007878962073-43362012-04-23doi: 10.3390/g3020078Raúl López-PérezMarc Vorsatz<![CDATA[Games, Vol. 3, Pages 56-77: Patience or Fairness? Analyzing Social Preferences in Repeated Games]]>
http://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).Games2012-03-2131Article10.3390/g301005656772073-43362012-03-21doi: 10.3390/g3010056John DuffyFélix Muñoz-García<![CDATA[Games, Vol. 3, Pages 41-55: Games with Synergistic Preferences]]>
http://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.Games2012-03-1531Article10.3390/g301004141552073-43362012-03-15doi: 10.3390/g3010041Julian Jamison<![CDATA[Games, Vol. 3, Pages 30-40: Coordination, Differentiation and Fairness in a Population of Cooperating Agents]]>
http://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.Games2012-03-0531Article10.3390/g301003030402073-43362012-03-05doi: 10.3390/g3010030Anne-Ly DoLars RudolfThilo Gross<![CDATA[Games, Vol. 3, Pages 1-29: Responder Feelings in a Three-Player Three-Option Ultimatum Game: Affective Determinants of Rejection Behavior]]>
http://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.Games2012-02-1331Article10.3390/g30100011292073-43362012-02-13doi: 10.3390/g3010001Hans-Rüdiger PfisterGisela Böhm<![CDATA[Games, Vol. 2, Pages 463-464: Acknowledgment to Referees]]>
http://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. [...]Games2011-12-2024Editorial10.3390/g20404634634642073-43362011-12-20doi: 10.3390/g2040463Games Editorial Office<![CDATA[Games, Vol. 2, Pages 452-462: The Resolution Game: A Dual Selves Perspective]]>
http://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.Games2011-12-0924Article10.3390/g20404524524622073-43362011-12-09doi: 10.3390/g2040452Dimitri MigrowMatthias Uhl<![CDATA[Games, Vol. 2, Pages 434-451: Unraveling Public Good Games]]>
http://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.Games2011-11-2124Article10.3390/g20404344344512073-43362011-11-21doi: 10.3390/g2040434Pablo Brañas-GarzaMaria Paz Espinosa<![CDATA[Games, Vol. 2, Pages 412-433: Building Trust—One Gift at a Time]]>
http://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.Games2011-09-2724Article10.3390/g20404124124332073-43362011-09-27doi: 10.3390/g2040412Maroš ServátkaSteven TuckerRadovan Vadovič<![CDATA[Games, Vol. 2, Pages 365-411: Spite and Reciprocity in Auctions]]>
http://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.Games2011-09-1623Article10.3390/g20303653654112073-43362011-09-16doi: 10.3390/g2030365Naoko NishimuraTimothy N. CasonTatsuyoshi SaijoYoshikazu Ikeda<![CDATA[Games, Vol. 2, Pages 355-364: Strictly Dominated Strategies in the Replicator-Mutator Dynamics]]>
http://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.Games2011-09-1423Article10.3390/g20303553553642073-43362011-09-14doi: 10.3390/g2030355Segismundo S. IzquierdoLuis R. Izquierdo<![CDATA[Games, Vol. 2, Pages 333-354: The Minority of Three-Game: An Experimental and Theoretical Analysis]]>
http://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.Games2011-09-0923Article10.3390/g20303333333542073-43362011-09-09doi: 10.3390/g2030333Thorsten ChmuraWerner Güth<![CDATA[Games, Vol. 2, Pages 302-332: The Price of Anarchy for Network Formation in an Adversary Model]]>
http://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.Games2011-08-2323Article10.3390/g20303023023322073-43362011-08-23doi: 10.3390/g2030302Lasse Kliemann<![CDATA[Games, Vol. 2, Pages 277-301: Voluntary versus Enforced Team Effort]]>
http://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.Games2011-08-1923Article10.3390/g20302772773012073-43362011-08-19doi: 10.3390/g2030277Claudia KeserClaude Montmarquette<![CDATA[Games, Vol. 2, Pages 257-276: A Choice Prediction Competition for Social Preferences in Simple Extensive Form Games: An Introduction]]>
http://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.Games2011-07-2523Article10.3390/g20302572572762073-43362011-07-25doi: 10.3390/g2030257Eyal ErtIdo ErevAlvin E. Roth<![CDATA[Games, Vol. 2, Pages 235-256: The Existence of Perfect Equilibrium in Discontinuous Games]]>
http://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.Games2011-07-1523Article10.3390/g20302352352562073-43362011-07-15doi: 10.3390/g2030235Oriol Carbonell-Nicolau<![CDATA[Games, Vol. 2, Pages 209-234: Competing in Several Areas Simultaneously: The Case of Strategic Asset Markets]]>
http://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.Games2011-04-1222Article10.3390/g20202092092342073-43362011-04-12doi: 10.3390/g2020209Manfred Nermuth<![CDATA[Games, Vol. 2, Pages 200-208: Market Entry Prediction Competition 2010]]>
http://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.Games2011-04-1222Commentary10.3390/g20202002002082073-43362011-04-12doi: 10.3390/g2020200Wasilios HariskosJohannes LederKinneret Teodorescu<![CDATA[Games, Vol. 2, Pages 187-199: Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games]]>
http://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.Games2011-03-2121Article10.3390/g20101871871992073-43362011-03-21doi: 10.3390/g2010187Wei ChenShu-Yu LiuChih-Han ChenYi-Shan Lee<![CDATA[Games, Vol. 2, Pages 163-186: A Scent of Lemon—Seller Meets Buyer with a Noisy Quality Observation]]>
http://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.Games2011-03-1821Article10.3390/g20101631631862073-43362011-03-18doi: 10.3390/g2010163Mark VoorneveldJörgen W. Weibull<![CDATA[Games, Vol. 2, Pages 136-162: A Loser Can Be a Winner: Comparison of Two Instance-based Learning Models in a Market Entry Competition]]>
http://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.Games2011-03-1621Article10.3390/g20101361361622073-43362011-03-16doi: 10.3390/g2010136Cleotilde GonzalezVarun DuttTomás Lejarraga<![CDATA[Games, Vol. 2, Pages 114-135: Do I Really Want to Know? A Cognitive Dissonance-Based Explanation of Other-Regarding Behavior]]>
http://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.Games2011-02-1821Article10.3390/g20101141141352073-43362011-02-18doi: 10.3390/g2010114Astrid MattheyTobias Regner<![CDATA[Games, Vol. 2, Pages 87-113: Nonspecific Networking]]>
http://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.Games2011-02-1721Article10.3390/g2010087871132073-43362011-02-17doi: 10.3390/g2010087Jacques DurieuHans HallerPhilippe Solal<![CDATA[Games, Vol. 2, Pages 52-86: Toward a Theory of Play: A Logical Perspective on Games and Interaction]]>
http://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.Games2011-02-1621Article10.3390/g201005252862073-43362011-02-16doi: 10.3390/g2010052Johan Van BenthemEric PacuitOlivier Roy<![CDATA[Games, Vol. 2, Pages 21-51: Intergroup Prisoner’s Dilemma with Intragroup Power Dynamics]]>
http://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.Games2011-02-0821Article10.3390/g201002121512073-43362011-02-08doi: 10.3390/g2010021Ion JuvinaChristian LebiereJolie M. MartinCleotilde Gonzalez<![CDATA[Games, Vol. 2, Pages 16-20: Correlated Individual Differences and Choice Prediction]]>
http://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.Games2011-02-0721Short Note10.3390/g201001616202073-43362011-02-07doi: 10.3390/g2010016Luke Lindsay