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Games, Volume 6, Issue 3 (September 2015), Pages 175-393

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Research

Open AccessArticle What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma
Games 2015, 6(3), 175-190; doi:10.3390/g6030175
Received: 4 April 2015 / Revised: 1 June 2015 / Accepted: 8 June 2015 / Published: 25 June 2015
Cited by 5 | PDF Full-text (210 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
Open AccessArticle The Loser’s Bliss in Auctions with Price Externality
Games 2015, 6(3), 191-213; doi:10.3390/g6030191
Received: 21 April 2015 / Revised: 24 June 2015 / Accepted: 24 June 2015 / Published: 3 July 2015
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Abstract
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
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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. Full article
(This article belongs to the Special Issue Experimental Studies of Social Dilemma Games) Printed Edition available
Open AccessArticle Fairness and Trust in Structured Populations
Games 2015, 6(3), 214-230; doi:10.3390/g6030214
Received: 5 June 2015 / Revised: 11 July 2015 / Accepted: 13 July 2015 / Published: 20 July 2015
Cited by 4 | PDF Full-text (658 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
Open AccessArticle The Evolvability of Cooperation under Local and Non-Local Mutations
Games 2015, 6(3), 231-250; doi:10.3390/g6030231
Received: 23 May 2015 / Revised: 17 July 2015 / Accepted: 17 July 2015 / Published: 23 July 2015
Cited by 3 | PDF Full-text (1459 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
Open AccessArticle Unfazed by Both the Bull and Bear: Strategic Exploration in Dynamic Environments
Games 2015, 6(3), 251-261; doi:10.3390/g6030251
Received: 8 July 2015 / Revised: 10 August 2015 / Accepted: 12 August 2015 / Published: 18 August 2015
Cited by 1 | PDF Full-text (1031 KB) | HTML Full-text | XML Full-text
Abstract
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.,
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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. Full article
(This article belongs to the Special Issue Psychological Aspects of Strategic Choice)
Open AccessArticle Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation
Games 2015, 6(3), 262-272; doi:10.3390/g6030262
Received: 2 July 2015 / Revised: 13 August 2015 / Accepted: 14 August 2015 / Published: 18 August 2015
Cited by 3 | PDF Full-text (504 KB) | HTML Full-text | XML Full-text
Abstract
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;
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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. Full article
(This article belongs to the Special Issue Psychological Aspects of Strategic Choice)
Figures

Open AccessArticle Bargaining over Strategies of Non-Cooperative Games
Games 2015, 6(3), 273-298; doi:10.3390/g6030273
Received: 22 June 2015 / Revised: 10 August 2015 / Accepted: 17 August 2015 / Published: 31 August 2015
Cited by 1 | PDF Full-text (2003 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Bargaining Games)
Open AccessArticle Stable Sampling Equilibrium in Common Pool Resource Games
Games 2015, 6(3), 299-317; doi:10.3390/g6030299
Received: 4 June 2015 / Revised: 19 August 2015 / Accepted: 26 August 2015 / Published: 31 August 2015
Cited by 2 | PDF Full-text (259 KB) | HTML Full-text | XML Full-text
Abstract
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
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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. Full article
(This article belongs to the Special Issue Experimental Studies of Social Dilemma Games) Printed Edition available
Open AccessArticle Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure
Games 2015, 6(3), 318-346; doi:10.3390/g6030318
Received: 2 June 2015 / Accepted: 21 August 2015 / Published: 7 September 2015
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Abstract
In this paper, we deduce a condition for a strategy S1 to be more abundant on average at equilibrium under weak selection than another strategy S2 in a population structured into a finite number of colonies of fixed proportions as the population size
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In this paper, we deduce a condition for a strategy S1 to be more abundant on average at equilibrium under weak selection than another strategy S2 in a population structured into a finite number of colonies of fixed proportions as the population size tends to infinity. It is assumed that one individual reproduces at a time with some probability depending on the payoff received in pairwise interactions within colonies and between colonies and that the offspring replaces one individual chosen at random in the colony into which the offspring migrates. It is shown that an expected weighted average equilibrium frequency of S1 under weak symmetric strategy mutation between S1 and S2 is increased by weak selection if an expected weighted payoff of S1 near neutrality exceeds the corresponding expected weighted payoff of S2. The weights are given in terms of reproductive values of individuals in the different colonies in the neutral model. This condition for S1 to be favoured by weak selection is obtained from a strong migration limit of the genealogical process under neutrality for a sample of individuals, which is proven using a two-time scale argument. The condition is applied to games between individuals in colonies with linear or cyclic dominance and between individuals belonging to groups represented by subsets of a given set. Full article
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
Open AccessArticle Bargaining Mechanisms for One-Way Games
Games 2015, 6(3), 347-367; doi:10.3390/g6030347
Received: 1 June 2015 / Revised: 20 August 2015 / Accepted: 27 August 2015 / Published: 8 September 2015
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Abstract
We introduce one-way games, a two-player framework whose distinguishable feature is that the private payoff of one (independent) player is determined only by her own strategy and does not depend on the actions taken by the other (dependent) player. We show that the
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We introduce one-way games, a two-player framework whose distinguishable feature is that the private payoff of one (independent) player is determined only by her own strategy and does not depend on the actions taken by the other (dependent) player. We show that the equilibrium outcome in one-way games without side payments and the social cost of any ex post efficient mechanism can be far from the optimum. We also show that it is impossible to design a Bayes–Nash incentive-compatible mechanism for one-way games that is budget-balanced, individually rational and efficient. To address this negative result, we propose a privacy-preserving mechanism based on a single-offer bargaining made by the dependent player that leverages the intrinsic advantage of the independent player. In this setting the outside option of the dependent player is not known a priori; however, we show that the mechanism satisfies individual rationality conditions, is incentive-compatible, budget-balanced and produces an outcome that is more efficient than the equilibrium without payments. Finally, we show that a randomized multi-offer extension brings no additional benefit in terms of efficiency. Full article
(This article belongs to the Special Issue Bargaining Games)
Open AccessArticle Alleviation and Sanctions in Social Dilemma Games
Games 2015, 6(3), 368-380; doi:10.3390/g6030368
Received: 29 June 2015 / Revised: 14 September 2015 / Accepted: 16 September 2015 / Published: 21 September 2015
PDF Full-text (403 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
This paper reports an experiment which compares behaviour in two punishment regimes: (i) a standard public goods game with punishment in which subjects are given the opportunity to punish other group members (democratic punishment regime) and (ii) a public goods game environment where
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This paper reports an experiment which compares behaviour in two punishment regimes: (i) a standard public goods game with punishment in which subjects are given the opportunity to punish other group members (democratic punishment regime) and (ii) a public goods game environment where all group members exogenously experience an automatic reduction of their income (irrespective of their behaviour) and are given the opportunity to alleviate the automatic penalty (undemocratic punishment regime). We employ a within-subjects design where subjects experience both environments and control for order effects by alternating their sequence. Our findings indicate that average contributions and earnings in the undemocratic punishment environment are significantly lower relative to the standard public goods game with punishment. We also observe that in the undemocratic environment average contributions decay over time only when subjects have experienced the standard public goods game with punishment. As a result, alleviation is significantly less when subjects have experienced the standard public goods game with punishment compared to when they do not have such experience. However, the assignment of punishment is robust irrespective of the order in which the games are played. Full article
(This article belongs to the Special Issue Experimental Studies of Social Dilemma Games) Printed Edition available
Open AccessArticle Representing Others in a Public Good Game
Games 2015, 6(3), 381-393; doi:10.3390/g6030381
Received: 6 July 2015 / Revised: 14 September 2015 / Accepted: 16 September 2015 / Published: 21 September 2015
Cited by 1 | PDF Full-text (392 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
In many important public good situations the decision-making power and authority is delegated to representatives who make binding decisions on behalf of a larger group. The purpose of this study is to compare contribution decisions made by individuals with contribution decisions made by
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In many important public good situations the decision-making power and authority is delegated to representatives who make binding decisions on behalf of a larger group. The purpose of this study is to compare contribution decisions made by individuals with contribution decisions made by group representatives. We present the results from a laboratory experiment that compares decisions made by individuals in inter-individual public good games with decisions made by representatives on behalf of their group in inter-group public good games. Our main finding is that contribution behavior differs between individuals and group representatives, but only for women. While men’s choices are equally self-interested as individuals and group representatives, women make less self-interested choices as group representatives. Full article
(This article belongs to the Special Issue Experimental Studies of Social Dilemma Games) Printed Edition available
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