Cooperation in a repeated game with random payment function

1988 ◽  
Vol 25 (3) ◽  
pp. 478-491 ◽  
Author(s):  
Ilan Eshel ◽  
Daphna Weinshall
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Rules Of The Game

A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

Cooperation in a repeated game with random payment function

1988 ◽  
Vol 25 (03) ◽  
pp. 478-491
Author(s):  
Ilan Eshel ◽  
Daphna Weinshall
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Rules Of The Game

A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

scholarly journals Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

Games ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 100 ◽  
Author(s):  
Shun Kurokawa ◽  
Joe Yuichiro Wakano ◽  
Yasuo Ihara
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolutionary Model ◽  
Repeated Game ◽  
Evolution Of Cooperation ◽  
Fixation Probability ◽  
Non Linear ◽  
Repeated Prisoner’S Dilemma ◽  
Tit For Tat ◽  
Repeated Prisoner's Dilemma

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects.

scholarly journals Payoff Control in the Iterated Prisoner's Dilemma

2018 ◽  
Author(s):  
Dong Hao ◽  
Kai Li ◽  
Tao Zhou
Keyword(s):  
Prisoner's Dilemma ◽  
Control Strategies ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Feasible Region ◽  
Iterated Prisoner's Dilemma ◽  
Long Run ◽  
Game Player ◽  
New Strategies ◽  
Iterated Prisoner’S Dilemma

Repeated game has long been the touchstone model for agents’ long-run relationships. Previous results suggest that it is particularly difficult for a repeated game player to exert an autocratic control on the payoffs since they are jointly determined by all participants. This work discovers that the scale of a player’s capability to unilaterally influence the payoffs may have been much underestimated. Under the conventional iterated prisoner’s dilemma, we develop a general framework for controlling the feasible region where the players’ payoff pairs lie. A control strategy player is able to confine the payoff pairs in her objective region, as long as this region has feasible linear boundaries. With this framework, many well-known existing strategies can be categorized and various new strategies with nice properties can be further identified. We show that the control strategies perform well either in a tournament or against a human-like opponent.

scholarly journals Cooperation in the Finitely Repeated Prisoner’s Dilemma*

2017 ◽  
Vol 133 (1) ◽  
pp. 509-551 ◽  
Author(s):  
Matthew Embrey ◽  
Guillaume R Fréchette ◽  
Sevgi Yuksel
Keyword(s):  
Prisoner's Dilemma ◽  
Meta Analysis ◽  
Basin Of Attraction ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Backward Induction ◽  
Repeated Prisoner’S Dilemma ◽  
The Subject ◽  
Repeated Prisoner's Dilemma

Abstract More than half a century after the first experiment on the finitely repeated prisoner’s dilemma, evidence on whether cooperation decreases with experience—as suggested by backward induction—remains inconclusive. This article provides a meta-analysis of prior experimental research and reports the results of a new experiment to elucidate how cooperation varies with the environment in this canonical game. We describe forces that affect initial play (formation of cooperation) and unraveling (breakdown of cooperation). First, contrary to the backward induction prediction, the parameters of the repeated game have a significant effect on initial cooperation. We identify how these parameters impact the value of cooperation—as captured by the size of the basin of attraction of always defect—to account for an important part of this effect. Second, despite these initial differences, the evolution of behavior is consistent with the unraveling logic of backward induction for all parameter combinations. Importantly, despite the seemingly contradictory results across studies, this article establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; conditional on establishing cooperation, the first defection round moves earlier with experience. Simulation results generated from a learning model estimated at the subject level provide insights into the long-term dynamics and the forces that slow down the unraveling of cooperation.

scholarly journals Strong and Safe Nash Equilibrium in Some Repeated 3-Player Games

2019 ◽  
Vol 65 (3) ◽  
pp. 271-295 ◽  
Author(s):  
Tadeusz Kufel ◽  
Sławomir Plaskacz ◽  
Joanna Zwierzchowska
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Equilibrium Payoff ◽  
Equilibrium Strategies ◽  
Strong Nash Equilibrium ◽  
Player Game ◽  
Stage Game

The paper examines an infinitely repeated 3-player extension of the Prisoner’s Dilemma game. We consider a 3-player game in the normal form with incomplete information, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage, players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players’ payoffs do not exceed the nondeviating player payoff more than by a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale’s good strategies described in Smale’s paper (1980), where the repeated Prisoner’s Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.

Zu brav oder zu böse? Mobbing-Opfer und Abgelehnte im Prisoner's Dilemma-Paradigma

1999 ◽  
Vol 30 (2/3) ◽  
pp. 179-193 ◽  
Author(s):  
Beate Schuster
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma

Zusammenfassung: Der soziometrische Status und der Viktimisierungsstatus von 5. bis 11. Klässlern wurde ermittelt, der Status hypothetischer InteraktionspartnerInnen sowie deren angebliche Wahlen variiert, und die Reaktionen im Gefangenendilemma erfaßt. Die Reaktionen wurden sowohl durch die experimentell vorgegebenen als auch durch die erwarteten Wahlen der InteraktionspartnerInnen bestimmt: Kooperative Zuege wurden eher kooperativ, und kompetitive Zuege eher kompetitiv beantwortet. Darüber hinaus vermieden Mobbingopfer kompetitive Züge, während zwei Untergruppen der Abgelehnten gegensätzliche Strategiepräferenzen aufwiesen: Versuchspersonen, die sowohl Ablehnung als auch Mobbing erfahren («Viktimisiert-Abgelehnte») verhielten sich besonders kooperativ; abgelehnte ProbandInnen, die nicht viktimisiert werden («Nicht-viktimisiert-Abgelehnte») dagegen vergleichsweise kompetitiv. Die kooperativen Wahlen viktimisierter Versuchspersonen wurden nicht erwidert: Die Versuchspersonen reagierten gegenüber den Viktimisierten kompetitiver als sich die Viktimisierten ihrerseits gegenüber ihren InteraktionspartnerInnen verhielten. Diese Befunde bestätigen die Notwendigkeit, bei «Abgelehnten» zwei Untergruppen auf der Basis der Viktimisierungsdimension zu unterscheiden. Die Befunde werden ferner vor dem Hintergrund der Hypothese diskutiert, daß die Submissivität potentieller Opfer mit zu ihrer Viktimisierungs-Erfahrung beiträgt.

Facial Likability and Smiling Enhance Cooperation, but Have No Direct Effect on Moralistic Punishment

2016 ◽  
Vol 63 (5) ◽  
pp. 263-277 ◽  
Author(s):  
Laura Mieth ◽  
Raoul Bell ◽  
Axel Buchner
Keyword(s):  
Conditional Probability ◽  
Direct Effect ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Prisoner’S Dilemma Game ◽  
Costly Punishment ◽  
Prisoner's Dilemma Game ◽  
Moralistic Punishment

Abstract. The present study serves to test how positive and negative appearance-based expectations affect cooperation and punishment. Participants played a prisoner’s dilemma game with partners who either cooperated or defected. Then they were given a costly punishment option: They could spend money to decrease the payoffs of their partners. Aggregated over trials, participants spent more money for punishing the defection of likable-looking and smiling partners compared to punishing the defection of unlikable-looking and nonsmiling partners, but only because participants were more likely to cooperate with likable-looking and smiling partners, which provided the participants with more opportunities for moralistic punishment. When expressed as a conditional probability, moralistic punishment did not differ as a function of the partners’ facial likability. Smiling had no effect on the probability of moralistic punishment, but punishment was milder for smiling in comparison to nonsmiling partners.

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