Long-run cooperation in the one-shot Prisoner's Dilemma: A hierarchic evolutionary approach

Abstract We study the effects of ambiguity on long-run cooperation in infinitely repeated strategic games. Using a simple parametric model of ambiguity, we study conditions for sustaining cooperative equilibria in the long-run. We apply our framework to the prisoner’s dilemma and duopoly models. We find that (i) ambiguity may affect the game’s structure eventually making the noncooperative equilibrium ex ante preferred; (ii) higher levels of ambiguity make long-run cooperation less likely since it makes punishment schemes less effective; and (iii) large levels of ambiguity may preclude the possibility of mutually beneficial long-run agreements, even when cooperation is beneficial from an ex ante perspective.

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Evolutionary prisoner's dilemma games with one-dimensional local interaction and imitation

Advances in Applied Probability ◽

10.1239/aap/1240319580 ◽

2009 ◽

Vol 41 (1) ◽

pp. 154-176 ◽

Cited By ~ 3

Author(s):

Hsiao-Chi Chen ◽

Yunshyong Chow

Keyword(s):

Convergence Rate ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Local Interaction ◽

One Dimensional ◽

Long Run ◽

Action Dynamics ◽

The Impact ◽

Full Cooperation ◽

Long Run Equilibrium

In this paper we explore the impact of imitation rules on players' long-run behaviors in evolutionary prisoner's dilemma games. All players sit sequentially and equally spaced around a circle. Players are assumed to interact only with their neighbors, and to imitate either their successful neighbors and/or themselves or the successful actions taken by their neighbors and/or themselves. In the imitating-successful-player dynamics, full defection is the unique long-run equilibrium as the probability of players' experimentations (or mutations) tend to 0. By contrast, full cooperation could emerge in the long run under the imitating-successful-action dynamics. Moreover, it is discovered that the convergence rate to equilibrium under local interaction could be slower than that under global interaction.

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Social surplus determines cooperation rates in the one-shot Prisoner's Dilemma

Games and Economic Behavior ◽

10.1016/j.geb.2016.08.010 ◽

2016 ◽

Vol 100 ◽

pp. 113-124 ◽

Cited By ~ 17

Author(s):

Gary Charness ◽

Luca Rigotti ◽

Aldo Rustichini

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Social Surplus ◽

The One

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A Non-Cooperative Pareto-Efficient Solution to the One-Shot Prisoner’s Dilemma

SSRN Electronic Journal ◽

10.2139/ssrn.1831969 ◽

2011 ◽

Author(s):

Haoyang Wu

Keyword(s):

Efficient Solution ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Pareto Efficient ◽

The One

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The Effect of Incentives: The Value of Reputation

10.1093/oso/9780190076559.003.0007 ◽

2021 ◽

pp. 99-118

Author(s):

Jason Brennan ◽

William English ◽

John Hasnas ◽

Peter Jaworski

Keyword(s):

Game Theory ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Moral Goodness ◽

Long Run ◽

Self Interest ◽

Reputation Effects

It is useful to model the temptation to act wrongly using the prisoner’s dilemma, one of the most important games in game theory. The prisoner’s dilemma appears to show that the pursuit of self-interest can paradoxically lead to situations in which everyone makes choices they know will undermine their self-interest. However, introducing the possibility of repeated, self-sorting prisoner’s dilemmas with reputation effects reveals something important about the connection between self-interest and morality: We have strong incentives not to cheat because in the long run, we do best by developing the reputation for being honest. However, unfortunately, this also introduces an incentive to exaggerate our moral goodness and to engage in moral grandstanding.

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THE DIVERSITY IN THE DECISION FACILITATES COOPERATION IN THE SEQUENTIAL PRISONER'S DILEMMA GAME

Advances in Complex Systems ◽

10.1142/s0219525911002962 ◽

2011 ◽

Vol 14 (03) ◽

pp. 377-401 ◽

Cited By ~ 8

Author(s):

TETSUSHI OHDAIRA ◽

TAKAO TERANO

Keyword(s):

Decision Making ◽

Prisoner's Dilemma ◽

Conflicts Of Interest ◽

Prisoner’S Dilemma ◽

Prisoner’S Dilemma Game ◽

Mutual Cooperation ◽

Prisoner's Dilemma Game ◽

Novel Method ◽

The One ◽

High Level

The condition of cooperation in social conflicts of interest has been an interesting topic. On the one hand people usually desire to make their own profit. On the other hand, they mutually cooperate. This fact has motivated many researchers. Some solutions for this question have been proposed, and particular studies indicate that the diversity in decision-making or relationships promotes cooperation. In this research, we achieve the diversity by utilizing the novel method that refers to the mechanism of correction regarding each probability that every strategy comes to the representative by decision-making of group. This mechanism works when difference between the probability of the first and others becomes quite large. If once every group adopts this corrected decision, he/she achieves mutual cooperation of high level in the sequential prisoner's dilemma game in case the number of strategies (= players) is within the definite range. We also note that this game can effectively describe the property of evolution of strategy only with a small number of players. When each group has many players, in contrast to previous research, the decision with correction also has an effect on the suppression of prevalence of defection. In addition, we also show that the decision of this model is analogous to the system of redistribution of revenue, which provides balance of strength between several teams in professional sports.

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Temptation to Defect May Promote Cooperation in Prisoner’s Dilemma Game

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.602-605.3783 ◽

2014 ◽

Vol 602-605 ◽

pp. 3783-3786 ◽

Cited By ~ 1

Author(s):

Qiu Hui Pan ◽

Jia Lin Jia ◽

Kun Jiang ◽

Ming Feng He

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Time Step ◽

Prisoner’S Dilemma Game ◽

Prisoner's Dilemma Game ◽

The One

In this paper, basing on the prisoner’s dilemma model proposed by M.A.Nowak, we present a model to research the action of temptation to defect in prison’s dilemma model. Firstly, we determine whether a player changes its strategy depends on a Fermi equation which is related to the payoffs of the player and its neighbors. If the player changes its strategy next time step, it will select the strategy adopted by the one who gets the highest payoff among its neighbors as its own strategy. Form the results we find that when four neighbors are considered, the density of cooperators will present a downtrend. Well, when eight neighbors are considered, the density of cooperators will decline at the beginning and increase suddenly afterwards. When twelve neighbors are considered, if the density of cooperators is reduced to zero, cooperation will appear again. Thus, the increase of temptation to defect may promote cooperation.

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Note on Howard's Theory of Meta-Games

Psychological Reports ◽

10.2466/pr0.1969.24.3.849 ◽

1969 ◽

Vol 24 (3) ◽

pp. 849-850 ◽

Cited By ~ 7

Author(s):

Richard J. Harris

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Prisoner’S Dilemma Game ◽

Prisoner's Dilemma Game ◽

The One

The logic of Nigel Howard's theory of meta-games, hailed by Anatol Rapoport as providing a normative solution to the one-play Prisoner's Dilemma game, actually applies only to a refereed version of that game.

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