When is tit-for-tat unbeatable?

Duersch, Peter; Oechssler, Jörg; Schipper, Burkhard C.

doi:10.1007/s00182-013-0370-1

Cited by 29 publications

(24 citation statements)

References 24 publications

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“…This implies that conformity can help to avoid inequality between the two players [ 44 – 45 ]. In particular, when one of p 1 and p 2 equals to 1, | E ( S 1 )− E ( S 2 )| must be less than T − S , which is the maximal payoff difference between outcomes in the one-shot PD game [ 10 , 11 ]. However, when p 1 + p 2 = 0, the payoff difference between the two players is linearly increasing in , where the player with higher initial cooperative level is exploited by the other.…”

Section: Resultsmentioning

confidence: 99%

Evolution of Conformity in Social Dilemmas

et al. 2015

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People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner’s dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious “dominant” strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals’ strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players’ choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.

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Section: Resultsmentioning

confidence: 99%

Evolution of Conformity in Social Dilemmas

et al. 2015

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“…For instance in Axelrod's tournament, the dominating strategy (Tit-fortat) was not the most complex of all the proposed strategies (Axelrod, 1980). Further, research in economics also indicate that repeated games and social interactions do not always select for more complex strategies, and these results were obtained either by taking into account explicitly the costs of cognitive complexity (Binmore & Samuelson, 1992) or, more recently, in the absence of such costs (Duersch, Oechssler, & Schipper, 2014;Horv ath, Kov a rík, & Mengel, 2012;Mohlin, 2012). All this suggests that it is relevant to try to characterize the type of games species are playing in nature (or the social problems they face), in order to characterize the real demands on social cognition.…”

Section: Evolutionary Paths To Increased Cognitionmentioning

confidence: 99%

A model for the evolution of reinforcement learning in fluctuating games

Dridi

Lehmann

2015

Animal Behaviour

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Keywords: evolution of cognition evolutionarily stable learning rules explorationeexploitation trade-off repeated games social interactions trial-and-error learning Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

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“…For instance, Duersch, Oechssler, and Schipper (2012) characterize the class of symmetric two-player games in which imitate-if-better cannot be beaten by any other decision rule no matter how sophisticated. Similarly, Duersch, Oechssler, and Schipper (2014) show that in symmetric two-player game tit-for-tat cannot be beaten by any other decision rule if and only if the game is an exact potential game. Another paper related to our work is Ellison (1997), who analyzes a large population which besides of players following a version of fictitious play also contains a single rational player.…”

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confidence: 87%

“…Their focus is on estimating such learning models with experimental data. There are only a few theoretical papers on learning in games in which players follow different learning theories (Banerjee and Weibull, 1995 Schipper, 2012Schipper, , 2014. They focus on the evolutionary selection or relative success of different boundedly rational learning rules.…”

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confidence: 99%

Strategic Control of Myopic Best Reply in Repeated Games

Schipper

2011

SSRN Journal

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How can a rational player strategically control a myopic best reply player in a repeated two-player game? We show that in games with strategic substitutes or strategic complements the optimal control strategy is monotone in the initial action of the opponent, in time periods, and in the discount rate. As an interesting example outside this class of games we present a repeated "textbook-like" Cournot duopoly with non-negative prices and show that the optimal control strategy involves a cycle.

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When is tit-for-tat unbeatable?

Cited by 29 publications

References 24 publications

Evolution of Conformity in Social Dilemmas

Evolution of Conformity in Social Dilemmas

A model for the evolution of reinforcement learning in fluctuating games

Strategic Control of Myopic Best Reply in Repeated Games

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