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The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's… (More)

This note characterizes the impact of adding rare stochastic mutations to an " imitation dynamic, " meaning a process with the properties that any state where all agents use the same strategy is absorbing, and all other states are transient. The work of Freidlin and Wentzell [10] and its extensions implies that the resulting system will spend almost all of… (More)

In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash equilibria correspond to stable fixed points that are always evolutionarily stable. However, in finite populations… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Abstract We analyze a class of imitation dynamics with mutations for games with any… (More)

Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of… (More)

The repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the opponent has defected. But TFT has two weaknesses: (i) it cannot… (More)

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be… (More)

Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy.… (More)