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标题：Evolutionary games on the lattice: death and birth of the fittest
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作者：Eric Foxall ; Nicolas Lanchier
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：271-298
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This paper investigates the long-term behavior of an interacting particlesystem of interest in the hot topic of evolutionary game theory. Each site of the d-dimensional integer lattice is occupied by a player who is characterized by one of twopossible strategies. Following the traditional modeling approach of spatial games,the configuration is turned into a payoff landscape that assigns a payoff to eachplayer based on her strategy and the strategy of her 2d neighbors. The payoff is theninterpreted as a fitness, by having each player independently update their strategyat rate one by mimicking their neighbor with the largest payoff. With these rules,the mean-field approximation of the spatial game exhibits the same asymptoticbehavior as the popular replicator equation. Except for a coexistence result thatshows an agreement between the process and the mean-field model, our analysisreveals that the two models strongly disagree in many aspects, showing in particularthat the presence of a spatial structure in the form of local interactions plays a keyrole. More precisely, in the parameter region where both strategies are evolutionarystable in the replicator equation, in the spatial model either one strategy winsor the system fixates to a configuration where both strategies are present. Inaddition, while defection is evolutionary stable for the prisoner’s dilemma game inthe replicator equation, space favors cooperation in our model.
关键词：Interacting particle systems; evolutionary game theory; evolutionary;stable strategy; replicator equation; prisoner’s dilemma; cooperation.