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Some Analytical Properties of the Model for Stochastic evolutionary Games in Finite Populations with Non-uniform Interaction Rate

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Communications in Theoretical Physics 2013年第7期60卷 37-47页

作者： QUAN Ji WANG Xian-Jia GuangDong Electric Power Design Institute China Energy Engineering Group Co. Ltd Guangzhou 510663 China Department of Management and Economics Tianjin University Tianjin 300072 China Institute of Systems Engineering Wuhan University Wuhan 430072 China School of Economics and Management Wuhan University Wuhan 430072 China

Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, 'The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations.' In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to

关键词： stochastic evolutionary games non-uniform interaction rate finite population evolutionary stablestate

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