【作者】 刘晓萍；

【导师】 丁占文；

【作者基本信息】 江苏大学 ， 应用数学， 2009， 硕士

【摘要】 演化博弈理论最重要的基本概念是演化稳定策略(ESS)。ESS能够成功抵御其他变异策略的入侵。另一方面,一个策略是否是种群长期演化选择的结果,也在于其能否在种群演化过程中成功进入。进入者策略是能够成功进入种群的策略,所以长期演化过程中也可能被种群中的个体所采用。本文旨在从抵御入侵与可以进入两个角度分析策略的演化稳定性。本文基于单种群多人矩阵博弈与一类非矩阵博弈模型,讨论演化稳定策略(ESS)、邻域进入者策略(NIS)与全局进入者策略(GIS)三个主要概念,并着重研究了ESS、NIS、GIS的性质及关系,获得了相应的结论。在多人矩阵博弈模型中,GIS一定是ESS;GIS、ESS不能共存,除非策略本身是ESS;GIS具有唯一性;若存在多个ESS则无GIS。二人矩阵博弈中,ESS与NIS等价;GIS是全局优超的,从而在动力系统中是全局渐近稳定的。多人矩阵博弈与二人矩阵博弈有着不同的性质与结论。在非矩阵博弈模型中,具有一定线性性时ESS与NIS等价,并且具有与矩阵博弈相同的性质:GIS一定是ESS;GIS、ESS不能共存,除非策略本身是ESS;GIS具有唯一性;若存在多个ESS则无GIS。最后讨论了策略的可入侵性与不可入侵性,并分别得到可入侵性及不可入侵性在连续、离散动力系统中的等价条件。更多还原

【Abstract】 Evolutionary stable strategy (ESS) is the basic concept of Evolutionary Game Theory. ESS can successfully resist the invasion of other strategy. On the other hand, it is important for a strategy to enter the population occupied by other strategy if it can be the evolutionary stable choice by the population in the long run. Invader strategy is a strategy that be able to invade all established communities, so it also can be adopted by the individuals of population in the long run. We analyze the evolutionary stability from two aspects: resisting the invasion of other strategy and successfully invading the population.In this paper, we discuss the concepts of evolutionary stable strategy (ESS), neighborhood invader strategy (NIS) and global invader strategy (GIS) in matrix game and a kind of non-matrix game. The main content is the properties of ESS, NIS,GIS and relationship among them, hence some correspond conclusions.In multi-player matrix game, we show that: a GIS is always an ESS; a GIS cannot coexist with an ESS unless it is itself an ESS; If a GIS exists, then it is unique; If there is more than one ESS, then there are no GIS. We also get the conclusion that in a pair wise game MS is equivalent to ESS, GIS is globally superior and it is globally asymptotically stable in the dynamics of duplicator. Also, there are some results in multi-player games different from those in pair wise games.In non-matrix game, NIS is equivalent to ESS on the assumption that the payoff is linear. And we get the same properties as multi-player matrix game: a GIS is always an ESS; a GIS cannot coexist with an ESS unless it is itself an ESS; if a GIS exists, then it is unique; if there is more than one ESS, then there are no GIS.Finally, we discuss the invasion and non-invasion of the strategy, and get the equivalent conditions of the invasion and non-invasion in continuous-time dynamic and discrete-time dynamic.更多还原