【摘要】 引入分位数定义了随机支付值的偏好,并在此偏好的基础上定义带随机支付双矩阵博弈的纳什均衡.建立了有限种群进行带随机支付2×2双矩阵博弈的演化博弈模型,应用有限状态空间的拟生灭过程刻画了在有随机扰动的博弈环境中有限理性个体的学习调整动态,描述了理性演化的不确定性过程,讨论了拟生灭过程的平稳分布与演化模型的长期均衡以及博弈的纳什均衡之间的关系.最后,基于分块矩阵的Guass消去法给出求解模型稳态分布的数值算法,并通过数值实例对演化博弈模型均衡解的实现进行了说明.更多还原

【Abstract】 In this paper,the preferences on stochastic payoffs are defined by quantile,and the Nash equilibrium of the bimatrix game with stochastic payoffs is given base on the preferences.And then,the bimatrix game with stochastic payoffs are modeled as a finite,state dependent quasi birth and death process for describing the adjust dynamic in the game with stochastic perturbation.The relations between the steady-state probabilities of the evolutionary game model and the long run equilibrium as well as Nash equilibrium are discussed also.Furthermore,an efficient numerical method based on block Gaussian elimination is proposed to compute the steady-state probabilities.In particular,some examples and numerical results are given to show the efficiency of this method.更多还原