Evolutionary Game Method based on QBD for 2×2 Bimatrix Game with Stochastic Payoffs
基于拟生灭过程的随机支付2×2双矩阵博弈演化模型

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.