Evolutionary Game Model of 2 × 2 Stochastic Bimatrix Game based on Quasi Birth and Death Process

In this article, the preferences for stochastic payoffs are defined by quantile, and the definition of Nash equilibrium of the stochastic bimatrix game is given based on the preferences. Then the bimatrix game with stochastic payoffs is modeled as a finite, state-dependent quasi birth and death process, to describe the adjust dynamic in the game, with perturbations. The relations between the steady-state probabilities of the quasi birth and death process and Nash equilibrium are discussed by the evolutionary game model. In addition, an efficient numerical method based on block Gaussian elimination is proposed to compute the steady-state probabilities, and some examples as well as numerical results are given to prove its efficiency.