A Kind Of Stochastic Repeated Games Base On Memory One Strategy

The behavior of cooperation among individuals has always been the most concerned topics in evolutionary game theory.As one of the effective mechanisms to promote cooperating,it is necessary to study the repeated games.The game among individuals in real world is subject to many factors,so it is meaningful to further study the memory-one strategies in the iterated prisoner's dilemma,the repeated snowdrift games and the public goods in this thesis.The first chapter of our paper mainly introduces the research background of zero-determinant strategy in repeated games and some preliminary knowledge about evolutionary dynamics and zero-determinant strategy.In the second chapter,we discuss the evolution of memory-one strategies in finitely repeated games.Based on the Moran process of the well-mixed population,death-birth and birth-death updating on cycle graphs,we study the evolutionary dynamics of the individuals who use memory-one strategy.Then based on the three special strategies,we derive the conditions that selection opposes the fixation of the invading individual,and the conditions for the strategy to be risk-dominant.We mainly discuss the zero-determinant strategy in iterated snowdrift games in the third chapter.Firstly,based on the snowdrift games with penalty behavior,we calculate the feasible region of zero-determinant strategy in infinitely repeated games.Then we study the feasible region of a special zero-determinant strategy in finitely repeated games.In the fourth chapter,based on the public goods,we mainly discuss the zero-determinant strategy in finitely repeated games.We derive the general conditions for the existence of zero-determinant strategy.Then we obtain the feasible region of the pinning strategy and extortion strategy.The fifth chapter presents the conclusion of our thesis,and points out the directions of further study.