A Research Of Zero-Determinant Strategies Based On The Snowdrift Game

In the past half century,game theory has been widely used in many fields as an effective tool to explore the interaction between individuals.Researchers have found that the existence of zero-determinnat strategies for the prisoner’s dilemma game in 2012,which can unilaterally enforce the long-term payoffs of both players to achieve a linear relationship.Unlike the prisoner’s dilemma,the snowdrift game as a classical model in game theory,which has two kinds of pure Nash equilibrium,and cooperation is more likely to exist in it.Therefore,the snowdrift game is worth to be studied both in theoretical research and in pratical applications.This paper studied the zero-determinant strategies and its expansion strategies based on the snowdrift game,and systematically researches the zero-determinant strategies in the snowdrift game with two-player,multiplayer and arbitrary action space cases.1)Based on the two-player snowdrift game,the special properties of equalizer strategies,extortion strategies and generosity strategies are studied.It is proved that the existence and parameters’ feasible regions of zero-determinant strategies in the two-player snowdrift game.We also research the good strategies and robust strategies in the two-player snowdrift game,after expanded the Press-Dyson vector into three-dimensional space,we find the good strategies and robust strategies,which are subset of good strategies.We have obtained the method of the good strategies and the conditions for the existence of robust zero-determinant strategies in the snowdrift game.2)We extend the two-player snowdrift game to the cases of multiplayer and arbitrary action space.The basic properties of the zero-determinant strategies in the multiplayer snowdrift game are researched,and the relationships among the parameters’ feasible regions of three important subsets of zero-determinant strategies,the population size and the payoff table have been found.We prove that after expanded the definition of zero-determinant strategies into high order differential form,the zero-determinant strategies are existed in snowdrift game with arbitrary action space cases,and obtained the feasible regions of its parameters.3)We have compared the research results of this paper with the existed results in the prisoner’s dilemma,we find that the parameters’ feasible regions of extortion strategies in the snowdrift game are always smaller than the regions of extortion strategies in the corresponding prisoner’s dilemma,and there are no greedy extortion strategies in the snowdrift game.We also explained the reason for the decrease of parameters’ feasible regions of good strategies in the snowdrift game.