Research On Evolutionary Dynamics Of Stochastic Game Based On Memory-two Strategy

Cooperation phenomenon is widespread in social and biological systems.Under-standing the evolutionary dynamics of cooperation can provide insights for overcoming social dilemmas and optimizing multi-agent systems.Evolutionary game theory provides a powerful theoretical framework for the dynamic interaction of strategies between in-dividuals,and has always attracted the attention of researchers in the fields of biology,mathematics,social sciences,and computer science.Traditionally,evolutionary games mainly study the unchanging game environment.In recent years,researchers have paid more and more attention to the changes of the game environment.In the existing research,only the one-shot games are considered.The game environment determines the change of individual decision-making,but it is impossible to explore the evolution process of the mutual influence between individual decision-making and the game environment in the long-term game.For this reason,in recent years,a research framework that com-bines stochastic game and evolutionary game theory has been proposed.Considering the individual use memory-one strategy,research has shown that the interaction between in-dividual behavior and the environment can provide an effective mechanism to improve cooperative behavior.Based on stochastic game and evolutionary game theory,this the-sis discusses the evolutionary dynamics of individuals in a stochastic game based on the memory-two strategy in a population containing four classic strategies:ALLC,ALLD,WSLS,and TFT.This thesis considers a stochastic game of 2 × 2 games with two different returns.Firstly,study the evolution of the state-independent deterministic stochastic game in which the two game models are both the prisoner's dilemma type game.The study found that un-der a reasonable mechanism,the stochastic game based on the memory-two strategy can promote the emergence of cooperation,and produce a higher rate of stable cooperation than the stochastic game based on the memory-two strategy.In addition,the impact of important system parameters(such as payoff matrix,learning rate,error rate,population size)on evolution is further analyzed.The results show that the cooperative advantage of the stochastic game based on the memory-two strategy is robust under these parame-ters.Then I found that in the stochastic game,there are multiple state transition rules that enable individuals to escape the prisoner's dilemma,promote the emergence of coopera-tion,and provide effective methods for designing reasonable mechanisms and promoting cooperative behavior.Further analysis found that when the rewards for cooperative be-havior become larger and larger,the stable cooperation rate also becomes larger and larger,and the success of the WSLS strategy or the ALLC strategy is strongly correlated with the improvement of the group's cooperative behavior.Secondly,this thesis studies the evolution of the state-independent deterministic stochas-tic game with two game models of different game types.Consider the low-yield game model as the prisoner's dilemma game,and the high-yield game model as the snowdrift game or the deer hunting game.The results of this thesis show that the stochastic game can also improve and maintain the cooperative behavior of the population.Subsequently,we change the payoff parameters of the high-yield game model,and explore the dynamic evo-lution relationship between the evolution of cooperation in the population and the payoff parameters and the transition rules.The study found that when the transition rules satisfy the high-frequency cooperative behavior and can be transferred to the high-yield game,the cooperative behavior of the population can be effectively improved.At this time,if the payoff parameters satisfy the deer hunting game or the harmony game,individuals tend to cooperate fully;If the payoff parameters meet the prisoner's dilemma game or the snowdrift game,when the transition rule imposes a certain penalty on the betrayal,it will also produce a high cooperation rate.Finally,the evolution of two specific probabilistic state transition stochastic game models is studied.And the results show that as long as the cooperative behavior is trans-ferred to a high-yield environment with a certain probability,the cooperative behavior can be significantly improved.