Theoretical Research On The Alliance Of Punishment Strategy And Exclusive Strategy Can Effectively Promote Cooperation

Recent studies have shown that in the game of public goods,the defection can be effectively resisted and the emergence of cooperation can be promoted by punishing defection,rewarding cooperation,and setting credit labels.Furthermore,the introduction of these new strategies leads to second-order social dilemmas.But it has also been found that punishment strategy and exclusion strategy can form alliances in the population structure of the model in which participants adopt pure strategies and use Fermi dynamics to spontaneously solve the second-order social dilemmas.But these studies were limited to participants using pure strategy and Fermi dynamics.In this paper,we extend the population structure of the model and make the participants in the model have the process of death and birth by combining with the ecological dynamics into the evolutionary game.According to the participants' tendency to usually choose multiple strategies,we assume that the participants adopt the mixed strategies in the model.We built this new particular model of population structure and analyzed the social dilemmas in the new model in contrast to earlier studies.First of all,we found in the classical model,we found that our model was more able to promote the emergence of cooperative phenomena than the Fermi dynamics model,and the system could reach a higher cooperative frequency with a smaller synergy factor.Secondly,when the classical model is introduced into the punishment strategy and the exclusion strategy,it is found in our model that the punishment strategy and the exclusion strategy can still be as effective as in the Fermi dynamics model and can even bear higher costs to eliminate the defection.On the one hand,we found the condition that the punishment strategy and exclusive strategy to form an alliance to effectively eliminate defection are that the punishment strategy and the exclusion strategy with a probability of zero in the mixed strategy of participants can freely increase through mutation(that is,they can form a large number Participants in the mixed strategy have a probability of non-zero punishment and exclusion strategy).On the other hand,although both the basic income and the basic cost can promote the emergence of cooperation by providing a good environment for the alliance of the punishment strategy and the exclusion strategy,the basic cost can only be achieved when the cost borne by the exclusion strategy is not very large.When the exclusion cost is large,although the basic cost can also promote the emergence of cooperation,the cooperation at this time is not caused by the alliance of punishment strategy and exclusive strategy.