Modeling Of Multi-person Stag Hunt Game And Analyzing Of The Evolutionary Dynamics Of Cooperation

In recent years,how cooperative behavior emerges and is maintained in a multiperson interactive group has attracted widespread attention from scholars in the fields of mathematics,complex networks,computer science,biology,economics,and sociology.Although there has been a lot of study on the evolutionary dynamics of cooperation of multi-person games,there are few researches in the multi-person stag hunt game.Therefore,this thesis establishes a multi-person stag hunt game model based on the two-person stag hunt and studies the evolutionary dynamics of cooperation of the model under different frameworks.The main work and research results of this thesis are as follows:Firstly,in the infinite well-mixed population,the evolutionary dynamics of cooperation in the multi-person stag hunt game is studied by using replicator equation,and it is found that there always exists only one interior equilibrium which is unstable.The result is not affected by changing the threshold,the payoff of hare hunter,and the group size.These results have also been verified through numerical simulations.In the infinite well-mixed population,the evolutionary dynamics of cooperation of the positive correlation multi-person stag hunt game and the negative correlation multi-person stag hunt game are also studied through numerical simulations.The study finds that there also exists only one unstable interior equilibrium in the two multi-person stag hunt game models.The result remains valid by changing some parameters.It is shown that the evolutionary dynamics of cooperation of the multi-person stag hunt game is robust in the infinite well-mixed population.Secondly,this thesis investigates the game in finite well-mixed populations by applying pairwise comparison updating rule,and observes that the equation of gradient of selection always has a unique interior root,which is consistent with the finding in infinite populations.The result is not affected by changing the parameters.The evolutionary dynamics of cooperation in the two multi-person stag hunt games are also studied in the finite population.The research results show that these two systems also have an internal root,and the existence of internal root is not changed with the change of parameters.It is found that the evolutionary dynamics of cooperation in the multi-person stag hunt game is robust in the finite population.Finally,this thesis uses the network structure to describe the interactions in the multi-person stag hunt game in the structured population,and studies the evolutionary dynamics of cooperation of the multi-person stag hunt game under pairwise comparison updating rule by means of the pair approximation approach.When the threshold is equal to the number of the group,by means of theoretical analysis and numerical simulations,it is found that the evolutionary dynamics of cooperation in the multi-person stag hunt game are affected by the ratio of the payoff of the successful stag hunter to the payoff of the hare hunter.There are three evolutionary outcomes,namely,stag hunters occupy the entire population,hare hunters occupy the whole population,and there is an internal unstable equilibrium in the system.Furthermore,this thesis also analyzes the evolutionary dynamics of cooperation in the game when the threshold is less than the number of the group through numerical simulations.It is shown that the results in this case are the same as those in the previous case.