Stochastic Game Dynamics On Typical Networks

Stochastic game has been an important research aspect on game theory in recent years.In the real world,individuals' actions affect the game environment,which in turn,impacts the actions taken by its members.For further research on stochastic game,we study the interaction between the game states and strategies,which based on a stochastic game model on lattice networks.In this model,the interaction between individuals is determined by lattice networks.The game environment switches among multiple game states with some rules,which are determined by the individuals' actions.Individuals who help each other induce a more favorable game environment.As a solid theoretical foundation,evolutionary game theory is widely used to study the dynamic game environment.The combination of stochastic game theory and evolutionary game theory,we study the strategies' dynamics on lattice networks and the corresponding mechanisms that promote the evolution of specific strategies.In addition,we also study the assortment mechanism based on strategies and exclusion mechanism in the evolution of cooperation.The main results of this paper are as follows:1.We introduce the assortment mechanism in finite population to explore the influence of this mechanism on cooperation under different benefits.The results show that as long as the degree of assortment is strong enough,the level of cooperation can be significantly improved,and the individuals with high cooperativeness can occupy the whole group.The benefit function does not affect this result,but affects the distribution of the strategy.The growth rate of the benefit curve affects the peak of the strategy distribution curve,and determines the best response strategy.In order to verify the effectiveness of the assortment mechanism,we introduce the evaluation mechanism based on the weighted value of the strategy distribution.Through the verification of the evaluation mechanism,it further proves that the proposed assortment mechanism can promote the emergence of cooperation.2.We introduce the two exclusion mechanisms in the finite population to explore the influence of "many-to-one" and "one-to-one" exclusion mechanism on the evolution of cooperation.The results show that both of the two exclusion mechanisms can effectively weaken the competitiveness of defection and promote the evolution of cooperation.In low exclusion cost,peer exclusion is better than pool exclusion.Otherwise,the pool exclusion mechanism prevails.3.We introduce stochastic game on lattice networks to study the competitiveness of memory-one strategies.In single-state prisoner's dilemma games,when the benefit is high enough,the network can isolate and slow down the competition among the strategies,so that the cooperation can emerge and maintain.This effect of network on population results in a variety of stable evolutionary states: one dominated strategy,or multiple dominated strategies,or multiple coexistence strategies in a statistical sense.Stochastic game is introduced into the structural population,and it is found that this introduction enhances the advantage of "win-stay,lose-shift",which occupies the highest distribution.With numerical simulation,we give the benefit region of cooperation emergence and explore the dependencies between the cooperation and "win-stay,lose-shift".