Multi-Strategy Evolutionary Game On Complex Networks

Evolutionary game theory integrates the achievements of evolutionary biology theory in classical game theory.In the past,the game theory of group evolution is based on the mixed homogeneous group,and the other structured group evolutionary game theory has not been analyzed too much.The aim of this paper is to compare and analyze the group evolutionary game under the two circumstances.At the same time,we consider the participant strategy as the two strategy and the three strategy.First,based on the replication dynamic equation,the mathematical model of the 2×2 and 3×3 symmetric game of the regular network group is established,and its evolution law is analyzed.The similarities and differences between the regular network group and the traditional mixed uniform group evolution are compared and analyzed.It is found that the two groups are almost no difference when the population size is infinitely large,and the scale of the group is almost no difference.When the rule network group and the mixed homogeneous group have the same and different replication dynamic equation singularity,that is,the proportion of the coexistence is different,and the rule network group takes longer time when it reaches the equilibrium.Secondly,based on the "imitation optimal" strategy updating rule,the 2 x 2 and 3 x 3 symmetric game of irregular network groups are studied,and the similarities and differences between the irregular network group and the traditional mixed uniform group evolution are compared and analyzed.It is found that the equilibrium state of the game reached by the two parties is inconsistent under the same condition;at the same time,the irregular network is in the irregular network.When the group reaches the state of coexisting equilibrium,the equilibrium state is not stable but in dynamic change,and the strategy of the node with large degree on the irregular network is more easily adopted by other individuals.At the same time,based on the case simulation of irregular network group 2×2 and 3×3 symmetric game,the difference of group evolution under the two different strategies of "imitation optimal" and Fermi rule is compared and analyzed.It is found that the time of the group reaching equilibrium is faster under the "imitation optimal"rule.