Research On Delayed Replicator Dynamics Based On Matrix Games

Evolutionary game dynamics is an important theoretical tool to study finite rational problems in games,and the most common method is using replicator equation to describe the game model.It is practical consideration to study the influence of the delay factors and mutation mechanism on the replicator dynamics behavior for studying the problem of the game.This paper study the dynamics behavior of the replicator dynamics system is based on the classical asymmetric sex game model,the generalized asymmetric sex game model and the three strategies cyclic dominant game model,and the main work can be divided into the following three parts.In the first part,the delay replicator dynamics system based on the classical asymmetric sex game model,analyzing the influence of different fixed delays in both game players on replicator dynamics behavior.The results show that the fixed delay does not affect the stability of the equilibrium point of the replicator dynamics system,but it is found by numerical simulation analysis the fixed delay slows the rate at which the system reaches the stability state in contrast to the no delay case.And when both game players are affected by the delay,it will accelerate the rate of the strategy evolution to the strategy stable state if the delay time is long.In the second part,this part analyzes the dynamics behavior of the delay replicator dynamics system based on the generalized asymmetric sex game model.In the case of random distributed delay and different fixed delay in both game players,discussing the stability influence of the intermediate evolutionary stability strategy of the delay in group,the delay between group and the mixed delay in replicator dynamics system.Then the stability conditions of intermediate evolutionary stability strategy is asymptotically stable are derived.In the third part,the delay replicator dynamics system based on the three strategies cyclic dominant game model,modeling the three strategies cyclic dominant game model with the global mutation mechanism or the single mutation mechanism respectively.Analyzing the effect of stability to the internal equilibrium points of the delayed replicator dynamics system for the different mutation mechanisms.The results show that the delay can change the dynamics behavior of replicator dynamics system with different mutation mechanisms.Then the stability of the internal equilibrium point of the delayed replicator dynamics system is analyzed by different mutational mechanisms through numerical simulations.