Natural selection bet ween two games with environmentai feedback

Evolutionary game theory has extensively investigated situations in which several gamesare competing against each other at the same time,but the model only assumes sym-metric interactions in homogeneous environments.Now,the population is consideredin heterogeneous environments,individuals in the population occupy a different qualityof patches,and individual fitness depends not only on the interaction between individ-uals,but also on the quality of the environment.Here,by establishing a mathemati-cal framework,we analyze the natural selection between two strategies and two gamesin heterogeneous environments.Furthermore,we analyze the natural selection of Pris-oner's Dilemma and Hawk-Dove games theoretically to demonstrate the dynamics ofcooperators and defectors in their choice of environment and their respective games.Asexpected,the distribution of games and strategies changes with time.Based on differentinitial population compositions,we also discuss the invasion problem of games from dif-ferent perspectives.To one's surprise,we can find that good quality patches attract allindividuals;the long-term dynamics in invariant rich environments is the same as thedynamics of symmetric interactions in homogeneous environments.