Multi-species Game Of One Model And The Evolutionarily Stable Strategy

It is well know that the important shortcoming of classical non-cooperative game theory is the rationalistic foundation.Not only is it required that agents be optimizers, but it also presumes a large degree of coordination of different agent's expectations. With the development of evolutionary game theory,the puzzle of classical non-cooperative game theory has been well solved.In the first part,we mainly illustrate the development of evolutionary game theory,the research survey in home and abroad and the leading contents of research in the text.The second part is preliminary,we present the concepts of Nash-equilibrium and population dynamics.The third part is the primary content of this paper,firstly,under taking into consideration the influence of the population states on the individual's payoffs in the evolutionary dynamics,an general form of two-species game is proposed.The ESS model of two-species game in this general form is then established.The results shows that our ESS has the similar properties of the ESS of single species and,when the payoff is linear,meet the similar first-order and second-order best-reply conditions of single species.Secondly,because of the limitation of the definition of above ESS,the stability of the Replicator dynamic isn't hold,so we give the strict ESS of two-species,and when the payoff map is continuous,convex or linear,we have some results such as the equivalent conditions of the strict ESS and its local stability of the Replicator dynamics.Lastly,we extend the strict ESS of two species and its stability into n-species Game,and as an example of the extensive form,a matrix game is then studied.