Evolutionary Game And Evolutionary Tautology

The main theme of this dissertation is Evolutionary Game Theory(EGT),which concerns about evolution and game theory by definition.Whereas the whole picture of EGT is show from a logical viewpoint.Actually it is the Evolutionary Game Theory in Logic.The traditional game theory comes first,and then followed evolutionary game theory,and then the logic behind EGT.In chapter one there comes four disseminated misunderstandings of Darwinism in the first section.Analysis of these misunderstandings practically accentuated the key ideas of Darwinism.Lamarckism suggested that the players could influence the strategies applied by themselves,unfortunately this is quite the opposite of Darwinism.In a evolu-tionary game all the strategies are inherited rather than chosen by the players themselves.The mathematical model of evolutionary game definitely ruled out any assumption of cognitive concepts of the players,especially the ability to judge and decide the strategies themselves.Actually the strategies defined the species,not the other way round.A pop-ulation of species is often treated as the object to be selected by nature,however,in most cases this is totally wrong.In this paper the phenotypes and species are treated as the objects to be selected by nature rather than a population.And the independent variable v in G-function is the device to trace a specific strategy in a population.The background of evolution given in this paper is mainly presented in the biological terms,however in the end of this chapter it is noted that all these ideas could applied to any strategies rather than strategies in the form of phenotypes.In solving optimization problems the genetic algo-rithm also borrowed terms in genetics,but the problems are much diverse than biological problems.As the model of evolution game is described in the form of differential equations,the beginning of chapter two introduced basic ideas of differential equation and stability theory of it,which is the key idea to define Evolutionary Stable Strategy(ESS).The formal definition of ESS and Ecologically Stable Equilibrium(ESE)is defined on open sets which calls for topology knowledge given in this chapter.After that there comes the classical definition of game in its extensional form.when this definition is compared with evolution games the different features between them are quite obvious.And then the preliminary model of evolutionary game is introduced,which is the corner stone of more complex models followed.In the end of this chapter the logic of game theory is outline the relation of logic and game in one direction,and the last chapter gave the other.The more concrete and detailed mathematical model of evolution game is discussed in chapter three.In fact evolutionary games is base on traditional games,and the relation-ship between became much clear as the G-function in the model showed.In the ecological game it is the iterated classical game that actually played,and new strategy introduced in the equilibrated population by mutant or intrusion.The G(v,u,x)is actually fitness func-tion with an individual parameter v,which allowed strategy concerned dynamic could be analyzed by the graph of G-function known as adaptive landscape.The adaptive land-scape server as a snapshot of the ecological game in a equilibrium state,and the specific strategy run through all the possible strategies that included in the strategy space.The details of the evolutionary game is practically the setup of the G-function.With the definition of G-function there comes the Evolutionary Stable Strategy(ESS)in chapter four.Before the definition of ESS the definition of Ecologically Stable Equilibrium(ESE)is introduced in the first place.And before the idea of ESE Ecologically Equilibrium should be defined ahead.It should be noted that ESE is a population equilibrium,while ESS is a strategy equilibrium,and the bridge is coalition vector which sorting out the strategies associated with the equilibrium non-zero population density of species in front of the strategy vector.The last theorem in chapter five is actually associated population density vector back to the strategy vector.Thus stable in population density and stable in strategies are theoretically the same.And in this sense the essence of Darwinism could be capsulated in a tautology,such that,stable strategies are stable.Where the last stable in this tautology means population density stable.