Asymmetric Evolutionary Game And Its Application

In the case of constant payoff matrix,the evolutionary stability strategy of asymmetric evolutionary game can only be a pure strategy combination of 0 and1.What circumstances can a non-zero or one equilibrium become an evolutionary stable strategy? A series of researches have been carried out in this paper:(1)The mathematical knowledge related to the stability of equilibrium point in two-dimensional first-order plane linear system model,analyzes the stability conditions related to equilibrium point,and uses the linear approximation and Routh Hurwitz criterion and other related theoretical methods to verify the method of Jacobian matrix judging the stability of equilibrium point in asymmetric evolutionary game model.When the payoff of asymmetric evolutionary game is constant,we get the criterion that the equilibrium point of the model becomes the evolutionary stable strategy.At the same time,we also get the conclusion that the evolutionary stable strategy can only be a pure strategy combination of 0 and 1 in the case of constant payoff matrix.(2)In this paper,the proportion of one-sided strategy selection is introduced into the asymmetric evolutionary game model,and the dynamic payoff matrix is constructed.In this case,the condition that the equilibrium point of the copied dynamic equation becomes the asymptotic stable point is studied,and the potential evolutionary stable strategy combinations of the dynamic system are obtained,and these potential evolutionary stable strategies are brought into the Jacobian matrix for verification.Some conditions for the evolutionary stability strategy are obtained and corresponding examples are given.Finally,the conclusion of this single parameter asymmetric evolutionary game model is applied to the decision-making model of rural labor return,and some factors affecting the decision-making of rural labor return are obtained,and some policy suggestions for the government to reasonably guide the rural labor return are given.(3)The proportion of strategy choice between the two sides is introduced into the asymmetric evolutionary game model,and some conclusions are obtained that the equilibrium point of the duplicated dynamic equation becomes an asymptotically stable point.Firstly,the sufficient and necessary conditions for these four equilibrium points((0,0),(0,1),(1,0),(1,1))to become an asymptotically stable strategy are studied.When the payment is a linear function and the equations are assumed to have solutions,the sufficient conditions for the non-zero and non-one equilibrium points to become an asymptotically stable strategy are studied.The conditions for the equations to have solutions and the conditions for the non-zero and non-one equilibrium points to become an asymptotically stable strategy when the payment is a nonlinear function are obtained.Finally,some examples are given.