A Related Study Of Approximate Optimal Response Kinetics

The individuals of population games are bounded rational.Namely,they may not be able to choose the optimal strategy,but to seek a better strategy through adjustment strategy.In order to solve the problem that how the bounded rational individuals adjust the strategy,we study the approximate optimal response dynamics and its stability in this thesis.The main contents as follows:Firstly,we establish a new revision protocol under bounded rationality,then we get a new dynamics–the approximate optimal responses dynamics.Then we prove that the new dynamics satisfy three properties: forward invariance,positive correlation and Nash stationarity.At last,we prove the existence of the solution of the approximate optimal response dynamics.Secondly,we discuss the evolutionary stability of the approximate optimal responses dynamics.We construct the Lyapunov function for the approximate optimal response dynamics in the potential game and stable game.Moreover,some examples are illustrated to verify the theoretical results.Finally,we establish a single population game model for the green supply chain management,whose payoff function is nonlinear.Then we use the replication dynamics,the best response dynamics and the approximate optimal response dynamic to analyze the stability of the Nash equilibrium of the game.