A Related Study Of Weak Pareto-Nash Balance In A Dual-target Potential Game

In this thesis,we mainly research the weakly Pareto-Nash equilibrium points and Pareto-Nash equilibrium points for bi-objective potential games.On one hand,we research the relationship between the weakly Pareto-Nash equilibrium of bi-objective potential games and the weakly Kuhn-Tucker point of corresponding potential function,which has been generalized to multi-objective potential games.On the other hand,we research the relationship between the weighted equilibrium of multi-objective potential games,the weighted Kuhn-Tucker point of corresponding potential function and the weakly Pareto-Nash equilibrium of multi-objective potential games.This thesis is organized as follows.Chapter 1,the background is introduced which contains the history of development and research status of game theory,population games,multi-objective population games and potential games,such as the results of existence and stability of the equilibrium points.Chapter 2,we briefly introduce the model of population games and the definition of Nash equilibrium points,by busing geometry for further interpretation.Chapter 3,we reviews multi-objective population games and weakly Pareto-Nash equilibrium.Chapter 4,we overview basic notions of potential games,introduce the existence of Nash equilibrium and the stability under evolutionary dynamics.Chapter 5,firstly,the bi-objective potential game and its weakly Pareto-Nash equilibrium are defined.Secondly,based on the optimality condition in multi-objective optimization theory,a weakly Kuhn-Tucker point of the potential function is proved to be a weakly Pareto-Nash equilibrium of bi-objective potential games,which has been generalized to multi-objective potential games.Finally,we give an example to show the results of the connection.Chapter 6,based on the weighted muilt-objective potential game,we get the weighted equilibrium of multi-objective potential games and the weighted Kuhn-Tucker point of corresponding potential function are equivalent.Further,we research the relationship with the weakly Pareto-Nash equilibrium.