Posedness Of Multi-goal Game

In this paper, we mainly study well-posedness for weakly Pareto-Nash equilibrium points of multiobjective games. As applications, we obtain the corresponding results for Nash equilibrium points. To begin with, we discuss Hadamard well-posedness for weakly Pareto-Nash equilibrium points of multiobjective games in two kinds of situation: one is that we only consider the perturbations of payoff functions: the other is. that we consider not only the perturbations of payoff functions but also the perturbations of strategy sets. Moreover, the concepts are given of asymptotic weakly Pareto-Nash equilibrium and Levitin-Polyak weakly Pareto-Nash equilibrium. Finally, Tykhonov well-posedness and Levitin-Polyak well-posedness are separately obtained for weakly Pareto-Nash equilibrium points of the multiobjective game.In chapter 1, the background is introduced which includes the history and recent development of game theory and well-posedness.In chapter 2, we give some preliminaries, namely, the continuity and convexity of vector-valued function, the related concepts and theorems of set-valued mapping. We also introduce the concept of the multiobjective game.In chapter 3, we discuss Hadamard well-posedness for weakly Pareto-Nash equilibrium points of a game including two kinds of situations, and obtain an existence result for weakly Pareto-Nash equilibrium points of the multiobjective game in passing.In chapter 4. we establish the concepts of asymptotic weakly Pareto-Nash equilibrium and Levitin-Polyak weakly Pareto-Nash equilibrium, then we discuss Tykhonov well-posedness and Levitin-Polyak well-posedness for weakly Pareto-Nash equilibrium points of multiobjective games.