Existence Of Equilibrium Pairs For A Class Of Generalized Games

In this paper,new existence theorems of equilibrium pairs for free n-person general-ized games are obtained via introducing notions of the ordered monotone completeness of spaces and proximally ordered contraction of set valued mappings in a partially ordered linear metric space,as well as the theoretical tool for which is the best proximity point theorem obtained by authors.In general,proximal distance contractive is used in liter-ature exists,and it is inevitable to consider the continuity of operators.We replace the previous method with the proximally ordered contractive set-value mapping.It is without continuity requirements for set valued mappings and the contractive condition is weaker than the common distance contractions.At the same time,we use the maximum element existence theorem in non-compact settings,so that our conclusions don't need the re-quirement of compactness.Thus,the results generalize and improve several well-known results.Besides,we provide examples to illustrate the applicability of our results.The full text is divided into four chapters:Chapter 1 is introduction.We introduce game theory from the background and re-search status and other sides.In this chapter,we introduce the research route of the best approximation point(fixed point),the model of generalized game and its equilibrium in detail.In addition,we also find that there is a certain demand for the study of discontinu-ous game without compactness in real life.At the end of this chapter,we also narrate the full text arrangement.Chapter 2 is preliminaries.In this chapter,some basic concepts,theorems and lem-mas related to this paper are given.For example,order theory in metric space,concepts of equilibrium pairs in generalized game,the best approximation point theorems and the maximum element theorems.These will play important roles in the following chapters.Chapter 3 is the main results.In this chapter,we present the sufficient conditions for the existence of equilibrium pairs of n-person generalized free game.In addition,examples are provided to illustrate the generality and applicability of the conclusions.Chapter 4 is the summary and prospect.In this chapter,we summarize the full text,discuss about some shortcomings and put forward some feasible directions for the future research.