Existence And Stability Of α-core In Fuzzy Game

Nash equilibrium（NE）and core are two important solution concepts of the non-cooperative games.In the past,many scholars have done a large number of studies concerning the existence and stability of these two solutions,and have obtained fruitful results.However,the stability of normal form games and fuzzy games with certain concave and continuity on the bounded rationality,and the nonemptiness and stability of-cores for generalized fuzzy games have not been considered by scholars.Therefore,in order to improve and supplement the previous research,in this thesis,we first study the stability of the normal form games and fuzzy games under the bounded rationality.Furthermore,we introduce the concept of-cores into the generalized fuzzy games by considering the cooperative behavior of different players,and define the concept of the-cores of generalized fuzzy games.Finally,we study the nonemptiness and stability of-cores for the generalized fuzzy games.We divide the full text into 5 chapters,and the specific contents are as follows:In Chapter 1,we mainly discusses the research background and current research situation of the fuzzy games,the nonemptiness and stability of-cores in noncooperative game,and the stability of game equilibrium under bounded rationality.And the main research contents and innovation points of this thesis are given.Chapter 2 mainly introduces the basic mathematical knowledge employed in this thesis,including the continuity of set-valued mapping,the definition of fuzzy sets and fuzzy set-valued mapping,and related concepts as well as important lemmas,etc.In Chapter 3,we mainly study the stability of the-cores for two classes of the games under bounded rationality.First,we construct a bounded rationality model with abstract rationality function,and investigate the stability of-cores for the normal form game.And then we construct another bounded rationality model with abstract rational-ity function and study the stability of-cores for the fuzzy game.In Chapter 4,we first prove the nonemptiness of-cores for a class of generalized games with fuzzy preference correspondence by using the nonemptiness theorem of the-cores for the generalized game of Kajii^[1].Then we construct the problem space of a class of-cores for generalized fuzzy games with the certain concave and continuity,and prove that the-cores for generalized fuzzy games have the property of well-posedness.Finally,the characteristics of generalized strong well-posedness and well-posedness of generalized fuzzy game are given.In Chapter 5,we mainly derived the summary of the full text as well as the outlook for the future.