Study On The Fuzzy N-Person Non-Cooperative Games And Its Solving Method

For the reasons of uncertainty of human game environments, variety of objects, multiplicity of decision makers and high complexity of decision actions, researchers have studied new game theories and methods ceaselessly. Meanwhile, this has promoted fuzzy sets theory applied to game theory. Consequently, fuzzy game theory emerged as a branch of game theory in 1970's. Soon afterwards, a few research achievements appeared and mainly solved some problems of the following aspects: fuzziness of strategy sets, imprecision of payoff matrixes, the concept of solutions of fuzzy games, fuzzy coalition, fuzzy multiobjects and so on. However, there are few articles which comprehensively depict and study N-person game with fuzzy sets theory. This paper tries to do some research on fuzzy N-person non-cooperative games and its solving methods.Firstly, using the ideal of saddle point of two-person zero-sum matrix games for reference, the paper proposes the definition of the security point of N-person non-cooperative games, regards it as the solution of the games, gives its properties and solving method and proves that it is an optimal strategy profile. Based on those, the paper depicts three cases of fuzzy N-person non-cooperative games and makes some explanations to their solving methods.Secondly, on the basis of security point, the definitions of some security points of multiobjective N-person non-cooperative games which are regarded as the solutions are presented and some demonstrations are given here. At the same time, the preference information of players are embodied by objective weight vectors and ranking functions of fuzzy numbers. Then fuzzy N-person non-cooperative games in the situation that players know others' preference information or not are depicted here, with the solving methods of their security points discussed and the fuzzy payoffs and practically formed strategy profiles compared and proved.