Theory Study And Application Of Several Solutions Of Convex Multi-choice Games

In game theory, solutions of cooperative games have been always a research focus. The most extensively concerned problem in cooperative game theory is how to divide the total earnings of the grand coalition if all players cooperate. Various solution concepts have been proposed to handle these problems, including core, Weber sets, Shapley value and so on, each kind of which satisfies a certain rational behavior and reasonable principle. As an emerging branch of game theory, multi-choice game theory has attracted many scholars' interests since it emerged, some research results appeared one after another. The purpose of this paper is to extend mature theories of classic cooperative games to multi-choice cooperative games, convex multi-choice games, and repeated multi-choice cooperative games by revising and perfecting, It affords theoretic bases for players to select coalitions in the game. So it has biggish applied value and it avoids unnecessary loss because of failure in selecting coalitions.Firstly, this paper defines the potential of multi-choice game cooperative games, and shows the relationship between the multi-choice Shapley value and potential. The PZ Shapley values are gained, meanwhile some axiomatic descriptions of PZ Shapley value are proposed.Secondly, by introducing a priori unions, we get the multi-choice games with a priori unions, the coalitional core and coalitional Weber sets are given, in the following some properties related to them are studied.Finally, we introduce some basic concepts of repeated cooperative game theories first, then expand a repeated cooperative game with weighted function to a repeated multi-choice cooperative game. In the following, some new characterizations of convex multi-choice game are given by using the notions of exactness and superadditivity. We prove that each element of the Weber set of a convex multi-choice game is extendable to a limas.