Research On The Solutions Of Repeated Stochastic Cooperative Game

In game theory, stochastic cooperative game and repeated games gradually becomes a research focus and has received a generous concern. The most studied problem in stochastic cooperative game is how to divide the total earnings of grand coalition if the payoff to coalition is uncertain. Many solution concepts have been proposed to handle this problem, each kind of which satisfies a certain rational behavior and reasonable principle. The aim of this paper is to study classical solutions of repeated cooperative games and repeated stochastic cooperative games , such as core and stable set ,then give some properties which these solution satisfies in order to a better understanding of the player's behavior in the repeated cooperative games and repeated stochastic cooperative games.In repeated cooperative games and repeated stochastic cooperative games, For choosing different prefer relations, we construct different models of repeated stochastic cooperative games, and give different sollutions of these games. Such as core,weak core,Ï„- core,stable set and weak stable set. Then we discuss the characters of these sollutions.This paper is organized as follows: First, we take the model of repeated cooperative game, which introduced by Jorge Oviedo in 1999 as a base, and we give the conception of weak core,Ï„- core,stable set and weak stable set by redefining the notion of domination, then discuss the properties of these solutions; Second, we take the model of stochastic cooperative games, which introduced by Suijs et al in 2000 as a base, then defines the conception of repeated stochastic cooperative games, and give the conception of weak core,Ï„- core,stable set and weak stable set by redefining the notion of domination, then discuss the properties of these solutions; Finally, we give the conception of certainty equivalents of repeated stochastic cooperative games applying the notion of certainty equivalents of stochastic cooperative games which introduced by Suijs et al (2000) , and show that such a repeated stochastic cooperative games satisfies properties like nonemptiness of the core , superadditivity and convexity if and only if the corresponding deterministic repeated cooperative games satisfies these properties.