Research On The Solution Of Stochastic Game

In game theory, stochastic cooperative game and stochastic matrix game have received a generous concern and become a research focus. The most extensively studied problem in cooperative game theory is how to divide the total earnings of the grand coalition if all players cooperated. Many solution concepts have been proposed to handle these problems, which satisfy a certain rational behavior and reasonable principle. The research on the stochastic matrix game is that we discuss the matrix game which element is stochastic variable. The purpose of this paper is to extend mature theoretics of classic matrix games to stochastic matrix game by revising and perfecting, so we can settle out the value of this game, it has biggish applied value in modern time. And we take the model of stochastic cooperative games, which introduced by Suijs et al in 2000 as a base, define the balancedness,the core and the Shapley value of this game, and discuss the relations among the balancedness,the core and the Shapley value of this game.In classic matrix games model, supposed the payoff matrix is a real matrix. In fact, it is not easy to settle out the payoff matrix accurately. The paper introduce stochastic matrix games to deal with the uncertainty of the payoff matrix and extend the range of cooperation among players. In addition, it makes research and popularization of games solutions in concrete case more reasonable and more realistic. In stochastic cooperative game, for choosing different prefer relations, we construct different models of stochastic cooperative games, and give different solutions of these games.This paper is organized as follows: First, introduction, it provides development histories of classical games theory, background and practical value of the paper. Second, we introduce some basic concepts of classic game theories, stochastic matrix game and stochastic bimatrix game, define the optimal statege and game value, define the dominate principle and the equilibrium point. Third, we take the model of stochastic cooperative games, which introduced by Suijs et al in 2000 as a base, define the balancedness,the core and the Shapley value of this game, and we discuss the characters of these solutions. Finally, we discuss the ZS-value of the stochastic game.