The Stability Of Solutions In Dynamic Cooperative Game

Cooperation is the basis of human civilization. The global economy shows deep cross-integration with the deep development of social information and the rise of the Internet economy. Cooperative game has become the forefront of international management scientific research.This paper will focus on the strategic stability of solutions for the dynamic cooperative game, in which the time consistency is the starting point and the networked contact of players and the uncertainty(randomness) of the game process are the main features. The methods of constructing Nash or strong Nash equilibrium are proposed and existence theorems of equilibrium are proved for different dynamic cooperative games, which guarantee the strategic stability of long-range cooperative agreements. The main works in this dissertation include:Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments. From these, the time-consistent cooperative agreement can be strategically supported by epsilon-Nash or strong epsilon-Nash equilibrium. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibrium can be constructed. Based on imputation distribution procedures, a model of infinite stage game with a coalition structure is proposed. The existence of Nash or strong Nash equilibrium in such a game is proved, which guarantees the strategic support of cooperation. A kind of new characteristic function is defined which enables an equilibrium to be constructed in the case with delayed strategies. We provide conditions when the cooperative behavior resulting in the dynamic Shapley value can be supported by a strong Nash equilibrium. We propose trigger strategies for coalition deviation from cooperation and prove the existence of a strong epsilon-perfect equilibrium for the class of stochastic games played over event trees.The theory is adopted for the repeated Prisoner’s dilemma game which is a classical problem of dynamic games. This research can innovate and develop the cooperative game theory, shorten the gap between theory and practice.