The Construction Of Dynamic Cooperative Game Solution Algorithms, And Dynamic Stability

The games dealt with in this thesis are all games with perfect information. This thesis aims to study the dynamic optimal solution of the partial cooperative game and the game with the simple coalitional structure in finite extensive form. Two partial cooperative types are presented in the study: one is that the coalition of players keep monotonous increase in the partial cooperative course, i.e. the players are not permitted to alter the declared options;the other is that the players still can leave coalition to adopt individual behavior or join other coalition after adopting the cooperation behavior to join the coalition by canceling the above limit.The first chapter is concerned with the partial cooperative game in finite extensive form existing monotonous limit whose key characteristic is that the behavior of each player is a combination of cooperative and individual behaviors. In this chapter the players no longer leave once they join the coalition according to the principle of partial cooperative game, displaying the characteristic of the monotonous increase of coalition of players.The second chapter studies one new simple division method of coalition structure through following the idea of division of coalition structure in the partial cooperation game in one new game model. The key characteristic is that each player before making a choice informs other players by declaring he will cooperate or play individually, and the decision to cooperate or not will be an element of players' strategy.The third chapter studies general partial cooperative game in finite extensive form, i.e. the players still can leave coalition to adopt individual behavior or join other coalition after joining the coalition by trying to cancel the limit to the monotonous increase of coalition of players. The essential reason why coalition of players can be formed and keep stable is explored by redefining the partial cooperative game, which is one of the main creative achievements in this thesis.In the above three chapters the concept of the best response to Nash Equilibrium is established to construct characteristic functions of completely cooperative game based on members in coalitions for obtaining the solution of game, and the new principle of optimal behaviors is proposed. By introducing nucleolus when individual rationality cannot be met, the dynamic optimal solution, i.e. the optimal solution PGN- vector of partial cooperative game and game with the simple coalitional structure in finite extensive form are given, and an algorithm of the optimal game trajectory is established as well.