The Optimal Coalition Structure Of The Dynamic Response

The games dealt with in this thesis are all games with perfect information. First, this thesis aims to study the optimal coalitional structure and time-consistency problems of the discrete game separately. A new approach of forming coalitional partitions according to choosing cooperative partners is considered, which is different from the traditional approach according to the cooperation behavior. Second, this thesis analyzes the possibility of covert cooperation in the process of solving the game using the method of descending order. Third, the conception of time-consistency of the differential game is extended into that of discrete game and examples are showed. At last, this thesis studies differential time-optimal games of pursuit with two persons of continuous games.The first chapter is concerned with a new approach of forming coalitional partitions according to choosing cooperative partners of games with perfect information, which is an important innovation. Supposing players form coalitional partition on the first stage of the game all the possible coalitional partition can be formed. The specific process of forming the coalitional partition can be shown. Thereafter, each player acts in the interest of coalition to which he belongs.The second chapter studies method of descending order. The course of solving problems can be accelerated using the factor game and auxiliary game, but it appears that the solution of the factor game is neither the non-cooperative equilibrium (non-cooperative situation) nor the cooperative optimal solution(cooperative situation). The second important innovation is founded during the course of solving questions, which is the example of calculation shows the possible tendency of covert cooperation we called in the cooperative situation. And the covert cooperation may bring players better interest. Furthermore, cooperative interest may turn better when the covert cooperation changed into public cooperation.The third chapter studies time-consistency of the partial cooperative game in finite extensive form with perfect information. The conception of time-consistency is re-defined in the discrete situation, and a theorem of distinguishing the time-consistency of a special class of games.On the base of study the discrete game the continuous game can be transited into naturally, but this chapter is limited in the continuous symmetrical situation with two persons. Actually there is no perfect system dealing with n - persons internationally. The last chapter studies the differential game of pursuit and a special type of them--- differential time-optimal games of pursuit, and the theorem of dividing the whole pursuit apace.