Cooperative Game Solution And Its Applied Research

Believes of game theory introduced into research of economics was called the second revolution of economics. From this, we can see the importance of game theory in application. But for a long time, the cooperative game theory was almost forgotten since it was mostly applied in politic fields, except a rapidly progress in the 1940s and 1950s. At the same time, non-cooperative game was widely used in many fields and founded a relative perfect system. Until 1980s, people gradually became convinced of that in the economic system there not only need competition, but also need cooperation. Then cooperative game theory meets a new chance of development.Compared with non-cooperative game theory, cooperative game theory is far from perfect. The three basic problems of cooperative game theory which is the solutions of cooperative games, the construction and its stability of the solutions and the forming mechanism of the solutions are all unsolved. In the application field, there is already some research, but they are mostly concentrated in some simple applications. Cooperative game theory can be divided into two sorts: two-person and n-person cooperative game. The former is also called two-person bargaining problem, its solutions are represented by the Nash bargaining solution. The later is so called coalitional game, whose solutions are composed by two sorts: the dominate solution which is represented by Core and the value-estimated solution which is represented by the Shapley Value as we all know. However the dominate solution is used a fat lot because of its faults. Which is mostly used is the Shapley Value.In this paper, we talked on the solutions in common use, such as Nash bargaining solutions, the K-S solutions, and give some analysis of both the advantages and the disadvantages firstly. Then we bring forward a new solution which we called it the improved K-S solution bases on both the K-S solution and the player's contributions of coalitional games. In this solution, the payoff of each player is the direct ratio of his contribution. So this result is more reasonable. In the n-person cooperative game theory, the uncertainty problem of coalitional payoffs was studied. The classic cooperative game theory can not model this sort of problems with random coalitional payoffs. Because the coalitional payoffs is computed by a pessimistic approach, which suppose that given a coalition, the persons not belong to it form another coalition to antagonize the given coalition. However, this hypothesis is often not satisfied. We give an example of a voting game in which players can disclaim to show this point. In this paper, the concept of condition-payoff was introduced, two improved solutions of the Shapley value are brought forward. Also, we proved that although the two solutions are different, they both satisfy the Efficiency Symmetry and Additivity axiom. For the game with limit carrier, there are one and only one solution exist.We found two sorts of game models in this paper to show the application of cooperative game theory, they are the supply chain game and the voting game models. In chapter 2, the game model of a supply chain with one supplier and one manufacturer is founded, which is solved by the improved K-S solution; In chapter 3, two models of a supply chain with many suppliers and one manufacturer are founded, which are solved by the Shapley Value. And both the equilibrium solution and its uncertainty of the models are analyzed, some suggestions are also proposed. In chapter 4, a voting game model with players can disclaim freely is founded, which is solved by the two improved solutions of n-person cooperative games with random coalitional payoffs introduced in the same chapter. Its uncertainty is also analyzed.