The Application Research Of Game Based On The Mixed Strategies And Shapley Value

Game theory is a very important subject in social science. With the rapid development of modern economy, game theory is increasingly recognized. Game theory is widely used in many fields in our life. With the progressive development and deepening of game theory, wide application and rich research, game theory has become a powerful tool and measure. However, traditional solution has some limitations. Analysing with examples and selecting appropriate methods for solving are made on the development of game theory more challenges.This thesis contains the following:Firstly, this thesis discusses the penny matching model in game theory, combines the example of democratic nomination and abstracts out the penny matching model of cadre management, meanwhile, makes use of methods of programming and MATLAB for obtaining the equilibrium of mixed strategies. It makes a brief study on the application of game theory in cadre management.Secondly, this thesis discusses cooperative game. On the basis of reading and researching a large number of relevant literatures, it generalizes the knowledge of cooperative game theory. According to the Shapley value satified with the symmetry axion, effectiveness axion, additivety axion and uncertainty of Shapley value, it discusses the Shapley solution of cooperative game, and lists the example of supply chain system.Finally, this thesis discusses the MATLAB simulation of game theory. It contains pure strategies problem, mixed strategies problem and minimax search and Alpha-Beta search in computer game. It makes the best use of the advantage of MATLAB, and compiles the saddle point function, the payoff function, constraints transform function and minimax search function and Alpha-Beta search function, presents the procedure to solve game theory effectively.