| Differential game is a game theory that describs the phenomenon or regularities by using differential Equations. According to the pay-off functions, the Differential games are divided into two categories: Quntitative differential game and Qualitative differential game. In accordance with the information structure, each kind of differential game is classfied into fixed type differential game and random differential game. This paper will focus on the Quntitative differential game with fixed type information structure. The main content will be presented as follows:1. For a security investment decision ,the reasonal modling is a good method. Many methods are based on the static model, but not on the dynamic perspective, Under the assumption that security price will bound uncertaintly, this paper studies a security investment decision problem with the worst-case optimization method. According to the differential game model of some paper. Firstly, the saddle point of the model will be analyzed by the theory of differential games. Then, the differential game will be solved by using max-min principle. Finally, the optimal strategies of investor is obtained.2. The N-player differential game of nonlinear system, which is based on the thought of T-S fuzzy modeling, has been translated into many linear subsystems. Then, the model of N-player noncooperative differential game has been established. A simulation for 4-player noncooperative differential game has been made and it's results has illuminated the feasibility of the resolution scheme.3. This paper also studies the N-player differential games of nonlinear system and the neural networks . Based on the variational principle, the relation between the weights of network and the optimal controlling strategies is well proved theoretically. Each player in the N-player noncooperative differential game wants to minimize his pay-off function ,which unifies the learning process of neural network. |
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