| Summary: | 博士 === 國立中山大學 === 電機工程學系研究所 === 90 === ABSTRACT
Usually, real game problems encountered in our daily lives are so complicated that the existing methods are no longer sufficient to deal with them. This motivates us to investigate several kinds of differential game problems, which have not been considered or solved yet, including a pursuit-evasion game with n pursuers and one evader, a problem of guarding a territory with two guarders and two invaders, and a payoff-switching differential game.
In this thesis, firstly the geometric method is used to consider the pursuit-evasion game with n pursuers and one evader. Two criteria used to find the solutions of the game in some cases are given. It will be shown that the one-on-one pursuit-evasion game is a special case of this game.
Secondly, the problem of guarding a territory with two guarders and two invaders is considered both qualitatively and quantitatively. The investigation of this problem reveals a variety of situations never occurring in the case with one guarder and one invader. An interesting thing found in this investigation is that some invader may play the role as a pursuer for achieving a more favorable payoff in some cases. This will make the problem more complicated and more difficult to be solved.
The payoff-switching differential game, first proposed by us, is a kind of differential game with incomplete information. The main difference between this problem and traditional differential games is that in a payoff-switching differential game, any one player at any time may have several choices of payoffs for the future. The optimality in such a problem becomes questionable. Some reasoning mechanisms based on different methods will be provided to determine a reasoning strategy for some player in a payoff-switching differential game. A practical payoff-switching differential game problem, i.e., the guarding three territories with one guarder against one invader, is presented to illustrate the situations of such a game problem. Many computer simulations of this example are given to show the performances of different reasoning strategies. The proposition of the payoff-switching differential game is an important breakthrough in dealing with some kinds of differential games with incomplete information.
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