三步矩阵对策上的无中生有计及其实例

Nothing Yielding Fruit Trick on a Three-stage Matrix Game and Its Living Example

基于一个历史实例及假定:①三步矩阵对策中赢得矩阵都不变,②每步都是局中人1先行动,③对于每步对策,局中人2观测不到对手究竟使用了何策略;但局中人1可以观测到对手所用的策略,建立了三步矩阵对策上的无中生有计(《三十六计》中的第七计)的对策模型.研究了当局中人2中计,半识破和完全识破对手的无中生有计时的赢得和所用的策略的情况.并用上述实例对模型作了说明.

This paper is supported by a historical living example and the assumption： ① winning matrix is constant in three-stage game, ② player 1 first takes a action in each stage, and ③ for each stage game, the player 2 can not observe which pure strategy the opponent is using; the player 1 can observe his opponent＇s that. We shall make a game model of nothing yielding fruit trick （the seventh one in ＂the thirty-six stratagems＂） on three-stage matrix game. Then we study the player 2＇s winning and used pure strategies when he is trapped into, semi-see through and whole-see through the opponent＇s nothing yielding fruit trick, respectively. Finally, we show the model by the above-mentioned historical living example.