一类多步矩阵对策上的计策问题

Tricks on a Multi-stage Matrix Game

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.

A trick model on a multi-stage matrix game is studied by using ordered tree, which can describe series of stratagems and luring enemy to be trapped, and so forth. The game system is assumed to be closed, i. e, its information environment will not be considered. Our assumptions are that it is the two players＇ common knowledge that 1） each winning matrix, 2） each player＇s strategies set and 3） each player＇s rationality. Our results are that 1） give the concepts of optimal tricks chain and turning opponent＇s trick against him and so on, 2） study inherent probability that a player is trapped into a tricks chain and that he sees through a tricks chain, respectively, and 3） discuss the case when a player had better use a tricks chain of his own initiative and when passivity.