理论数学

Vol.3 No.6 (November 2013)

多样极小极大定理在零和动态对局问题(I)
Multicriteria Minimax Theorem on Two-Person Ze-ro-Sum Dynamic Game Problem (I)

 

作者:

赖泳伶 :国立嘉义大学资工系,嘉义市

赖汉卿 :国立清华大学数学系,新竹市

 

关键词:

极小极大定理上下界数值函数鞍值函数动态对局Minimax Theorem Upper (Lower) Value Function Saddle Value Function Dynamic Game

 

摘要:

考虑一个两人零和动态对局上的极小极大问题。我们将极小极大定理以一个随机对局系统建立损失和获益的总值函数,并证明极小极大定理在某些条件下存在鞍值函数,导出这个动态对局系统存在一平衡点。本文举一个简易的例子,说明协议的对局运作下,说明这个动态对局的架构与极小极大定理的相互关系。
Considering a minimax problem to a two-person zero-sum dynamic game, we establish the total value function of game losses and gains in a stochastic game system. It could perform a minimax theorem. Moreover, we prove that minimax theorem is established by the stochastic space of their strategy spaces for the two-person zero-sum dynamic game under the law of motion. It is also established that the saddle value function exists under certain natural conditions so that the equilibrium point exists in this dynamic game system. A practical example could be employed to our framework in the context.

文章引用:

赖泳伶 , 赖汉卿 (2013) 多样极小极大定理在零和动态对局问题(I)。 理论数学, 3, 388-393. doi: 10.12677/PM.2013.36059

 

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