基于后悔度的博弈剔除算法的逻辑认知分析

The Epistemic Analysis of Eliminate Algorithm in Game Theory Based on Regret Degree

博弈分析中存在大量的逻辑问题,通过认知逻辑可以精确表达主体间认知互动中的推理。首先,构建了基于后悔度的博弈认知模型,从选手选择某一策略所导致的后悔度分析主体的理性特征,为多种博弈剔除算法的认知机制提供统一的逻辑刻画。其次,基于后悔度模型,重提主体理性定义,并证明该理性可作为公开宣告的事实,借助公开宣告逻辑,为Halpern等人提出的重复最大最小化后悔度算法提供合理的逻辑认知基础。

A number of logical issues remain in game theory analysis: for instance,an inference based on cognitive interaction between individuals can be accurately modeled through epistemic logic.Firstly,Regret Degree——a game epistemic model which is used to analyze the character of individuals' rationality in terms of the degree of regret resulting from player's strategy of decision-making,provides a unified means to characterize the cognitive mechanism within multiple game eliminate algorithms;secondly,based on the Model of Regret Degree,agent' rationality is redefined,which functions to be an evidence for public announcement logic.Thus,public announcement logic provides a reasonable and epistemic foundation for the algorithms of maximizing or minimizing regret degree(by Halpern et al.).