完整揭示纳什均衡概念的内涵及解决囚徒的困境

Complete Disclosure of the Connotations of Nash Equilibrium Concept and Solution to the Prisoners’ Dilemma

摘要: 为了解决囚徒的困境所引起的不一致性，有必要对以往论证的有效性进行重新审查，结果发现，纳什均衡概念的内涵并未得到完整的揭示，从而，纳什均衡及占优策略等概念的定义需要修正；答案所具有的逻辑必然性是两个囚徒应该和能够进行合作的理由和条件。结论：① 囚徒的困境发生的原因在于，参与人在推理时把假设对方的选择当作是逻辑上在先的，把自己的策略当作是逻辑上属后的，但事实上双方是同时做出选择的，而且，如果形成的策略组合不是纳什均衡，那么，它在理论上就不具有存在性。② 在囚徒困境的博弈中，最优方案是可证的。③ 不存在占优策略和占优策略均衡。④ “两人都认罪”与“两人都不认罪”都是纳什均衡。⑤ 纳什均衡、亚当·斯密的“看不见的手”原理和帕累托最优是协调的。

Abstract: In order to solve the inconsistency caused by prisoners’ dilemma, it is necessary to re-examine the validity of the previous argumentation. The results reveal that the connotations of Nash Equilibrium Concept fail to be completely disclosed, and thus it is necessary to rectify the definitions of Nash Equilibrium, Dominant Strategy and other concepts; the logical necessity of the answer is the reason and condition for two prisoners to cooperate with each other. Conclusion: ① The reason for the occurrence of Prisoners’ Dilemma is as follows: logically, one side involved in the dilemma intends to regard ahead the selection of the assumptive opposite side but behind his own strategy in times of inference, but in fact, the both sides typically make their own selections simultaneously, and if resultant strategy profile is not Nash Equilibrium, it should not have existed in theory. ② In the game of Prisoner’s Dilemma, the optimal plan is provable and there. ③ There is no dominant strategy and dominant strategy equilibrium. ④ Both the “guilty plea of both sides” and “plea of not guilty of both sides” are Nash Equilibrium. ⑤ Nash Equilibrium, the “invisible hand” theory of Adam Smith and Pareto optimality are coordinated.