基于共识程度的双体博弈纳什均衡拓展研究

Development of Nash Equilibria of Biform Games Based on Degree of Common Knowledge

首先对一般双体博弈的策略进行拓展,提出共识纳什均衡的概念,并证明其存在性;根据共识程度的降低提出其他3种拓展形式——近似共识纳什均衡、局部共识纳什均衡和局部近似共识纳什均衡,并举例进行说明;然后,对各种均衡形式下的合作效率进行分析和比较。研究表明,共识纳什均衡的利益分配是基于信息本身——竞争环境的特殊形式,它是具有效率的。其他3种形式均衡的效率低于共识纳什均衡,但仍高于双体博弈纳什均衡。共识纳什均衡和其他3种形式的均衡为参与人组织更具效率的合作提供了渠道和理论解释。

The paper firstly develops the general strategies of biform games,proposes the concept of common knowledge Nash equilibrium（CKNE）,and then presents the proof of its existence.The paper proposes other three forms of equilibria-almost common knowledge Nash equilibrium（ACKNE）,part Common knowledge Nash equilibrium（PCKNE） and part almost common knowledge Nash equilibrium（PACKNE）,and gives some examples.It also analyzes the efficiencies of different equilibria.Research results show that the distribution of benefit in CKNE is partly decided by the information itself-a special form of competition environment,and it is efficient.The efficiency of three other forms of equilibria is lower than CKNE,but still higher than Nash equilibrium（NE） of biform games.The four developed forms of biform games＇ equilibria can provide methods and theoretical explanation for organizing more efficient cooperation.