Research on Foundation of Game Theory, Rationality and Human Behaviors from the view point of Epistemic Logic

(1)提出了“同意不同意”与共同信念的逻辑，这是逻辑非全知观点中“意识与共同信念”多模态逻辑的延伸。证明了“同意不同意”定理的句子在逻辑上是可证明的，并且证明了该逻辑对所有有限模型都是正确的。(2)提出了博弈前的沟通过程，该过程导致战略形式博弈的纳什均衡。在交流过程中，每个参与者预测其他参与者的行动，并根据协议通过消息私下交流自己的猜测。所有收到信息的参与者都会学习并修正他们的猜测。经过长时间的交流，他们达到了纳什均衡：我们表明，如果协议不包含循环，那么玩家在修订过程中的猜测将导致长期博弈的纳什均衡。(3)在$p$信念系统中，更多的参与者达成共识：他们以比自己的后验更大的概率来交流他们相信的事件。我们证明了在长期运行中，每个修正后验序列收敛于一个极限值，并且证明任意两个极限值必须相同。(4)研究了在两名以上参与者在没有公开公告的情况下结对互动的情况下，沟通会导致参与者对决策达成共识的图论条件。结果表明，在通信图不包含循环的情况下，他们的决策是一致的。与具有分区信息结构的标准知识模型不同，对玩家的知识没有任何要求。(5)提出了“效用最大化者”逻辑$L^{um}$，这是两个参与者模态逻辑系统的扩展。根据博弈论给出了$L^{um}$的声音模型。该模型表明，如果两个效用最大化的参与者相互认为各自采取优势行动，即使他们拥有不同的信息，他们也必须采取相同的行动。我们注意到逻辑$L^{um}$具有有限模型性质。(6)在不确定性条件下的纯交换经济中，交易者愿意交易一定量的国家商品，并且他们知道自己的期望。如果初始禀赋配置是理性预期均衡，即使交易者在没有共同先验假设的情况下具有信息的非分割结构，所有交易者对这些条件的共同知识也会阻止交易。在证明中，合理期望均衡的概念的扩展和事前帕累托最优禀赋作为均衡的特征是至关重要的。强调交易者信息的划分结构在无交易定理中不起作用。少

(1) The logic of 'agreeing to disagree' with common-belief is presented which is an extension of a multi-modal logic of 'awareness and common-belief' in the logically non-omniscient point of view. It is shown that the sentence of the 'agreeing to disagree' theorem is provable in the logic and that the logic is sound for all finite models.(2) A pre-play communication-process is presented which leads to a Nash equilibrium of a strategic form game. In the communication process each player predicts the other players' actions, and he/she communicates privately his/her conjecture through message according to a protocol. All the players receiving the messages learn and revise their conjectures. After a long round of the communications they reach a Nash equilibrium: We show that the profile of players' conjectures in the revision process leads a Nash equilibrium of a game in the long run if the protocol contains no cycle.(3) The communication process in the $p$-belief system is presented which … More reaches consensus among many players : They communicate the events that they believe with probability greater than their own posteriors. We show that in the long run each sequence of revised posteriors converges to a limiting values and show that any two limiting values must be same.(4) The graph-theoretical conditions under which communication will lead to consensus among players about their decisions in circumstances are investigated where there are more than two players and they interact in pair without public announcement. It is shown that consensus on their decisions can be guaranteed if the communication graph contains no cycle. Where none of the requirements for player's knowledge is imposed as in the standard model of knowledge with partitional information structure.(5) The logic of 'utility maximizers' $L^{um}$ is proposed which is an extension of a system of modal logic for two players. The sound models according to $L^{um}$ are given in terms of game theory. It is shown for the models that two utility maximizing players must take the same action if they mutually believe that each takes a dominant action, even when they have different information. We remark that the logic $L^{um}$ has the finite model property.(6) In a pure exchange economy under uncertainty the traders are willing to trade of the amounts of state-contingent commodities and they know their expectations. Common-knowledge about these conditions among all traders can preclude trade if the initial endowments allocation is a rational expectations equilibrium, even when the traders have the non-partition structure of information without the common prior assumption. In the proof it plays essential role to extend the notion of a rational expectations equilibrium and to characterize ex-ante Pareto optimal endowments as the equilibrium. It is emphasized that the partition structure of information in the traders plays no roles in the no trade theorem. Less