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

(1)提出了具有共同信念的“同意不同意”逻辑，它是“意识和共同信念”多模态逻辑在逻辑非全知观点下的扩展。证明了“同意不同意”定理的句子在逻辑中是可证明的，并且该逻辑对所有有限模型都是合理的。(2)提出了一个游戏前的沟通过程，导致一个战略形式的博弈的纳什均衡。在通信过程中，每个局中人预测其他局中人的行动，并且他/她根据协议通过消息私下传达他/她的猜想。所有收到消息的玩家都在学习和修改他们的策略。经过长时间的沟通，他们达到一个纳什均衡：我们表明，从长远来看，如果协议不包含周期，球员的简历在修订过程中导致一个游戏的纳什均衡。(3)给出了p-信念系统中的通信过程， 关于我们 在许多参与者之间达成共识：他们传达的事件，他们相信的概率大于自己的后验。我们证明，从长远来看，每个修正后验序列都会收敛到一个极限值，并证明任何两个极限值必须相同。(4)的图论条件下，通信将导致球员之间的共识，他们的决定的情况下，有两个以上的球员，他们在没有公开宣布对互动进行了调查。结果表明，如果通信图中不包含环，则可以保证它们的决策一致。其中没有任何要求的球员的知识是强加在标准模型的知识与分割的信息结构。(5)逻辑的“效用最大化”$L^{um}$提出这是一个扩展系统的模态逻辑两个球员。根据$L^{um}$给出的声音模型是博弈论。它示出的模型，两个效用最大化的球员必须采取相同的行动，如果他们相互相信，每个采取主导行动，即使他们有不同的信息。我们注意到逻辑$L^{um}$具有有限模型性质。(6)在不确定性下的纯交换经济中，交易者愿意交易一定数量的状态相依商品，他们知道自己的预期。如果初始禀赋分配是一个理性预期均衡，那么所有交易者对这些条件的共同知识可以阻止交易，即使交易者具有非分割信息结构而没有共同的先验假设。在证明过程中，扩展了理性预期均衡的概念，并将事前帕累托最优禀赋刻画为均衡，起到了至关重要的作用。强调交易者的信息分配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