Research on Foundation of Dynamic Processes Reaching Consensus from Epistemic Logical Point of View

本研究的目的是探讨两个问题：(i)达成共识的认知过程的基础及其在博弈论中的应用；(2)不确定信息不完全条件下交易经济的认知基础，其中交易者具有多模态的意识逻辑。我们得到了以下结果：(1)给出了s5 -知识模型中的沟通过程，该过程通过鲁棒性信息导致战略形式博弈的纳什均衡。在交流过程中，每个参与者在自己的私人信息下预测其他参与者的行动。玩家根据交流图通过消息私下交流他们的猜测，每个消息的接收者学习并修改他/她的猜测。这里的重点是每个参与者发送的不是关于他/她个人猜想的准确信息，而是关于猜想的准确可靠信息。在这种情况下，我们可以证明定理1：(2)我们提出了不确定性下的经济概念的扩展，称为意识结构经济，在不完全信息下，每个交易者都在自己的意识和信念下做出决策。定理2：在不确定的纯交换经济中，假设交易者具有意识结构，并具有严格的单调偏好。然后，事后核心与经济意识中所有预期均衡配置的集合一致。

The purposes of this research are to investigate two points:(i) The foundation of the epistemic process reaching consensus, and its application to Game Theory ;(ii) The epistemic foundation of exchange economy under uncertainty with incomplete information, where traders have a multi-modal logic of awareness We obtained the following results :(1) A communication process in the S5-knowledge model is presented which leads to a Nash equilibrium of a strategic form game through robust messages. In the communication, process each player predicts the other players' actions under his/her private information. The players communicate privately their conjectures through message according to the communication graph, where each recipient of the message learns and revises his/her conjecture. The emphasis is on that each player sends not exact information about his/her individual conjecture but robust information about the conjectures to an accuracy In these circumstances we can show that Theorem 1 : The players' predictions about the other players' actions regarding as the future beliefs converge in the long run, and those convergent the beliefs that constitute a Nash equilibrium of the game even when the communication-graph is not acyclic(2) We present an extended notion of economy under uncertainty, called an economy with awareness structure, where each trader makes decision in his/her awareness and belief under incomplete information. We show the no trade theorem' under generalized expectations equilibrium in the extended economy :Theorem 2: In a pure exchange economy under uncertainty, the traders are assumed to have an awareness structure and to have strictly monotone preferences. Then the ex-post core coincides with the set of all expectations equilibrium allocations in awareness for the economy.