Research on the Foundation of Interactive Decision Theory from Epistemic Logical Aspect.

本研究的目的是探讨两点：（1）达成共识的认知过程的基础及其在博弈论中的应用;（2）不完全信息下交易所经济的认知基础，交易者具有意识和信念的多模态逻辑。该阶段设置如下：参与者在有限状态空间上以相同的先验分布开始。此外，它们具有由对应于模态逻辑S4的非划分结构给出的私有信息。每个参与者根据通信图通过消息私下地传达他/她对其他参与者的行动的信念，并且消息的接收者更新她/他的信念。当一个玩家与另一个玩家通信时，其他玩家不会被告知消息的内容。在这些 ...更多信息 定理1：局中人对其他局中人行动的预测作为未来信念，从长远来看是收敛的，即使通信图不是无环的，这些收敛的信念也构成了博弈的纳什均衡。(2)本文首先提出了交易者决策的多模态逻辑KT，其次建立了经济理性预期均衡的扩展概念，最后着重从模态逻辑的角度研究了事后核心与理性预期均衡配置之间的关系。假设交易者有多主体模态逻辑KT：它是命题逻辑的扩展，有许多模态算子，只需要公理（T）“每个交易者不知道一个句子，只要它不为真。逻辑具有非分割的信息结构，每个信息结构都给出了逻辑的解释。每个交易者都有自己的效用函数，这是可测量的，但他/她并不被认为是完全知道的功能。证明了定理2：在广义信息下的纯交换无原子经济中，假设交易者具有多模态逻辑KT，并且是风险厌恶的。然后，事后核心与经济的所有理性预期均衡配置的集合相一致。(3)我们提出了一个扩展的概念下的经济不确定性，称为经济的意识结构，其中每个交易者在他/她的意识和信念的不完全信息下作出决定。我们证明了广义预期均衡下的“无交易定理”：定理3：在不确定性下的纯交换经济中，假设交易者具有意识结构，并具有严格的单调偏好。如果初始禀赋是事前帕累托最优的，那么就不存在其他的意识期望均衡。少

The purposes of this research is 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 and belief.We obtained the following results :(1) We present the pre-play communication-process leading to a Nash equilibrium of a strategic form game. The stage sets up as follows : The players start with the same prior distribution on a finite state-space. In addition they have the private information given by the non-partition structure corresponding to the modal logic S4. Each player communicates privately his/her belief about the other players' actions through messages according to a communication-graph, and the receiver of the message updates her/his belief. When a player communicates with another, the other players are not informed about the contents of the message. In these … More circumstances we can show thatTheorem 1 : The players' predictions about the other players' actions regarding as the future beliefs converge in the long run, and those convergent beliefs constitute a Nash equilibrium of the game even when the communication-graph is not acyclic.(2) We propose the multi-modal logic KT by which the traders use making their decision, secondly to establish the extended notion of rational expectations equilibrium for the economy, and finally to investigate the relationship between the ex-post core and the rational expectations equilibrium allocations with emphasis on modal logical point of view. The stage is set by the following : Suppose that the trader have the multi-agent modal logic KT : It is an extension of the propositional logic with many modal operators requiring only the axiom (T) "each traders does not know a sentence whenever it is not true." The logic have non-partitional information structures, each of which gives an interpretation of the logic. Each trader has own utility function which is measurable, but he/she is not assumed to know the function completely. It is shown thatTheorem 2 : In a pure exchange atomless economy under generalized information, assume that the traders have the multi-modal logic KT and they are risk averse. Then the ex-post core coincides with the set of all rational expectations equilibrium allocations for the economy.(3) 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 3: In a pure exchange economy under uncertainty, the traders are assumed to have an awareness structure and to have strictly monotone preferences. If the initial endowment is ex-ante Pareto optimal then there exists no other expectations equilibrium in awareness. Less