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

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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