2007 Fiscal Year Final Research Report Summary
Research on Foundation of Dynamic Processes Reaching Consensus from Epistemic Logical Point of View
| Project/Area Number |
18540153
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ibaraki National College of Technology |
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Principal Investigator |
MATSUHISA Takashi Ibaraki National College of Technology, Department of Natural Sciences, Lecturer (40219473)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Epistemic logics / Information structure / Nash equilibrium / Core equivalence theorem / Economy under uncertainty / Rational expectations equilibrium / Communication / Protocol |
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| Research Abstract |
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.
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