2001 Fiscal Year Final Research Report Summary
Research on Foundation of Game Theory, Rationality and Human Behaviors from the view point of Epistemic Logic
| Project/Area Number |
12640145
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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 |
MATUSUHISA Takashi Ibaraki National College of Technology, Department of Natural Sciences, Assistant Professor, 自然科学科, 講師 (40219473)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Epistemic logics / Information structure / Hash equilibrium / Agreement theorem / Economy under uncertainty / Rational expectations equilibrium |
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| Research Abstract |
(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
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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
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