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2001 Fiscal Year Final Research Report Summary

Research on Foundation of Game Theory, Rationality and Human Behaviors from the view point of Epistemic Logic

Research Project

Project/Area Number 12640145
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionIbaraki National College of Technology

Principal Investigator

MATUSUHISA Takashi  Ibaraki National College of Technology, Department of Natural Sciences, Assistant Professor, 自然科学科, 講師 (40219473)

Project Period (FY) 2000 – 2001
KeywordsEpistemic logics / Information structure / Hash equilibrium / Agreement theorem / Economy under uncertainty / Rational expectations equilibrium
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 … More 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

  • Research Products

    (39 results)

All Other

All Publications (39 results)

  • [Publications] Takashi MATSUHISA: "Communication leading to Nash equilibrium"丸山 徹(編著):「経済の数理解析」京都大学数理解析研究所講究録. No.1165. 245-256 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Knowledge Structure in Decision Theory"伊藤正美(編著)「代数系、形式言語および計算理論」京都大学数理解析研究所講究録. No.1166. 170-177 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to Nash equilibrium"Abstracts in the First World Congress of Game Theory Society, Bilbao 2000. http://at.yoruku.ca/cgi-bin/amca/caez-89 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Logic of Decision Theory"Abstracts in the Ninth International Colloquium on Numerical Analysis, Computer Science and Applications, Plovdiv 2000. 136 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication, consensus and lattice structure of knowledge"Far East Journal of Applied Mathematics. Vol. 4No.3. 239-252 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Awareness, belief and agreeing to disagree"Far East Journal of Mathematical Sciences. Vol. 2No.6. 833-844 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuki HIRASE: "Reasoning about dominant Actions"丸山 徹(編著):「経済の数理解析」京都大学数理解析研究所講究録. No.1215. 169-181 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication reaching consensus"今岡輝男(編著)「代数的半群、形式言語および計算」京都大学数理解析研究所講究録. No.1222. 160-169 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Consensus on p-belief communication"今岡輝男(編著)「代数的半群、形式言語および計算」京都大学数理解析研究所講究録. No.1222. 170-179 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to Nash equilibrium II"T.Yanovskaya(Editor) : Logic, Games and Social Choices(LGS2), The Publishing Council of St.Petersburg University. 174-179 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to epsilon-Nash equilibrium"J.Morgan(Editor) : Extended abstracts of the XIV Italian Meeting of Game Theory and Applications. Ischia(Italy). 173-174 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Consensus on p-belief communication"International Journal of Applied Mathematics. Vol.8, No.2. 159-170 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Rational expectation can preclude trades"丸山 徹(編著)「経済の数理解析」京都大学数理解析研究所講究録. (印刷中). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryuichiro ISHIKAWA: "Rationality in final decisions leads to sequential equilibrium"丸山 徹(編著)「経済の数理解析」京都大学数理解析研究所講究録. (印刷中). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Model-robustness of equilibrium in game for model logics"小林ゆう治(編著)「代数系のアルゴリズムと計算論」京都大学数理解析研究所講究録. (印刷中). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Communication reaching consensus"W.Takahashi and T.Tanaka(Editor) : Proceedings of the Second International Conference of Non-Linear Analysis and Convex Analysis (NACA 2002), Hirosaki(Japan) Yokohama Publishing Co.Ltd.. (In press). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA: "Consensus on p-belief communication"W.Takahashi and T.Tanaka(Editor) : Proceedings of the Second International Conference of Non-Linear Analysis and Convex Analysis (NACA 2002), Hirosaki(Japan) Yokohama Publishing Co.Ltd.. (In press). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi MATSUHISA, T. MARUYANA (Editor): "Communication leading to Nash equilibrium"Mathematical Economics, KouKyuRoku, R.I.M.S. Kyoto University. No.1165. 245-256 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA, M. Ito (Editor): "Knowledge structure in Decision Theory"Algebraic Systems, Formal Languages and Computation, KouKyuRoku, R.I.M.S. Kyoto University. No.1166. 170-177 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA, Manabu TOMINAGA and Kazuyoshi KAMIYAMA: "Communication, consensus and lattice structure of knowledge"Far East Journal of Applied Mathematics. Volume 4 No.3. 239-252 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA and Syun-Suke USAMI: "Awareness, belief and agreeing to disagree"Far East Journal of Mathematical Sciences. Volume 2 No.6. 833-844 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuki HIRASE and Takashi MATSUHISA, T. MARUYANA (Editor): "Reasoning about dominant actions"Mathematical Economics, KouKyuRoku. No.1215. 169-181 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Emiko FUKUDA, Takashi MATSUHISA and Hisato SASANUMA, T. Imaoka (Editor): "Communication reaching consensus"Algebraic Semigroups, Languages and Computation, KouKyuRoku, R.I.M.S. Kyoto University. No.1222. 160-169 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryuichiro ISHIKAWA, Takashi MATSUHISA and Yohsuke AKAGAWA, T. Imaoka (Editor): "consensus on p-belief communication"Algebraic Semigroups, Languages and Computation, KouKyuRoku, R.I.M.S. Kyoto University. No.1222. 170-179 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA, T. Yanovskaya (Editor): "Communication leading to Nash equilibrium II"Logic, Games and Social Choices (LGS2), The Publish Coucil of St. Petersburg University. 174-179 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA, J. Morgan (Editor): "Communication leading to epsilon- Nash equilibrium"Extended Abstracts of the XIX Italian Meeting of Game Theory and Applications, Ischia 2001. 173-174 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryuichiro ISHIKAWA, Takashi MATSUHISA and YohSuke AKAGAWA: "Consensus on p-belief communication"International Journal of Applied Mathematics. Volume 8 No.2. 159-170 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Emiko FUKUDA, Takashi MATSUHISA and Hisato SASANUMA: "Communication reaching consensus"Proceedings of The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). 49-60 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryuichiro ISHIKAWA, Takashi MATSUHISA and Yohsuke AKAGAWA: "consensus on p-belief communication"The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). 131-136 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to Nash equilibrium"The First World Congress of Game Theory Society, Bilbao (Spain). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA: "Logic of Decision Theory"The Ninth International Colloquium on Numerical Analysis, Computer Science and Applications, Plovdiv (Bulgaria). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuki HIRASE and Takashi MATSUHISA: "Reasoning about dominant actions"R.I.M.S. Symposium Mathematical Economics, Kyoto University. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to Nash equilibrium II"Logic, Games and Social Choices, the Second International Conference (LGS2), St. Petersburg (Russia). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA: "Communication leading to epsilon- Nash equilibrium"The XIX Italian Meeting of Game Theory and Applications, Ischia (Italy). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Emiko FUKUDA, Takashi MATSUHISA and Hisato SASANUMA: "Communication reaching consensus"The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryuichiro ISHIKAWA, Takashi MATSUHISA and Yohsuke AKAGAWA: "consensus on p-belief communication"The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA and Ryuichiro ISHIKAWA: "Rational expectation can preclude trade"R.I.M.S. Symposium Mathematical Economics, Kyoto University. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryuichiro ISHIKAWA and Takashi MATSUHISA: "Rationality final decisions leads to sequential equilibrium"R.I.M.S. Symposium Mathematical Economics, Kyoto University. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi MATSUHISA: "Model-robustness of equilibrium in game for modal logic"R.I.M.S. Symposium Algorithms of Algebraic Systems and Computation, Kyoto University. (2002)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2004-04-14  

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