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2012 Fiscal Year Final Research Report

Study of the mathematical structure of social choice theory and economic theory

Research Project

  • PDF
Project/Area Number 20530165
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Economic theory
Research InstitutionDoshisha University

Principal Investigator

TANAKA Yasuhito  同志社大学, 経済学部, 教授 (10188344)

Project Period (FY) 2008 – 2012
Keywordsミクロ経済学 / 社会的選択理論
Research Abstract

In the first half I studied computability of social choice rules and general equilibrium solution, and using Cantor’s diagonal argument and constructive mathematics I proved that they are not computable. In the second half I investigated Brouwer’s fixed point theorem from the point of view of constructive mathematics. It is not generally constructively proved, but if we require that functions satisfy the condition called“sequential local non-constancy”, then this theorem can be constructive proved. And I applied this result to economic theory and game theory.

  • Research Products

    (33 results)

All 2013 2012 2011 2009 2008 Other

All Journal Article (32 results) (of which Peer Reviewed: 32 results) Remarks (1 results)

  • [Journal Article] Constructive Proof of the Fan-Glicksberg Fixed Point Theorem for Sequentially Locally Non-constant Multi-functions in a Locally Convex Space2013

    • Author(s)
      田中靖人
    • Journal Title

      IAENG International Journal of Computer Science

      Volume: vol. 40, No. Pages: 1-6

    • URL

      http://www.iaeng.org/IJCS/issues_v40/issue_1/IJCS_40_1_01.pdf

    • Peer Reviewed
  • [Journal Article] Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions2012

    • Author(s)
      田中靖人
    • Journal Title

      Advances in Fixed Point Theory

      Volume: Vol. 2, No. 4 Pages: 398-416

    • URL

      http://scik.org/index.php/afpt/article/view/622

    • Peer Reviewed
  • [Journal Article] Proof of the Gale-Nikaido lemma for sequentially locally non-constant multi-functions: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Journal of Mathematical and Computational Science

      Volume: Vol. 2, No. 6 Pages: 1743-1758

    • URL

      http://scik.org/index.php/jmcs/article/view/589

    • Peer Reviewed
  • [Journal Article] Various Notions about Constructive Brouwer's Fixed Point Theorem2012

    • Author(s)
      田中靖人
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: vol. 42, No. 3 Pages: 152-154

    • URL

      http://www.iaeng.org/IJAM/issues_v42/issue_3/IJAM_42_3_04.pdf

    • Peer Reviewed
  • [Journal Article] Constructive proof of the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions2012

    • Author(s)
      田中靖人
    • Journal Title

      International Journal of Computational and Mathematcal Sciences

      Volume: Vol. 6 Pages: 184-87

    • URL

      http://www.waset.org/journals/waset/v68/v68-146.pdf

    • Peer Reviewed
  • [Journal Article] On the maximum theorem: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      International Journal of Computational and Mathematcal Sciences

      Volume: Vol. 6 Pages: 173-75

    • URL

      http://www.waset.org/journals/waset/v68/v68-156.pdf

    • Peer Reviewed
  • [Journal Article] Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and the minimax theorem for two-person zero-sum games: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Advances in Fixed Point Theory

      Volume: Vol. 2, No. 2 Pages: 120-134

    • URL

      http://scik.org/index.php/afpt/article/view/283

    • Peer Reviewed
  • [Journal Article] A constructive version of Ky Fan's coincidence theorem2012

    • Author(s)
      田中靖人
    • Journal Title

      Journal of Mathematical and Computational Science

      Volume: Vol. 2, No. 4 Pages: 926-936

    • URL

      http://scik.org/index.php/jmcs/article/view/232

    • Peer Reviewed
  • [Journal Article] Brouwer's fixed point theorem with sequentially at most one fixed point: A construcvtive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Advances in Fixed Point Theory

      Volume: Vol. 2, No. 1 Pages: 9-17

    • URL

      http://scik.org/index.php/afpt/article/view/202

    • Peer Reviewed
  • [Journal Article] A proof of the existence of an approximate Nash equilibrium in a finite strategic game directly by Sperner's lemma: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Global Journal of Pure and Applied Mathematics

      Volume: Vol. 8 Pages: 219-228

    • Peer Reviewed
  • [Journal Article] Gale-Nikaido lemma and Sperner's lemma: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Advances in Theoretical and Applied Mathematics

      Volume: Vol. 7 Pages: 145-163

    • Peer Reviewed
  • [Journal Article] Proof of constructive version of Kakutani's fixed point theorem directly by Sperner's lemma and approximate mini-max theorem: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Advances in Applied Mathematical Analysis

      Volume: Vol. 7 Pages: 11-27

    • Peer Reviewed
  • [Journal Article] A proof of the existence of approximate core in NTU game directly by Sperner's lemma: A constructive analysis2012

    • Author(s)
      田中靖人
    • Journal Title

      Mathematics Applied in Science and Technology

      Volume: Vol. 4 Pages: 21-39

    • Peer Reviewed
  • [Journal Article] Brouwer's fixed point theorem with isolated fixed points and his fan theorem2012

    • Author(s)
      田中靖人
    • Journal Title

      ISRN Computational Mathematics

      Pages: 1-3

    • URL

      http://www.isrn.com/journals/cm/2012/843256

    • Peer Reviewed
  • [Journal Article] Constructive Proof of Brouwer's Fixed Point Theorem for Sequentially Locally Non-constant and Uniformly Sequentially Continuous Functions2012

    • Author(s)
      田中靖人
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: vol. 42 Pages: 1-6

    • URL

      http://www.iaeng.org/IJAM/issues_v42/issue_1/IJAM_42_1_01.pdf

    • Peer Reviewed
  • [Journal Article] Constructive proof of the existence of Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions2012

    • Author(s)
      田中靖人
    • Journal Title

      ISRN Computational Mathematics

      Pages: 1-9

    • URL

      http://www.isrn.com/journals/cm/2012/459459

    • Peer Reviewed
  • [Journal Article] Constructive versions of KKM lemma and Brouwer's fixed point theorem2012

    • Author(s)
      田中靖人
    • Journal Title

      International Journal of Computational and Applied Mathematics

      Volume: Vol. 7 Pages: 51-56

    • Peer Reviewed
  • [Journal Article] A proof of constructive version of Brouwer's fixed point theorem with uniform sequential continuity2012

    • Author(s)
      田中靖人
    • Journal Title

      ISRN Applied Mathematics

      Pages: 1-9

    • URL

      http://www.isrn.com/journals/appmath/2011/276040

    • Peer Reviewed
  • [Journal Article] Equivalence between an approximate version of Brouwer's fixed point theorem and Sperner's lemma: A constructive analysis2011

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics E-Notes

      Volume: Vol. 11 Pages: 238-243

    • URL

      http://www.math.nthu.edu.tw/%7Eamen/2011/101108-2.pdf

    • Peer Reviewed
  • [Journal Article] Proof of Constructive Version of the Fan-Glicksberg Fixed Point Theorem Directly by Sperner's Lemma and Approximate Nash Equilibrium with Continuous Strategies: A Constructive Analysis2011

    • Author(s)
      田中靖人
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: vol. 41, No. 2 Pages: 133-140

    • URL

      http://www.iaeng.org/IJAM/issues_v41/issue_2/IJAM_41_2_08.pdf

    • Peer Reviewed
  • [Journal Article] Equivalence between the existence of an approximate equilibrium in a competitive economy and Sperner's lemma: A constructive analysis2011

    • Author(s)
      田中靖人
    • Journal Title

      ISRN Applied Mathematics

      Pages: 1-15

    • URL

      http://www.isrn.com/journals/appmath/2011/384625

    • Peer Reviewed
  • [Journal Article] "A Constructive Analysis of Convex-Valued Demand Correspondence for Weakly Uniformly Rotund and Monotonic Preference2011

    • Author(s)
      田中靖人・佐藤敦宏
    • Journal Title

      Advances in Decision Sciences

      Pages: 1-7

    • URL

      http://www.hindawi.com/journals/ads/2011/960819

    • Peer Reviewed
  • [Journal Article] A proof of the existence of approximate Nash equilibrium in strategic game with multi-valued optimal responses directly by Sperner's lemma: A constructive analysis2011

    • Author(s)
      田中靖人
    • Journal Title

      Mathematical Modelling and Applied Computing

      Volume: Vol. 2 Pages: 309-319

    • Peer Reviewed
  • [Journal Article] On constructive versions of Tychonoff's and Schauder's fixed point theorems2011

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics E-Note

      Volume: Vol. 11 Pages: 125-132

    • URL

      http://www.math.nthu.edu.tw/%7Eamen/2011/100624-1.pdf

    • Peer Reviewed
  • [Journal Article] On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem2009

    • Author(s)
      田中靖人
    • Journal Title

      Decisions in Economics and Finance (the official publication of the Association for Mathematics Applied to Social and Economic Sciences)

      Volume: Vol. 32 Pages: 67-78

    • Peer Reviewed
  • [Journal Article] On the Equivalence of the Arrow Impossibility Theorem and the Brouwer Fixed Point Theorem when Indivudual Preferences are Weak Orders2009

    • Author(s)
      田中靖人
    • Journal Title

      Journal of Mathematical Economics

      Volume: Vol. 45 Pages: 241-249

    • Peer Reviewed
  • [Journal Article] Undecidability of Uzawa equivalence theorem and Cantor's diagonal arguments2009

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics E-Notes

      Volume: Vol. 9 Pages: 1-9

    • URL

      http://www.math.nthu.edu.tw/~amen/2009/070902-1.pdf

    • Peer Reviewed
  • [Journal Article] The HEX game theorem and the Arrow impossibility theorem: the case of weak orders2009

    • Author(s)
      田中靖人
    • Journal Title

      Metroeconomica

      Volume: Vol. 60 Pages: 77-90

    • Peer Reviewed
  • [Journal Article] Undecidability of the existence of dictator for strongly candidate stable voting procedures in an infinite society and Cantor's diagonal argument2008

    • Author(s)
      田中靖人
    • Journal Title

      Computational & Applied Mathematics

      Volume: Vol. 27 Pages: 251-268

    • Peer Reviewed
  • [Journal Article] Undecidability of Uzawa equivalence theorem and LLPO (Lesser limited principle of omniscience)2008

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics and Computation

      Volume: Vol. 201 Pages: 378-383

    • Peer Reviewed
  • [Journal Article] On the computability of binary social choice rules in an infinite society and the halting problem2008

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics and Computation

      Volume: Vol. 197, No. 2 Pages: 598-603

    • Peer Reviewed
  • [Journal Article] The Arrow impossibility theorem of social choice theory in an infinite society and Limited principle of omniscience2008

    • Author(s)
      田中靖人
    • Journal Title

      Applied Mathematics E-Notes

      Volume: Vol. 8 Pages: 82-88

    • URL

      http://www.math.nthu.edu.tw/~amen/2008/070202-2.PDF

    • Peer Reviewed
  • [Remarks]

    • URL

      http://yatanaka.doshisha.ac.jp

URL: 

Published: 2014-08-29  

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