社会的選択理論と理論経済の数学的構造についての研究

• 研究課題/領域番号: 20530165
• 研究種目: 基盤研究(C)
• 配分区分: 補助金
• 応募区分: 一般
• 研究分野: 理論経済学
• 研究機関: 同志社大学
• 研究代表者: 田中 靖人 同志社大学, 経済学部, 教授 (10188344)
• 研究期間 (年度): 2008 – 2012
• 研究課題ステータス: 完了 (2012年度)
• 配分額: 3,250千円 (直接経費: 2,500千円、間接経費: 750千円); 2012年度: 650千円 (直接経費: 500千円、間接経費: 150千円); 2011年度: 650千円 (直接経費: 500千円、間接経費: 150千円); 2010年度: 650千円 (直接経費: 500千円、間接経費: 150千円); 2009年度: 650千円 (直接経費: 500千円、間接経費: 150千円); 2008年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
• キーワード: ミクロ経済学 / 社会的選択理論 / 構成的数学 / 不動点定理 / 計算可能性 / constructive mathematics / Brouwer's fixed point theorem / Sperner's lemma / Tvchonoff's fixed point theorem / Schauder's fixed point theorem / ブラウワーの不動点定理 / 構成的証明 / スペルナーの補題 / ナッシュ均衡 / HEX game theorem / Arrow impossibility theorem / Brouwer fixed point theorem / quasi-transitive binary social choice rules / halting problem / 社会的選択 / 宇沢の同値定理 / 決定可能性 / カントールの定理 / NTUコア / Brouwerの不動点定理

研究概要

前半においては社会的選択ルールや一般均衡解の計算可能性を主に研究し,それらが計算可能でないことを構成的数学やカントールの対角線論法などを用いて証明した.後半では競争経済の均衡や非協力ゲームにおけるナッシュ均衡の存在証明に用いられるブラウワーの不動点定理を構成的数学の観点から検討し,一般には構成的に証明できないが関数にある条件を課せば証明可能であることを示し,それを経済理論,ゲーム理論に応用した.

研究成果

• [雑誌論文] Constructive Proof of the Fan-Glicksberg Fixed Point Theorem for Sequentially Locally Non-constant Multi-functions in a Locally Convex Space (2013)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: IAENG International Journal of Computer Science 巻: vol. 40, No. ページ: 1-6
  • URL: http://www.iaeng.org/IJCS/issues_v40/issue_1/IJCS_40_1_01.pdf
  • 査読あり
• [雑誌論文] Constructive Proof of the Fan-Glicksberg Fixed Point Theorem for Sequentially Locally Non-constant Multi-functions in a Locally Convex Space (2013)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: IAENG International Journal of Computer Science 巻: 40 ページ: 1-6
  • 査読あり
• [雑誌論文] Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Advances in Fixed Point Theory 巻: Vol. 2, No. 4 ページ: 398-416
  • URL: http://scik.org/index.php/afpt/article/view/622
  • 査読あり
• [雑誌論文] Proof of the Gale-Nikaido lemma for sequentially locally non-constant multi-functions: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Journal of Mathematical and Computational Science 巻: Vol. 2, No. 6 ページ: 1743-1758
  • URL: http://scik.org/index.php/jmcs/article/view/589
  • 査読あり
• [雑誌論文] Various Notions about Constructive Brouwer's Fixed Point Theorem (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: vol. 42, No. 3 ページ: 152-154
  • URL: http://www.iaeng.org/IJAM/issues_v42/issue_3/IJAM_42_3_04.pdf
  • 査読あり
• [雑誌論文] Constructive proof of the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: International Journal of Computational and Mathematcal Sciences 巻: Vol. 6 ページ: 184-87
  • URL: http://www.waset.org/journals/waset/v68/v68-146.pdf
  • 査読あり
• [雑誌論文] On the maximum theorem: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: International Journal of Computational and Mathematcal Sciences 巻: Vol. 6 ページ: 173-75
  • URL: http://www.waset.org/journals/waset/v68/v68-156.pdf
  • 査読あり
• [雑誌論文] 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 analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Advances in Fixed Point Theory 巻: Vol. 2, No. 2 ページ: 120-134
  • URL: http://scik.org/index.php/afpt/article/view/283
  • 査読あり
• [雑誌論文] A constructive version of Ky Fan's coincidence theorem (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Journal of Mathematical and Computational Science 巻: Vol. 2, No. 4 ページ: 926-936
  • URL: http://scik.org/index.php/jmcs/article/view/232
  • 査読あり
• [雑誌論文] Brouwer's fixed point theorem with sequentially at most one fixed point: A construcvtive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Advances in Fixed Point Theory 巻: Vol. 2, No. 1 ページ: 9-17
  • URL: http://scik.org/index.php/afpt/article/view/202
  • 査読あり
• [雑誌論文] A proof of the existence of an approximate Nash equilibrium in a finite strategic game directly by Sperner's lemma: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Global Journal of Pure and Applied Mathematics 巻: Vol. 8 ページ: 219-228
  • 査読あり
• [雑誌論文] Gale-Nikaido lemma and Sperner's lemma: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Advances in Theoretical and Applied Mathematics 巻: Vol. 7 ページ: 145-163
  • 査読あり
• [雑誌論文] Proof of constructive version of Kakutani's fixed point theorem directly by Sperner's lemma and approximate mini-max theorem: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Advances in Applied Mathematical Analysis 巻: Vol. 7 ページ: 11-27
  • 査読あり
• [雑誌論文] A proof of the existence of approximate core in NTU game directly by Sperner's lemma: A constructive analysis (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Mathematics Applied in Science and Technology 巻: Vol. 4 ページ: 21-39
  • 査読あり
• [雑誌論文] Brouwer's fixed point theorem with isolated fixed points and his fan theorem (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: ISRN Computational Mathematics ページ: 1-3
  • URL: http://www.isrn.com/journals/cm/2012/843256
  • 査読あり
• [雑誌論文] Constructive Proof of Brouwer's Fixed Point Theorem for Sequentially Locally Non-constant and Uniformly Sequentially Continuous Functions (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: vol. 42 ページ: 1-6
  • URL: http://www.iaeng.org/IJAM/issues_v42/issue_1/IJAM_42_1_01.pdf
  • 査読あり
• [雑誌論文] Constructive proof of the existence of Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: ISRN Computational Mathematics ページ: 1-9
  • URL: http://www.isrn.com/journals/cm/2012/459459
  • 査読あり
• [雑誌論文] Constructive versions of KKM lemma and Brouwer's fixed point theorem (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: International Journal of Computational and Applied Mathematics 巻: Vol. 7 ページ: 51-56
  • 査読あり
• [雑誌論文] A proof of constructive version of Brouwer's fixed point theorem with uniform sequential continuity (2012)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: ISRN Applied Mathematics ページ: 1-9
  • URL: http://www.isrn.com/journals/appmath/2011/276040
  • 査読あり
• [雑誌論文] Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Advances in Fixed Point Theory 巻: 2 ページ: 398-416
  • 査読あり
• [雑誌論文] Proof of the Gale-Nikaido lemma for sequentially locally non-constant multi-functions: A constructive analysis (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Journal of Mathematical and Computational Science 巻: 2 ページ: 1743-1758
  • 査読あり
• [雑誌論文] Various Notions about Constructive Brouwer’s Fixed Point Theorem (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: 42 ページ: 152-154
  • 査読あり
• [雑誌論文] 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 analysis (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Advances in Fixed Point Theory 巻: 2 ページ: 120-134
  • 査読あり
• [雑誌論文] A constructive version of Ky Fan's coincidence theorem (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Journal of Mathematical and Computational Science 巻: 2 ページ: 926-936
  • 査読あり
• [雑誌論文] Brouwer's fixed point theorem with sequentially at most one fixed point: A construcvtive analysis (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Advances in Fixed Point Theory 巻: 2 ページ: 9-17
  • 査読あり
• [雑誌論文] Brouwer's fixed point theorem with isolated fixed points and his fan theorem (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: ISRN Computational Mathematics 巻: 2012 ページ: 1-3
  • DOI: 10.5402/2012/843256
  • 査読あり
• [雑誌論文] Constructive Proof of Brouwer's Fixed Point Theorem for Sequentially Locally Non-constant and Uniformly Sequentially Continuous Functions (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: 42 ページ: 1-6
  • 査読あり
• [雑誌論文] Constructive proof of the existence of Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions (2012)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: ISRN Computational Mathematics 巻: 2012 ページ: 1-9
  • DOI: 10.5402/2012/459459
  • 査読あり
• [雑誌論文] Equivalence between an approximate version of Brouwer's fixed point theorem and Sperner's lemma: A constructive analysis (2011)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics E-Notes 巻: Vol. 11 ページ: 238-243
  • URL: http://www.math.nthu.edu.tw/%7Eamen/2011/101108-2.pdf
  • 査読あり
• [雑誌論文] 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 Analysis (2011)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: vol. 41, No. 2 ページ: 133-140
  • URL: http://www.iaeng.org/IJAM/issues_v41/issue_2/IJAM_41_2_08.pdf
  • 査読あり
• [雑誌論文] Equivalence between the existence of an approximate equilibrium in a competitive economy and Sperner's lemma: A constructive analysis (2011)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: ISRN Applied Mathematics ページ: 1-15
  • URL: http://www.isrn.com/journals/appmath/2011/384625
  • 査読あり
• [雑誌論文] "A Constructive Analysis of Convex-Valued Demand Correspondence for Weakly Uniformly Rotund and Monotonic Preference (2011)
  • 著者名/発表者名: 田中靖人・佐藤敦宏
  • 雑誌名: Advances in Decision Sciences ページ: 1-7
  • URL: http://www.hindawi.com/journals/ads/2011/960819
  • 査読あり
• [雑誌論文] A proof of the existence of approximate Nash equilibrium in strategic game with multi-valued optimal responses directly by Sperner's lemma: A constructive analysis (2011)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Mathematical Modelling and Applied Computing 巻: Vol. 2 ページ: 309-319
  • 査読あり
• [雑誌論文] On constructive versions of Tychonoff's and Schauder's fixed point theorems (2011)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics E-Note 巻: Vol. 11 ページ: 125-132
  • URL: http://www.math.nthu.edu.tw/%7Eamen/2011/100624-1.pdf
  • 査読あり
• [雑誌論文] Equivalence between an approximate version of Brouwer's fixed point theorem and Sperner's lemma : A constructive analysis (2011)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes 巻: 11 ページ: 238-243
  • 査読あり
• [雑誌論文] Equivalence between the existence of an approximate equilibrium in a competitive economy and Sperner's lemma : A constructive analysis (2011)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: ISRN Applied Mathematics 巻: 2011 ページ: 1-15
  • DOI: 10.5402/2011/384625
  • 査読あり
• [雑誌論文] On constructive versions of Tychonoff's and Schauder's fixed point theorems (2011)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes 巻: 11 ページ: 125-132
  • 査読あり
• [雑誌論文] Proof of Constructive Version of the Fan-Glicksberg Fixed Point Theorem Directly by Sperner's Lemma and Approximate Nash Equilibrium with Continuous Strategies (2011)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: IAENG International Journal of Applied Mathematics 巻: 41 ページ: 133-140
  • 査読あり
• [雑誌論文] A proof of constructive version of Brouwer's fixed point theorem with uniform sequential continuity (2011)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: ISRN Applied Mathematics 巻: 11 ページ: 1-9
  • DOI: 10.5402/2011/276040
  • 査読あり
• [雑誌論文] A proof of the existence of approximate Nash equilibrium in strategic game with multi-valued optimal responses directly by Sperner's lemma : A constructive analysis (2011)
  • 著者名/発表者名: Yasuhito Tanaka, Atsuhiro Satoh
  • 雑誌名: International Journal of Mathematics, Game Theory and Algebra 巻: (掲載確定)
  • 査読あり
• [雑誌論文] A constructive analysis of convex-valued demand correspondence for weakly uniformly rotund and monotonic preference (2011)
  • 著者名/発表者名: Yasuhito Tanaka, Atsuhiro Satoh
  • 雑誌名: Advances in Decision Sciences 巻: (掲載確定)
  • 査読あり
• [雑誌論文] On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem (2009)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Decisions in Economics and Finance (the official publication of the Association for Mathematics Applied to Social and Economic Sciences) 巻: Vol. 32 ページ: 67-78
  • 査読あり
• [雑誌論文] On the Equivalence of the Arrow Impossibility Theorem and the Brouwer Fixed Point Theorem when Indivudual Preferences are Weak Orders (2009)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Journal of Mathematical Economics 巻: Vol. 45 ページ: 241-249
  • 査読あり
• [雑誌論文] Undecidability of Uzawa equivalence theorem and Cantor's diagonal arguments (2009)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics E-Notes 巻: Vol. 9 ページ: 1-9
  • URL: http://www.math.nthu.edu.tw/~amen/2009/070902-1.pdf
  • 査読あり
• [雑誌論文] The HEX game theorem and the Arrow impossibility theorem: the case of weak orders (2009)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Metroeconomica 巻: Vol. 60 ページ: 77-90
  • 査読あり
• [雑誌論文] On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Decisions in Economics and Finance (the official publication of the Association for Mathematics Applied to Social and Economic Sciences Vol.32 ページ: 67-78
  • 査読あり
• [雑誌論文] On the Equivalence of the Arrow Impossibility Theorem and the Brouwer Fixed Point Theorem when Indivudual Preferences are Weak Orders (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Journal of Mathematical Economics Vol.45 ページ: 241-249
  • 査読あり
• [雑誌論文] Undecidability of Uzawa equivalence theorem and Cantor's diagonal arguments (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes(國立清華大学(台湾))(National Tsing Hua University) Vol.9 ページ: 1-9
  • 査読あり
• [雑誌論文] The HEX game theorem and the Arrow impossibility theorem : the case of weak orders (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Metroeconomica(Blackwell) 60 ページ: 77-90
  • 査読あり
• [雑誌論文] On the Equivalence of the Arrow Impossibility Theorem and the Brouwer Fixed Point Theorem when Indivudual Preferences are Weak Orders (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Journal of Mathemtical Economics 45 ページ: 241-249
  • 査読あり
• [雑誌論文] On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Decisions in Economics and Finance 32 ページ: 67-78
  • 査読あり
• [雑誌論文] Undecidability of Uzawa equivalence theorem and Cantor's diagonal arguments (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes 9 ページ: 1-9
  • 査読あり
• [雑誌論文] Brouwerの不動点定理によるNTUコアの存在証明 (2009)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: 同志社大学経済学論叢 60巻4号 ページ: 85-96
  • NAID: 110008138894
• [雑誌論文] Undecidability of the existence of dictator for strongly candidate stable voting procedures in an infinite society and Cantor's diagonal argument (2008)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Computational & Applied Mathematics 巻: Vol. 27 ページ: 251-268
  • 査読あり
• [雑誌論文] Undecidability of Uzawa equivalence theorem and LLPO (Lesser limited principle of omniscience) (2008)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics and Computation 巻: Vol. 201 ページ: 378-383
  • 査読あり
• [雑誌論文] On the computability of binary social choice rules in an infinite society and the halting problem (2008)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics and Computation 巻: Vol. 197, No. 2 ページ: 598-603
  • 査読あり
• [雑誌論文] The Arrow impossibility theorem of social choice theory in an infinite society and Limited principle of omniscience (2008)
  • 著者名/発表者名: 田中靖人
  • 雑誌名: Applied Mathematics E-Notes 巻: Vol. 8 ページ: 82-88
  • URL: http://www.math.nthu.edu.tw/~amen/2008/070202-2.PDF
  • 査読あり
• [雑誌論文] Undecidability of the existence of dictator for strongly candidate stable voting procedures in an infinite society and Cantor's diagonal argument (2008)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Computational & Applied Mathematics(SBMAC(Brazil)) Vol.27, No.3 ページ: 251-268
  • 査読あり
• [雑誌論文] Undecidability of Uzawa equivalence theorem and LLPO (Lesser limited principle of omniscience) (2008)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics and Computation(Elsevier) Vol.201, No.1 ページ: 378-383
  • 査読あり
• [雑誌論文] On the computability of binary social choice rules in an infinite society and the halting problem (2008)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics and Computation(Elsevier) Vol.197, No.2 ページ: 598-603
  • 査読あり
• [雑誌論文] The Arrow impossibility theorem of social choice theory in an infinite society and Limited principle of omniscience (2008)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes(國立清華大学(台湾))(National Tsing Hua University) Vol.8 ページ: 82-88
  • 査読あり
• [雑誌論文] Undecidability of the existence of dictator for strongly candidate stable voting procedures in an infinite society and Cantor's diagonal argument (2008)
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Computational & Applied Mathematics 27 ページ: 251-268
  • 査読あり
• [雑誌論文] Equivalence between the existence of an approximate equilibrium in a competitive economy and Sperner's lemma : A constructive analysis
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: ISRN Applied Mathematics, Hindawi Publishing Corporation. 掲載予定
  • 査読あり
• [雑誌論文] A proof of the existence of approximate core in NTU game directly by Sperner's lemma : A constructive analysis
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Mathematics Applied in Science and Technology, Research India Publications. 掲載予定
  • 査読あり
• [雑誌論文] A constructive analysis of convex-valued demand correspondence for weakly uniformly rotund and monotonic preference", with Atsuhiro Satoh
  • 著者名/発表者名: Yasuhito Tanaka, Atsuhiro Satoh
  • 雑誌名: Advances in Decision Sciences, Hindawi Publishing Corporation. 掲載予定
  • 査読あり
• [雑誌論文] A proof of the existence of approximate Nash equilibrium in strategic game with multi-valued optimal responses directly by Sperner's lemma : A constructive analysis
  • 著者名/発表者名: Yasuhito Tanaka, Yasuhito Tanaka
  • 雑誌名: International Journal of Mathematics, Game Theory and Algebra, Nova Science Publishers. 掲載予定
  • 査読あり
• [雑誌論文] On constructive versions of Tychonoff's and Schauder's fixed point theorems
  • 著者名/発表者名: Yasuhito Tanaka
  • 雑誌名: Applied Mathematics E-Notes, 國立清華大学(台湾)(National Tsing Hua University) 掲載予定
  • 査読あり
• [備考]
  • URL: http://yatanaka.doshisha.ac.jp
• [備考]
  • URL: http://yatanaka.doshisha.ac.jp/index.html