Study of the mathematical structure of social choice theory and economic theory
Project/Area Number |
20530165
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Economic theory
|
Research Institution | Doshisha University |
Principal Investigator |
|
Project Period (FY) |
2008 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
Keywords | 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 |
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.
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Report
(7 results)
Research Products
(69 results)