The stable set in a generalized assginment problem

• Project/Area Number: 16K17079
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Economic theory
• Research Institution: Shinshu University (2017-2018); Tokyo University of Science (2016)
• Principal Investigator: BANDO Keisuke 信州大学, 学術研究院社会科学系, 講師 (50735412)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: マッチング理論 / 安定集合 / 安定マッチング / 一般化割当て問題 / 安定集合解 / ゲーム理論 / ミクロ経済 / オークション / ミクロ経済学 / 割り当て問題

Outline of Final Research Achievements

We analyze the model of a generalized assignment problem in which many sellers trade with many buyers with monetary transfers. In this model, each agent may not has a quasi linear utility function. We investigate equilibrium behavior in the Von Neumann-Morgenstern (vNM) stable set, which is a solution concept proposed in cooperative game theory. We provide an algorithm that finds a vNM stable set under certain conditions. This algorithm can be interpreted as a collusion behavior among buyers (or sellers) in a multi-tem auction.

Academic Significance and Societal Importance of the Research Achievements

本研究では複数の買い手と複数の売り手の間の市場取引を行い、安定集合解を求めるアルゴリズムを新たに提案した。このアルゴリズムは、オークションで財を落札した勝者が財を落札できなかったある特定の敗者に対して金銭移転を行い、入札を控えさせるような交渉を表しており、オークションにおける談合行動が安定的な帰結として実現されうることを示唆している。

Research Products

• [Journal Article] A necessary and sufficient condition for weak Maskin monotonicity in an allocation problem with indivisible goods (2016)
  • Author(s): Keisuke Bando and Kenzo Imamura
  • Journal Title: Social Choice and Welfare Volume: 47 Issue: 3 Pages: 589-606
  • DOI: 10.1007/s00355-016-0984-x
  • Peer Reviewed
• [Presentation] Existence of a Stable Outcome under Observable Substitutability across Doctors in Many-to-Many Matching with Contracts (2019)
  • Author(s): Keisuke Bando, Toshiyuki Hirai
  • Organizer: East Asian Game Theory Conference 2019
  • Int'l Joint Research
• [Presentation] Existence of a Stable Outcome under Observable Substitutability across Doctors in Many-to-Many Matching with Contracts (2019)
  • Author(s): Keisuke Bando, Toshiyuki Hirai
  • Organizer: The 1st Mini-conference on Matching in Waseda 2019
• [Presentation] Existence of a Stable Outcome under Observable Substitutability across Doctors in Many-to-Many Matching with Contracts (2018)
  • Author(s): Keisuke Bando, Toshiyuki Hirai
  • Organizer: The Lisbon Meetings in Game Theory and Applications 2018
  • Int'l Joint Research
• [Presentation] Existence of a Stable Outcome under Observable Substitutability across Doctors in Many-to-Many Matching with Contracts (2018)
  • Author(s): Keisuke Bando, Toshiyuki Hirai
  • Organizer: RISS-CEE共催ワークショップ マッチング理論の現在とその社会実装に向けて
• [Presentation] On stable outcomes of the multilateral matching (2017)
  • Author(s): Keisuke Bando and Toshiyuki Hirai
  • Organizer: 一橋大学経済理論ワークショップ
  • Place of Presentation: 一橋大学
  • Year and Date: 2017-01-21
• [Presentation] On Stable Outcomes of the Multilateral Matching (2017)
  • Author(s): Keisuke Bando and Toshiyuki Hirai
  • Organizer: European Meeting on Game Theory (SING13)
  • Int'l Joint Research
• [Presentation] On Stable Outcomes of the Multilateral Matching (2017)
  • Author(s): Keisuke Bando and Toshiyuki Hirai
  • Organizer: 18th meeting of the Association for Public Economic Theory
  • Int'l Joint Research
• [Presentation] On Stable Outcomes of the Multilateral Matching (2017)
  • Author(s): Keisuke Bando and Toshiyuki Hirai
  • Organizer: East Asian Game Theory Conference 2017
  • Int'l Joint Research
• [Presentation] Essential μ-compatible subgames for obtaining a von Neumann-Morgenstern stable set in an assignment game (2016)
  • Author(s): Keisuke Bando and Yakuma Furusawa
  • Organizer: The 9th International Symposium on Algorithmic Game Theory (SAGT2016)
  • Place of Presentation: Liverpool, UK
  • Year and Date: 2016-09-21
  • Int'l Joint Research