Evaluation and Optimization of Market Mechanisms Based on Quantitative Analysis

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K18004
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: National Institute of Informatics
• Principal Investigator: Yokoi Yu 国立情報学研究所, 情報学プリンシプル研究系, 助教 (60805480)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: マッチング / アルゴリズム / 組合せ最適化 / 近似アルゴリズム / ゲーム理論 / メカニズムデザイン

Outline of Final Research Achievements

In this research, we analyzed the mathematical model of matching markets involving agents with preferences from the viewpoints of combinatorial optimization and game theory. For a matching model with lower quotas, for which the existence of a stable matching is not guaranteed, we take approaches such as relaxation of the solution concept and satisfying lower quotas approximately, and design efficient algorithms that achieve the desired properties in an approximate sense. In addition, we proposed and analyzed a decentralized matching model in which matching is formed by participants making successive decisions, and clarified the computational complexity and the conditions for the obtained matching to satisfy stability.

Free Research Field

組合せ最適化

Academic Significance and Societal Importance of the Research Achievements

選好をともなうマッチングモデルはこれまでにも盛んに研究がなされており，既に数多くの応用例をもつ．しかし実社会の問題の中には，その背景に起因した様々な付加的な要請をもつものや，既存のモデルの範疇を超えるものも数多く存在する．そしてそれらは，問題の構造上解をもたなかったり，計算量的な困難性を有していたりする．本研究で得られた新しいモデルに対する解析結果や，困難な問題に対する近似的な解法は，マッチング理論の応用可能性を高めることに貢献し得る．