2019 Fiscal Year Final Research Report
Pairwise solvable games: Theory and applications
| Project/Area Number |
17K03631
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Economic theory
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| Research Institution | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | ナッシュ均衡 / 被支配戦略の削除 / 交換可能性 / 進化均衡 / ゼロ和ゲーム |
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| Outline of Final Research Achievements |
A game is solvable if the set of Nash equilibria is nonempty and interchangeable. A pairwise solvable game is a two-person symmetric game in which any restricted game generated by a pair of strategies is solvable. We show that the set of equilibria in a pairwise solvable game is interchangeable, which implies that a pairwise solvable game is solvable if it possesses an equilibrium. Under a quasiconcavity condition, we derive a complete order-theoretic characterization and some topological sufficient conditions for the existence of equilibria, and show that if the game is finite, then an iterated elimination of weakly dominated strategies leads precisely to the set of Nash equilibria, which means that such a game is both solvable and dominance solvable. All results are applicable to symmetric contests, such as the rent-seeking game and the rank-order tournament, which are shown to be pairwise solvable. Some applications to evolutionary equilibria are also given.
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| Free Research Field |
ゲーム理論
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| Academic Significance and Societal Importance of the Research Achievements |
ゲーム理論の標準的分析において「解」としての役割を果たしているのは（ナッシュ）均衡である．その背後には，諸個人の行動選択は均衡に行き着くという想定がある．だが，これはどのような場合に正当化されるのだろうか．すなわち，均衡に至るどのようなメカニズムがあるのだろうか．
そのようなメカニズムに，被支配戦略の繰返し削除がある．本研究は，レント獲得ゲームなどの応用上重要なゲームを含む十分大きなゲームのクラスである対可解ゲームを新たに見出し，一定の条件のもと被支配戦略の繰返し削除によってその均衡が達成されることを明らかにすることにより，この均衡の基礎問題にひとつの解答を与えるものである．
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