| Project/Area Number |
16K05278
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 離散不動点定理 / 離散分離定理 / 離散凸解析 / ゲーム理論 / 純戦略均衡 / 共通不動点定理 / L凸集合 / 展開形ゲーム / マルコフ・角谷の共通不動点定理 / 中間値の定理 / 離散最適化 / スペルナーの補題 / 非線形計画法 / 不動点定理 / ナッシュ均衡 / 凸解析 / 二者択一の定理 / 最適化理論 / 応用数学 |
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| Outline of Final Research Achievements |
Our research focused on discrete and continuous structures on optimization theory, fixed point theory and its application to game theory. Nash used the fixed point theorem to show that any strategic game has a mixed strategy (rolling dice) equilibrium. The discrete fixed point theorem can be used to show the existence of a pure strategy (without rolling dice) equilibrium. In this study, we used the discrete fixed point theorem of accumulation mappings to show that games that bundle extensive-form games have a pure strategy equilibrium. He also used a discrete separation theorem to give a discrete common fixed point theorem on the L-convex set. Furthermore, regarding Sperner's lemma, labeling using a direction-preserving mapping showed that one of the vertices of any completely labeled subsimplex is a fixed point.
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| Academic Significance and Societal Importance of the Research Achievements |
最適化理論やゲーム理論は工学や経済学への応用を念頭に置いた数学理論である。Nashは不動点定理を用いて戦略形ゲームが混合戦略（サイコロを振る）均衡をもつことを示しノーベル経済学賞を受賞した。組合せ最適化問題の１つであるマッチングでは一人の男性が２人の女性と付き合うことは許されない。そのような問題ではサイコロを振らない純戦略均衡が必要になる。本研究では様々な離散不動点定理や離散分離定理を用いて、純戦略の存在に取り組んだ。
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