2009 Fiscal Year Final Research Report
Studies on continuous and discrete structures in optimization and game theory
| Project/Area Number |
18340031
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
KAWASAKI Hidefumi Kyushu University, 大学院・数理学研究院, 教授 (90161306)
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| Co-Investigator(Renkei-kenkyūsha) |
IWAMOTO Seiichi 九州大学, 大学院・経済学研究院, 教授 (90037284)
FUKUMOTO Yasuhide 九州大学, 大学院・数理学研究院, 教授 (30192727)
HYAKUTAKE Hiroto 九州大学, 大学院・数理学研究院, 准教授 (70181120)
TANINO Tetsuzo 大阪大学, 大学院・工学研究科, 教授 (50125605)
SHIRAISHI Shunsuke 富山大学, 経済学部, 教授 (60226313)
FUJITA Toshiharu 九州工業大学, 工学部, 准教授 (60295003)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 最適化 / ゲーム理論 / 離散不動点定理 / ナッシュ均衡 / 双対定理 / 動的計画法 / 縮小写像 / 3相分割問題 |
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| Research Abstract |
We have extended a duality theorem for the three-phase partition problem to two cases. One is the case that the optimal solution is degenerate, and the other is in higher dimensional space. We have given two types of discrete fixed point theorems. One is for monotone mappings and the other is for contraction mappings. We showed that the monotonicity is necessary in the two-person game. Further, we delete convexity assumption from discrete fixed point theorem based on Brouwer's fixed point theorem.
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