Game trees without a unique equilibrium distribution: A research by resource-bounded martingales
| Project/Area Number |
22540146
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Metropolitan University |
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Principal Investigator |
SUZUKI Toshio 首都大学東京, 理工学研究科, 准教授 (30235973)
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| Co-Investigator(Kenkyū-buntansha) |
KUMABE Masahiro 放送大学, 教養学部, 教授 (70255173)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 数学基礎論 / 数理論理学 / 計算量理論 / ゲーム理論 / 人工知能 / 命題論理 / 最適化問題 / ミニマックス定理 / アルゴリズム / 応用数学 / 情報基礎 |
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| Outline of Final Research Achievements |
(1) A martingale is a concept similar to probability attached to a tree. We investigate a resource-bounded martingale, where “resource-bounded” means that an algorithm with a certain constraint can compute it. On fundamental research of resource-bounded martingales, we published an academic paper. At the moment, this is the most important work among joint researches by Kumabe and Suzuki.
(2) A game tree is a tree diagram representing all possible moves of a given game. Here, we investigate a binary tree whose terminals are bi-valued. Such a tree is a Boolean formula, and a set of terminal values is a truth assignment. We have established a theory on the case where, among probability distribution on truth assignments, the equilibrium point is not unique.
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Report
(7 results)
Research Products
(42 results)
