Game trees without a unique equilibrium distribution: A research by resource-bounded martingales

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540146
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: SUZUKI Toshio 首都大学東京, 理工学研究科, 准教授 (30235973)
• Co-Investigator(Kenkyū-buntansha): KUMABE Masahiro 放送大学, 教養学部, 教授 (70255173)
• Project Period (FY): 2010-04-01 – 2015-03-31
• 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

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.

Free Research Field

数学基礎論，計算理論