| 研究実績の概要 |
In the second year, I was working on two topics:
1. I have been working with Takaaki Abe (PSE, Waseda University) on the dynamic coalition formation process. We introduce a concept called monotonic core allocation path (MCAP) for assignment games. We showed that for every assignment game, there is an order of players along which a MCAP exists. The strong connection of MCAP with extreme core allocations suggests some conflict between the stability of a coalition formation process and the fairness. We completed the paper “Monotonic Core Allocation Paths for Assignment Games”, which is revised and resubmitted to Social Choices and Welfare.
2. I provided an epistemic foundation for cooperative games by proof theory via studying the knowledge for players unanimously accepting only core payoffs. I first transformed each cooperative game into a decision problem. Then I used a modified KD-system in epistemic logic to describe a player's knowledge, decision-making criterion, and reasoning process. I characterized the core of a cooperative game in terms of players' knowledge. Based on it, I discussed the epistemic inconsistency behind Debreu-Scarf Theorem, that is, the increase of the number of replicas has invariant requirement on each participant's knowledge from the aspect of competitive market, while requires unbounded epistemic ability players from the aspect of cooperative game. I finished the paper “Knowledge and Unanimous Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game Theory” and presented it on LOFT 13 on July 18th, 2018.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
Because my paper was selected by LOFT 13 ((The 13th Conference on Logic and the Foundations of Game and Decision Theory, Bocconi University) and I presented there. LOFT, together with TARK, are the two best multidisciplinary international conferences on game theory, decision theory, computer science, and philosophy. I got many valuable comments for my paper and got to know may excellent researchers in those fields, which facilitated and escalated my research.
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| 今後の研究の推進方策 |
Now I am working on the structure features of dynamic games. I have done some research on a faithful representation of the chronological order of the moves in a dynamic game which plays a vital role in fields like epistemic game theory. Based on it, I would like to explore more on epistemic criteria of epistemic game theory and its complexity. Also, I am working on how to analyze some decision criterion by a newly developed modal logic system called “Know-wh” logic.
I will go to teach in the summer school on epistemic game theory in EPICENTER, Maastricht University this July, and I will discuss with researchers there about my idea. Also, I will enhance my coordination with logicians in Department of Philosophy, Peking University.
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