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Solymosi博士はゲーム理論分野の国際学術誌International Journal of Game Theory (IJGT)のAssociate Editorであり、協力ゲーム理論やOR,計算機理論などを横断する数学者です。産業経済研究所2024年度研究プロジェクト「ブロックチェーン技術、情報および知的財産権に関する経済分析」(研究代表:経済学部教授 大石尊之)との共催で、下記の講演を行います(対面とZoomのハイブリッド開催)。登録は不要です。奮ってご参加ください。
【発表論文】
Title: Core-related allocations in tree enterprise games Abstract: We consider a multi-agent decision situation where cooperation is possible but constrained by a hierarchical structure among the agents. The dependency relations are assumed to form a rooted tree graph. The root of the tree represents a "crucial" resource, while each other node represents an agent with a given profit-making potential that can only be realized if all agents along the path to the root also participate. Accessing the "crucial" resource involves a fixed cost.
We study stable allocations in such tree enterprise situations via solutions of associated cooperative games, called tree enterprise games. The value of a coalition of agents is determined by the total potential profits of its members who are connected to the root through other coalition members, subtracting the fixed cost of the "crucial" resource, which does not depend on the coalition being served. We examine the core of tree enterprise games and show that, under reasonable assumptions, it is non-empty and can be described by a polynomial-size system of linear constraints. This implies that the nucleolus of tree enterprise games can be computed in polynomial time. Furthermore, the algorithm solely requires the parameters of the tree enterprise situation; there is no need to explicitly generate all the exponentially many coalition values and use a general-purpose algorithm for nucleolus computation.
Two well-known special types of tree enterprise games are peer group games and bankruptcy games. The above-mentioned results concerning the core and nucleolus for these games are already well established. In the talk, we present some new observations regarding the less-studied Gately value for both types of games. |