The hypergraph matching game is a cooperative game defined on a hypergraph such that the vertices are the players, and the characteristic function is the value of a maximum hypergraph matching on a hypergraph induced by a coalition. 
In this talk, we study a computationally tractable condition of the hypergraph matching game, called the convexity.
First, we prove that the problem of checking whether a given hypergraph matching game is convex or not is solvable in polynomial time.
Second, we prove that the Shapley value of a given convex hypergraph matching game is exactly computable in polynomial time.
Finally, we consider the fractional hypergraph matching game and prove that if the fractional hypergraph matching game is convex, then its characteristic function coincides with the characteristic function of the corresponding (integral) hypergraph matching game.

Convexity of Hypergraph Matching Game

Social Choice and Cooperative Game Theory

technical paper

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). The aim of the joint conference is to provide a single, high-profile, internationally-respected archival forum for scientific research in the theory and practice of autonomous agents and multi-agent systems.

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AAMAS 2020

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). 

Soh Kumabe

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Convexity of Hypergraph Matching Game

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