Geometry of set functions in cooperative game theory

01/08/2023

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by   Dylan Laplace Mermoud, et al.

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They are many unexplored links between cooperative transferable utility games and convex, discrete or combinatorial geometry. In this paper, we investigate some of these links, such as the ones between cores of convex games and generalized permutohedra, also named polymatroids or base polyhedra. Another link that we investigate is the one between the resonance hyperplane arrangement and the set of sets of preimputations which are effective for a given coalition. These bridges can give interpretation and intuition to cooperative game theory, as well as bring new results and tools from other fields into the study of cooperative games.