Séminaires : Séminaire de Topologie

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Cooperative game theory studies how cooperation arises between individuals depending on the eventual gains that each possible coalition can obtain. This is modelled by the notion of a cooperative game, which amounts to the data of a set of players N and a set function from the power set P(N) to the real numbers. The main goal of this talk is to explain how one can study cooperative games using operad theory. We start by endowing the collection of all cooperative games with any number of players with an operad structure. Then, we will explain how the composition in this operad generalizes to the notions composition/aggregation of games considered before by Owen, Shapley, von Neumann and Morgenstern, and many others. Furthermore, we explicitly compute this operad in terms of generators and relations, and show that it corresponds via the Möbius transform to the operad encoding commutative triassociative algebras. If time permits, we will then explain how this operad structure restricts to many interesting classes of games (simple, balanced, capacities a.k.a fuzzy measures and convex functions, totally monotone, etc) and how one can obtain a new operad structure on the family of all generalized permutahedra using this.

Finally, we will explain how different solution concepts such as the core and the Shapley or the Banzhaf values interact with the composition of this operad. This is joint work with Dylan Laplace Mermoud, based on: https://arxiv.org/abs/2507.01969