Cooperative TU-games: Dominance, stable sets, and the core revisited

Article  -  Tuesday, 29 July 2025

Subiza, B.; Giménez-Gómez, J.M. and Peris, J.E. (2025): "Cooperative TU-games: Dominance, stable sets, and the core revisited", Journal of Mathematical Economics

"Stable sets are introduced by von Neumann and Morgenstern (1944) as «the solution» of a cooperative game. Later on, Gillies (1953) defines the core of the game. Both notions can be established in teStable sets were introduced by von Neumann and Morgenstern (1944) as "the solution" to a cooperative game. Later, Gillies (1953) defined the core of the game. Both concepts can be formulated in terms of dominance. It is well known that the core may be empty, while stable sets may fail to exist or may yield multiple proposals. We introduce a new dominance relation such that the stable set obtained under this notion (the delta-stable set) always exists, is unique, and coincides with the core of the cooperative gamewhenever the core is non-empty. We apply this concept to certain specific classes of transferable utility games (TU-games) that typically have an empty core: voting (majority) games, minimum cost spanning tree games with revenue, controlled capacitated networks, and m-sequencing games."

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