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

Begoña Subiza, José-Manuel Giménez-Gómez and Josep E. Peris

Journal of Mathematical Economics, 2025, vol. 119, issue C

Abstract: 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 terms of dominance. It is well known that the core may be an empty set, whereas stable sets may fail to exist, or may produce different proposals. We provide a new dominance relation so that the stable set obtained when applying this notion (the δ-stable set) always exists, it is unique, and it coincides with the core of the cooperative game, whenever the core is not empty. We apply this concept to some particular classes of TU-games having typically an empty core: voting (majority) games, minimum cost spanning trees games with revenue, controlled capacitated networks, or m-sequencing games.

Keywords: Dominance; Core; Stable set (search for similar items in EconPapers)
JEL-codes: C71 D63 D71 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:119:y:2025:i:c:s0304406825000540

DOI: 10.1016/j.jmateco.2025.103137

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