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 game
whenever 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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