Bargaining sets and the core in partitioning games

Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization problems. We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of the Mas–Colell, the classical, the semireactive, and the reactive bargaining sets with the core for interesting balanced subclasses of partitioning games, including assignment games, tree–restricted superadditive games, and simple network games.