van den Brink, Rene Katsev, Ilya van der Laan, Gerard
Year of Publication:
Tinbergen Institute Discussion Paper 11-036/1
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. Properties of solutions (the core, the nucleolus, the prekernel and the Shapley value) are given for games on union closed systems.
TU-game restricted cooperation union closed system core prekernel nucleolus