Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2009-07-17 Number: 09-064/1 Author-Name: Rene van den Brink Author-Workplace-Name: VU University Amsterdam Author-Name: Ilya Katsev Author-Workplace-Name: Russian Academy of Sciences Author-Name: Gerard van der Laan Author-Workplace-Name: VU University Amsterdam Title: Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems Abstract: This discussion paper led to a publication in 'Economic Theory', 47(1), 175-88.
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 (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. 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. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson rule for conference structures. Classification-JEL: C71 Keywords: TU-game, restricted cooperation, union closed system, Shapley value, permission value, superior graph, axiomatization File-Url: http://papers.tinbergen.nl/09064.pdf File-Format: application/pdf File-Size: 252510 bytes Handle: RePEc:tin:wpaper:20090064