The Core for Games with Cooperation Structure
A cooperative game consists of a set of players and a characteristic function that determines the maximal profit or minimal cost that each subset of players can get when they decide to cooperate, regardless of the actions of the rest of the players. The relationships among the players can modify their bargaining and therefore their payoffs. The model of cooperation structures in a game introduces a graph on the set of players setting their relations and in which its components indicate the groups of players that are initially formed. In this paper we define the core and the Weber set and the notion of convexity for this family of games.
KeywordsCooperative game A priori unions Core Weber set Cooperation structure Convexity
This research has been partially supported by the Spanish Ministry of Economy and Competitiveness ECO2013-40755-P, and by the FQM237 grant of the Andalusian Government.
The second author thanks the Agence Nationale de la Recherche for financial support under contract ANR-13-BSHS1-0010 (DynaMITE).
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