The aim of this paper is to introduce cooperative games with a feasible coalition system which is called antimatroid. These combinatorial structures generalize the permission structures, which have nice economical applications. With this goal, we …rst characterize the approaches from a permission structure with special classes of antimatroids. Next, we use the concept of interior operator in an antimatroid and we de…ne the restricted game taking into account the limited possibilities of cooperation determined by the antimatroid. These games extend the restricted games obtained by permission structures. Finally, we provide a computational method to obtain the Shapley and Banzhaf values of the players in the restricted game, by using the worths of the original game.
Abstract. We study cooperation structures with the following property: Given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. These combinatorial structures have a direct relationship with graph communication situations and conference structures à la Myerson. Characterizations of the Myerson value in this context are provided using the concept of basis for union stable systems. Moreover, TU-games restricted by union stable systems generalizes graph-restricted games and games with permission structures.
Mathematics Subject Classification 2000: 91A12
Abstract. In this paper, we study the position value for games in which partial cooperation exist, that is based on a union stable coalition system. The concept of basis is introduced for these systems, allowing for a de®nition of the position value. Moreover, an axiomatic characterization of the position value is provided for a speci®c class of union stable systems. Conditions under which convexity is inherited from the underlying game to the conference game, and the position value is a core vector of the restricted game are provided.1991 Mathematics Subject Classi®cation: 90D12
A game on a convex geometry is a real-valued function deÿned on the family L of the closed sets of a closure operator which satisÿes the ÿnite Minkowski-Krein-Milman property. If L is the boolean algebra 2 N then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axioms that give rise to a unique Shapley value for games on convex geometries.
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