R. van den Brink (RenĂ«)
http://repub.eur.nl/ppl/26532/
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http://repub.eur.nl/
RePub, Erasmus University RepositoryPlayers Indifferent to Cooperate and Characterizations of the Shapley Value
http://repub.eur.nl/pub/32657/
Sat, 07 Apr 2012 00:00:01 GMT<div>M. Conrado</div><div>E. Gonzalez-Aranguena</div><div>R. van den Brink</div>
n this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first new axiom expresses that the payoffs of two players who are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace t he second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values.A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure
http://repub.eur.nl/pub/21374/
Thu, 11 Nov 2010 00:00:01 GMT<div>R. van den Brink</div><div>I. Katsev</div><div>G. van der Laan</div>
Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems there is some hierarchical ordering of the players. In this paper we consider a class of games with a permission structure describing situations in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with a permission structure which economic applications include auction games, dual airport games, dual polluted river games and information market games.