The Shapley Transfer Procedure for NTU-Games

Abstract

A cooperative game is described by sets of feasible utility vectors, one set for each coalition. Such a game may arise from each situation where involved parties can achieve gains from cooperation. Examples range from exchange economies to cost allocation between divisions of multinationals or power distribution within political systems. The two central questions are: which coalitions will form; and on which payoffs will each formed coalition agree. Since an answer to the latter question seems a prerequisite to study the former question of coalition formation, most of the literature has concentrated on the question of payoff distribution. Specifically, the usual assumption is that the grand coalition of all players will form and then the question is which payoff vector(s) this coalition will agree upon. This question has been studied extensively for two special cases: games with transferable utility, and pure bargaining games. In a game with transferable utility, what each coalition can do is described by just one number: the total utility or payoff, which that coalition can distribute among its members in any way it wants. The underlying assumption is the presence of a common medium of exchange in which the players’ utilities are linear. For instance, the payoff is in monetary units and the players have linear utility for money.