A value for j-cooperative games: some theoretical aspects and applications

Abstract

A value that has all the ingredients to be a generalization of the Shapley value is proposed for a large class of games called j-cooperative games which are closely related to multi-choice games. When it is restricted to cooperative games, i.e. when j equals 2, it coincides with the Shapley value. An explicit formula in terms of some marginal contributions of the characteristic function is provided for the proposed value. Different arguments support it: (1) The value can be inferred from a natural probabilistic model. (2) An axiomatic characterization uniquely determines it. (3) The value is consistent in its particularization from j-cooperative games to j-simple games. This chapter also proposes various ways of calculating the value by giving an alternative expression that does not depend on the marginal contributions. This chapter shows how the technique of generating functions can be applied to determine such a value when the game is a weighted j-simple game. The chapter concludes by presenting several applications, among them the computation of the value for a proposed reform of the UNSC voting system.