We define multilinear extensions for multichoice games and relate them to probabilistic values and semivalues. We apply multilinear extensions to show that the Banzhaf value for a compound multichoice game is not the product of the Banzhaf values of the component games, in contrast to the...

We introduce and compare several coalition values for multichoice games. Albizuri defined coalition structures and an extension of the Owen coalition value for multichoice games using the average marginal contribution of a player over a set of orderings of the player’s representatives....

Cooperative games on antimatroids are cooperative games in which coalition formation is restricted by a combinatorial structure which generalizes permission structures. These games group several well-known families of games which have important applications in economics and politics. The current...

According to the work of Faigle [3] a static Shapley value for games on matroids has been introduced in Bilbao, Driessen, Jiménez-Losada and Lebrón [1]. In this paper we present a dynamic Shapley value by using a dynamic model which is based on a recursive sequence of static models. In this...

In the classical model of cooperative games, it is considered that each coalition of players can form and cooperate to obtain its worth. However, we can think that in some situations this assumption is not real, that is, all the coalitions are not feasible. This suggests that it is necessary to...

Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the...

Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the structure of posets by means of a recursive...

By focusing on the protectionist tendency found in the design of voting games, a thorough analysis is provided for the role of blocking coalitions in a simple game. We characterize those blocking families that univocally determine the game, and show that otherwise at least three games share a...

In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley...

In this article a new value for positive cooperative games is introduced. It generalizes the “proportional division of surplus” idea for two person games. A characterization by means of preservation of ratios and efficiency provides existence and uniqueness. Moreover, this value is the only...