Silvia Lorenzo-Freire

Computing power indices: Multilinear extensions and new characterizations

Abstract Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n -person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.

“Optimistic” weighted Shapley rules in minimum cost spanning tree problems

Abstract We introduce optimistic weighted Shapley rules in minimum cost spanning tree problems. We define them as the weighted Shapley values of the optimistic game v+ introduced in Bergantinos and Vidal-Puga [Bergantinos, G., Vidal-Puga, J.J., forthcoming. The optimistic TU game in minimum cost spanning tree problems. International Journal of Game Theory. Available from: ]. We prove that they are obligation rules [Tijs, S., Branzei, R., Moretti, S., Norde, H., 2006. Obligation rules for minimum cost spanning tree situations and their monotonicity properties. European Journal of Operational Research 175, 121–134].

Characterizations of the Deegan-Packel and Johnston power indices

Abstract In this paper, we provide a new characterization of the Deegan–Packel power index, which uses a new monotonicity property, and two characterizations of the Johnston power index by employing some usual properties of the literature and two new transfer properties. Finally, a real-world numerical example taken from the political field illustrates the main differences between these two indices.

The two-stage constrained equal awards and losses rules for multi-issue allocation situations

This paper considers two-stage solutions for multi-issue allocation situations, which are extensions of bankruptcy problems. Characterizations are provided for the two-stage constrained equal awards and constrained equal losses rules, based on the properties of composition up and composition down.

A characterization of the proportional rule in multi-issue allocation situations

In multi-issue allocation situations, we have to divide a resource among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present an axiomatic characterization of the proportional rule.

A characterization of Kruskal sharing rules for minimum cost spanning tree problems

In Tijs et al. (Eur J Oper Res 175:121–134, 2006) a new family of cost allocation rules is introduced in the context of cost spanning tree problems. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity.

The family of cost monotonic and cost additive rules in minimum cost spanning tree problems

In this article, we define a new family of rules in minimum cost spanning tree problems related with Kruskal’s algorithm. We characterize this family with a cost monotonicity property and a cost additivity property.

Balanced contributions for TU games with awards and applications

Abstract Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.

New characterizations of the constrained equal awards rule in multi-issue allocation situations

Multi-issue allocation situations are used to study the problem of having to divide an estate among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present several axiomatic characterizations of the constrained equal awards rule generalizing some characterizations of these rules in bankruptcy situations.

A generalization of obligation rules for minimum cost spanning tree problems

Tijs et al. [23] introduce the family of obligation rules for minimum cost spanning tree problems. We give a generalization of such family. We prove that our family coincides with the set of rules satisfying an additivity property and a cost monotonicity property. We also provide two new characterizations for the family of obligation rules using the previous properties. In the first one, we add a property of separability; and in the second one, we add core selection.