Gustavo Bergantiños

A fair rule in minimum cost spanning tree problems

We study minimum cost spanning tree problems and define a cost sharing rule that satisfies many more properties than other rules in the literature. Furthermore, we provide an axiomatic characterization based on monotonicity properties.

The optimistic TU game in minimum cost spanning tree problems

We associate an optimistic TU game with each minimum cost spanning tree problem. We define the worth of a coalition S as the cost of connecting agents in S to the source assuming that agents in N\S are already connected to the source, and agents in S can connect through agents in N\S. We study the Shapley value of this new game.

A non-cooperative approach to the cost spanning tree problem

Abstract.We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source.

Additivity in bankruptcy problems and in allocation problems

Abstract. We study the property of additivity in bankruptcy problems and in allocation problems. In bankruptcy problems we use this property to characterize the Talmudic rule proposed by Rabbi Ibn Ezra. Moreover we generalize this rule to every bankruptcy problem. Again, using additivity we characterize the rights egalitarian solution in allocation problems.

On values for generalized characteristic functions

In this work we study a new generalization for the Shapley value. We consider games in coalitional form in which the characteristic function is defined on all possible orders. These games are useful to model some economic situations. Different axiomatic characterizations are found for the new value using marginality, balanced contributions, the potential and the consistency property.ZusammenfassungIn dieser Arbeit wird eine Verallgemeinerung des Shapley-Wertes eingeführt und untersucht. Bei den zugrundeliegenden Spielen in Koalitionsform, die zur Modellierung einiger ökonomischer Sachverhalte geeignet sind, ist die charakteristische Funktion über allen Reihenfolgen der Koalitionsbildung definiert. Basierend auf den bekannten Eigenschaften des Shapley-Wertes werden verschiedene axiomatische Charakterisierungen dargestellt.

The proportional rule for problems with constraints and claims

Abstract In this paper we study how to distribute a resource among different agents who have claims on it when there are some constraints in the problem. This kind of problem generalizes, for instance, the class of bankruptcy problems. We introduce two single-valued rules based on the principle of proportionality. Some properties of the rules are given and some axiomatic characterizations are found.

“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].

Stability and voting by committees with exit

Abstract.We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà et al. 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying founder’s sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society.

Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms

In the context of minimum cost spanning tree problems, we present a bargaining mechanism for connecting all agents to the source and dividing the cost among them. The basic idea is very simple: we ask each agent the part of the cost he is willing to pay for an arc to be constructed. We prove that there exists a unique payoff allocation associated with the subgame perfect Nash equilibria of this bargaining mechanism. Moreover, this payoff allocation coincides with the rule defined in Bergantinos and Vidal-Puga [Bergantinos, G., Vidal-Puga, J.J., 2007a. A fair rule in minimum cost spanning tree problems. Journal of Economic Theory 137, 326-352].

On Exiting After Voting

We consider the problem of a society whose members must choose from a finite set of alternatives. After knowing the chosen alternative, members may reconsider their membership by either staying or exiting. In turn, and as a consequence of the exit of some of its members, other members might now find undesirable to belong to the society as well. For general exit procedures we analyze the exit behavior of members after knowing the chosen alternative. For the case of monotonic preferences we propose, for each chosen alternative, an unambiguous and meaningful prediction of the subset of members that will exit