Juan J. Vidal-Puga

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.

The Harsanyi paradox and the “right to talk” in bargaining among coalitions☆

We describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own “right to talk” when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.

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].

Forming coalitions and the Shapley NTU value

A simple protocol for coalition formation is presented. First, an order of the players is randomly chosen. Then, a coalition grows by sequentially incorporating new members in this order. The protocol is studied in the context of non-transferable utility (NTU) games in characteristic function form. If (weighted) utility transfers are feasible when everybody cooperates, then the expected subgame perfect equilibrium payoff allocation anticipated before any implemented game is the Shapley NTU value.

The Consistent Coalitional Value

We describe a value for nontransferable utility games with coalition structure. This value coincides with the consistent value for trivial coalition structures, and with the Owen value for transferable utility games with coalition structure. Furthermore, we present two characterizations: the first one using properties of balanced contributions and the second one using a consistency property.

Demand Commitment in Legislative Bargaining

Morelli (1999) provides a model of government formation in which the parties make payoff demands and the order of moves is chosen by the leading party. Morellis main proposition states that the ex post distribution of payoffs inside the coalition that forms is proportional to the distribution of relative ex ante bargaining power. We provide a counterexample in which the leading party is able to obtain the entire payoff; furthermore, there are coalitions for which proportional payoff division does not occur for any order of moves.

Merge-proofness in minimum cost spanning tree problems

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called merge-proofness. This property says that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using merge-proofness.

Demand bargaining and proportional payoffs in majority games

We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction).

A VALUE FOR PERT PROBLEMS

The PERT (Program Evaluation Review Technique) is a operational research tool used to schedule and coordinate activities in a complex project. We present two values for measuring the importance of each activity. Both values are obtained through an axiomatic characterization using three properties. The first value is characterized with separability, monotonicity, and order preservation. The second value is characterized with separability, equal treatment inside a component, and independence of large durations. We also present an application to the problem of how to share the surplus obtained when a project finishes before the expected completion time.