Julio González-Díaz

A natural selection from the core of a TU game: the core-center

We present a new allocation rule for the class of games with a nonempty core: the core-center. This allocation rule selects a centrally located point within the core of any such game. We provide a deep discussion of its main properties.

Paired comparisons analysis: an axiomatic approach to ranking methods

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that perform best with respect to the set of properties under consideration. A less known ranking method, generalised row sum, performs well too. We also study, among others, the fair bets ranking method, widely studied in social choice, and the least squares method.

Finitely repeated games: A generalized Nash folk theorem

Abstract This paper characterizes the set of feasible payoffs of finitely repeated games with complete information that can be approximated arbitrarily closely by Nash equilibria.

Matching and price competition: beyond symmetric linear costs

Bulow and Levin’s (2006) “Matching and Price Competition” studies a matching model in which hospitals compete for interns by offering wages. We relax the assumption of symmetric linear costs and compare the pricing equilibrium that results to the firm-optimal competitive equilibrium. With linear and asymmetric costs, competition in the pricing equilibrium may not be localized, but all other qualitative comparisons of Bulow and Levin (2006) hold. With non-linear and symmetric costs workers’ average utility in the pricing equilibrium may be higher than in the firm- optimal competitive equilibrium. With asymmetric and non-linear costs, firms need not choose scores from an interval in a pricing equilibrium, which may make competition even less localized.

First-price winner-takes-all contests

We introduce a unifying model for contests with perfect discrimination and show that it can be used to model many well-known economic situations, such as auctions, Bertrand competition, politically contestable rents and transfers, tax competition and litigation problems. Furthermore, we hope that the generality of our model can be used to study models of contests in settings in which they have not been applied yet. Our main result is a classification of the set of Nash equilibria of first-price winner-takes-all contests with complete information. Finally, we discuss the implications of our results in each one of the specific models.

The role of commitment in repeated games

We model the role of commitment in non-cooperative games by means of what we call unilateral commitments. We study their impact within the framework of repeated games with complete information. To do so, we revisit the main folk theorems for repeated games with complete information and check up to what extent the assumptions needed in the classic models can be relaxed in the model with unilateral commitments.

Towards an axiomatization of the core-center

The core-center is an allocation rule introduced in Gonzalez-Diaz and Sanchez-Rodriguez (Gonzalez-Diaz, J., Sanchez-Rodriguez, E., 2007. A natural selection from the core of a TU game: The core-center. International Journal of Game Theory 36, 27-46. doi: 10.1007/s00182-007-0074-5) for the class of games with a non-empty core. In this paper we present a weighted additivity axiom, which we call trade-off property, and use it to obtain two characterizations of the core-center.

Cores of convex and strictly convex games

We follow the path initiated by Shapley in 1971 and study the geometry of the core of convex and strictly convex games. We define what we call face games and use them to study the combinatorial complexity of the core of a strictly convex game. Remarkably, we present a picture that summarizes our results with the aid of Pascals triangle.

A silent battle over a cake

The division of a cake by n players is modeled as a (silent) game of timing. We show that such games admit a unique Nash equilibrium.

Loss allocation in energy transmission networks

In this paper we study a cost allocation problem that is inherent to most energy networks: the allocation of losses. In particular, we study how to allocate gas losses between haulers in gas transmission networks. We discuss four allocation rules, two of them have already been in place in real networks and two others that are defined for the first time in this paper. We then present a comparative analysis of the different rules by studying their behavior with respect to a set of principles set forth by the European Union. This analysis also includes axiomatic characterizations of two of the rules. Finally, as an illustration, we apply them to the Spanish gas transmission network.