Oriol Carbonell-Nicolau

Essential equilibria in normal-form games

A Nash equilibrium x of a normal-form game G is essential if any perturbation of G has an equilibrium close to x. Using payoff perturbations, we show that for games that are generic in the set of compact, quasiconcave, and generalized payoff secure games with upper semicontinuous sum of payoffs, all equilibria are essential. Some variants of this result are also established.

Voting Over Income Taxation

A major problem of the positive theory of income taxation is to explain why statutory income tax schedules in practice are marginal-rate progressive. While it is commonly believed that this is but a simple consequence of the fact that the number of relatively poor voters exceeds that of richer voters in general, putting this contention in a voting equilibrium context is not a trivial task. We do this here in the context of nonlinear taxation and attempt to provide a formal argument in support of this heuristic claim. We first establish the existence of mixed strategy equilibria and identify certain cases in which marginal-rate progressive taxes are chosen almost surely by the political parties. Unfortunately, we also find that if the tax policy space is not artificially constrained, the support of at least one equilibrium cannot be contained within the set of marginal-rate progressive taxes.

On the existence of pure-strategy perfect equilibrium in discontinuous games

We provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a players payoff function. Various economic games illustrate our results.

The existence of perfect equilibrium in discontinuous games

We prove the existence of a trembling-hand perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games.

Refinements of Nash equilibrium in potential games

We prove the existence of a pure-strategy trembling-hand perfect equilibrium in upper semicontinuous potential games, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. We also establish a more powerful result: the set of maximizers of an upper semicontinuous potential contains a strategically stable set of pure-strategy Nash equilibria.

A Positive Theory of Income Taxation

We explore the consequences of electoral competition for nonlinear income taxation. Our model is a dynamic version of the standard two-party electoral competition model adapted to nonlinear income taxation. The theory has a number of desirable features. First, equilibria always exist, even though the set of admissible tax policies is multidimensional. Second, the Nash set can be characterized generically, and its components give sharp predictions. Third, the features of equilibrium tax policies depend only on empirically meaningful fundamentals.Equilibrium tax schedules benefit the more numerous income groups and place the burden of taxation on income groups with fewer voters. For empirical income distributions, the features of an equilibrium tax schedule are reminiscent of Directors law of public income redistribution (Stigler [39]).

On the existence of Nash equilibrium in Bayesian games

We furnish conditions on the primitives of a Bayesian game that guarantee the existence of a Bayes-Nash equilibrium. By allowing for payoff discontinuities in actions, we cover various applications that cannot be handled by extant results.

Testing the Commitment Hypothesis in Contractual Settings: Evidence from Soccer

This paper designs and implements an empirical test to discern whether the parties to a contract are able to commit not to renegotiate their agreement. We study optimal contracts with and without commitment and derive an exclusion restriction that is useful to identify the relevant commitment scenario. The empirical analysis takes advantage of a data set on Spanish soccer player contracts. Our test rejects the commitment hypothesis. We argue that our conclusions should hold a fortiori in many other economic environments.

On equilibrium refinements in supermodular games

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We show that supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria outside the interior of the set of weakly dominated action profiles.