Xavier Vives

Price and quantity competition in a differentiated duopoly

This article analyzes the duality of prices and quantities in a differentiated duopoly. It is shown that if firms can only make two types of binding contracts with consumers, the price contract and the quantity contract, it is a dominant strategy for each firm to choose the quantity (price) contract, provided the goods are substitutes (complements).

NASH EQUILIBRIUM WITH STRATEGIC COMPLEMENTARITIES

Abstract Using lattice-theoretical methods, we analyze the existence and order structure of Nash equilibria of non-cooperative games where payoffs satisfy certain monotonicity properties (which are directly related to strategic complementarities) but need not be quasiconcave. In games with strategic complementarities the equilibrium set is always non-empty and has an order structure which ranges from the existence of a minimum and a maxinum element to being a complete lattice. Some stability properties of equilibria are also pointed out.

Duopoly Information Equilibrium: Cournot and Bertrand

In a duopoly model where firms have private information about an uncertain linear demand, it is shown that if the goods are substitutes (not) to share information is a dominant strategy for each firm in Bertrand (Cournot) competition. If the goods are complements the result is reversed. Furthermore the following welfare results are obtained:(i) With substitutes in Cournot competition the market outcome is never optimal with respect to information sharing but it may be optimal in Bertrand competition if the products are good substitutes. With complements the market outcome is always optimal.(ii) Bertrand competition is more efficient than Cournot competition.(iii) The private value of information to the firms is always positive but the social value of information is positive in Cournot and negative in Bertrand competition

Imperfect competition, risk taking, and regulation in banking

We develop a model of banking competition which allows us to disentangle the roles that limited liability, deposit insurance (both with flat and risk-based premia), and rivalry for deposits play in determining risk-taking incentives both in the asset and the liability side of the balance sheet. We find that in all market configurations (uninsured or insured) banking rivalry yields excessive deposit rates when social failure costs are high or when competition is intense. Maximal risk-taking incentives (on the liability and asset sides) exist with flat-premium deposit insurance and minimal with risk-based insurance. In an uninsured market risk taking on the asset side is implied by limited liability and the presence of moral hazard (asset risk not observable). With flat-premium deposit insurance maximum risk-taking incentives exist even if there is no moral hazard. Finally, we can extricate the role of rate and asset regulation both in the case of insured and uninsured deposits.

On the Efficiency of Bertrand and Cournot Equilibria with Product Differentation

In a differentiated products setting with n varieties it is shown, under certain regularity conditions, that if the demand structure is symmetric and Bertrand and Cournot equilibria are unique then prices and profits are larger and quantities smaller in Cournot than in Bertrand competition and, as n grows, both equilibria converge to the efficient outcome at a rate of at least 1n. If Bertrand reaction functions slope upwards and are continuous then, even with an asymmetric demand structure, given any Cournot equilibrium price vector one can find a Bertrand equilibrium with lower prices. In particular, if the Bertrand equilibrium is unique then it has lower prices than any Cournot equilibrium.

Strategic Supply Function Competition with Private Information

A Bayesian supply function equilibrium is characterized in a market where firms have private information about their uncertain costs. It is found that with supply function competition, and in contrast to Bayesian Cournot competition, competitiveness is affected by the parameters of the information structure: supply functions are steeper with more noise in the private signals or more correlation among the costs parameters. In fact, for large values of noise or correlation supply functions are downward sloping, margins are larger than the Cournot ones, and as we approach the common value case they tend to the collusive level. Furthermore, competition in supply functions aggregates the dispersed information of firms (the equilibrium is privately revealing) while Cournot competition does not. The implication is that with the former the only source of deadweight loss is market power while with the latter we have to add private information. As the market grows large the equilibrium becomes competitive and we obtain an approximation to how many competitors are needed to have a certain degree of competitiveness.

Complementarities and Games: New Developments

The theory of monotone comparative statics and supermodular games is presented as the appropriate tool to model complementarities. The approach, which has not yet been fully incorporated into the standard toolbox of researchers, makes the analysis intuitive and simple, helps in deriving new results and in casting new light on old ones. The paper takes stock of recent contributions and develops applications to industrial organization (oligopoly, R&D, and dynamics), finance (currency and banking crisis) and macroeconomics (adjustment and menu costs). Particular attention is devoted to Markov games and to games of incomplete information (including global games).

Infrastructure and education as instruments of regional policy: evidence from Spain

Regional policy and Spain infrastructure and education as instruments of regional policy: evidence from Spain Governments have often tried to influence the regional distribution of economic activity through supply-side measures such as investment in training and infrastructure. Using evidence from Spain, we examine whether such policies can have an impact and whether they have done so in the past. Our results indicate that disparities in the stocks of human and public capital account for a third of observed regional inequality, about evenly split between the two factors. Hence public investment can in principle be used to reduce regional disparity. Its actual impact, however, will depend both on its overall volume and on the extent to which its regional allocation does indeed vary with regional need. In Spain, investment in infrastructure has made only a small contribution to regional convergence, primarily because it has not in practice been allocated to redistribute across regions to any great extent. In contrast, EFRD transfers have clearly been allocated among regions with redistribution in mind. The impact of the Fund has been significant, but it has been limited by the relatively small size of the programme. — Angel de la Fuente and Xavier Vives

Trade association disclosure rules, incentives to share information, and welfare

In this article I propose a monopolistic competition framework to analyze the effects of different disclosure rules used by trade associations on the incentives to share information and on the welfare of consumers, firms, and society. This framework is appropriate whenever a single firm cannot influence aggregate market magnitudes, and serves as a benchmark for the analysis of information-pooling agreements abstracting from strategic considerations. I report two main results. First, a policy of nonexclusionary disclosure destroys the incentives to share information, while exclusionary disclosure preserves them. Second, information sharing increases expected total surplus with Cournot competition but decreases it with Bertrand competition in the context of a Quadratic-Normal model with demand uncertainty.

How Fast do Rational Agents Learn

A simple dynamic model of rational learning through market interaction by asymmetrically informed risk-neutral agents, uncertain about a valuation parameter but whose pooled information reveals it, is presented. The model is a variation of the classical partial equilibrium model of learning in rational expectations in which the market price is informative about the unknown parameter only through the actions of agents. It is found that learning from market prices and convergence to the rational expectations equilibrium is slow, at the rate 1/√n1/3 (where n is the number periods of market interaction), whenever the average precision of private information in the market is finite. Convergence obtains at the standard rate 1/√n if there is a positive mass of perfectly informed agents. Comparative static results on more refined measures of the speed of convergence with respect to basic technological and informational parameters are also provided.