On the Markovian efficiency of Bertrand and Cournot equilibria

We characterize and compare closed-loop (feedback) price and quantity strategies within a full-fledged dynamic model of oligopolistic competition in which production requires exploitation of a renewable productive asset. Unlike previous papers on the strategic exploitation of productive assets, we allow for imperfect product substitutability, which enables us to deal with price competition. We show that the traditional result that the Bertrand equilibrium is more efficient than the Cournot equilibrium does not necessarily hold in a Markovian environment, either in the short-run or at the stationary equilibrium, or using the discounted sum of welfare as a criterion for relative efficiency.

Equilibria in security markets with a continuum of agents

We prove the existence of a competitive equilibrium for exchange economies with a measure space of agents and for which the commodity space is ` p, 1 < p < +∞. A vector x = (xn) in ` p may be interpreted as a security which promises to deliver xn units of numeraire at state (or date) n. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini–Yannelis [21] and Podczeck [20]. In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

The set of equilibria of first-price auctions

In this note I specify the class of functions that are equilibria of symmetric first-price auctions.

Competitive equilibria in infinite-horizon collateralized economies with default penalties

Araújo, Páscoa and Torres-Martinez (2002) have shown that, without imposing either debt constraints or transversality conditions, Ponzi schemes are ruled out in infinite horizon economies with default when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2008) subsequently show that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. They also claim that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is ensured. The objective of this paper is two fold. First, contrary to what is claimed by Páscoa and Seghir (2008), we show that moderate default penalties do not always prevent agents to run a Ponzi scheme. Second, we provide an alternative condition on default penalties that is sufficient to rule out Ponzi schemes and ensure the existence of a competitive equilibrium.

Bertrand, Cournot and monopolistically competitive equilibria

Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.

Multiple equilibria and protectionism

In a nonnative approach, I analyze trade policies when the industrial sector genentes positive extemalities in production, and there are adjustments costs to changing production from one sector to the other. Protectionist trade policy can make workers intemalize the benetits from moving into the industrial sector, but it is a second best policy as it also causes consumption distortions. I show that if the govemment is able to fully commit to its tariff schedule for the future, the welfare maximizing policy is to maintain a positive tariff forever, even after all adjustment has already taken place . However, if the govemment is not able to commit at all, the only time consistent policy is zero tariff at any point in time. The time inconsistency of the full commitment policy is derived from the fact that in the model only production needs interference, and the production distortion is lagged one period with respect to the tariff wbile the consumption distortion is simultaneous to the tariff. In the intermediary case, i.e., when the government can commit for a limited period of time, the time consistent optimal tariff will be positive but lower than the "full commitment" tariff. This result indicates that some institutions that have always been considered pure sources of inefficiency, such as protectionist lobbying, may in fact be welfare improving in some cases!

Equilibria in exchange economies with financial constraints : beyond the Cass trick

We consider an exchange economy under incomplete financiaI markets with purely financiaI securities and finitely many agents. When portfolios are not constrained, Cass [4], Duffie [7] and Florenzano-Gourdel [12] proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass [4] in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financiaI market is constrained by convex restrictions, provided that financiaI markets are collectively frictionless.

HOPF BIFURCATION FROM LINES of EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.