p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players is repeatedly and randomly matched to play a symmetric n×n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash equilibrium of the static game. A strict Nash equilibrium is linearly stable under the perfect foresight dynamics if, independent of the current action distribution, there exists a consistent belief that any player necessarily plays the Nash equilibrium action at every revision opportunity. It is shown that a strict Nash equilibrium is linearly stable under the perfect foresight dynamics with a small degree of friction if and only if it is the p-dominant equilibrium with p<1/2. It is also shown that if a strict Nash equilibrium is the p-dominant equilibrium with p<1/2, then it is uniquely absorbing (and globally accessible) for a small friction (but not vice versa). Set-valued stability concepts are introduced and their existence is shown. Journal of Economic Literature Classification Numbers: C72, C73.     

Undominated Nash Implementation in Bounded Mechanisms

We study implementation in undominated Nash equilibrium by bounded mechanisms. (An undominated Nash equilibrium is a Nash equilibrium in which no agent uses a weakly dominated strategy. A mechanism is bounded if every dominated strategy is dominated by some undominated strategy.) We identify necessary conditions and sufficient conditions for such implementation. These conditions are satisfied in virtually all economic environments, and are also satisfied by interesting correspondences from the social choice literature. For economic settings, we provide a particularly simple implementing mechanism for which the undominated equilibrium outcomes coincide with those obtained from the iterative elimination of weakly dominated strategies. Journal of Economic Literature Classification Numbers: 022, 025, 026.     

Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

Summary. Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima. Received: February 16, 2000; revised version: July 7, 2001     

International Cross-Ownership and Strategic Trade Policies

The paper analyzes a model of strategic trade policies in the presence of international cross-ownership of firms that are heterogenous both in terms of costs and in terms of extent of foreign ownership. The equilibrium pattern of taxes and subsidies is characterized for any arbitrary cross-ownership profile, and any number of heterogenous firms. The equilibrium subsidy (or tax) given to any firm is shown to depend, in a separable manner, on the firm's characteristics and on the covariance of the distribution of cost and foreign ownership across firms. A neutrality theorem is proved concerning the Nash equilibrium of the game between governments: in equilibrium, the pattern of trade, the value of each firm, and world welfare are independent of the ownership pattern.     

Modelling the spot prices of various coffee types

We investigate long-run relationships among the spot prices of four coffee types. Two cointegrating vectors emerge: one between the prices of Arabica coffee varieties, and the other one between Unwashed Arabicas and Robusta. A persistence profile analysis shows a more rapid adjustment to equilibrium for the first compared to the second vector due to the fact that the former involves the Arabica coffees, which are more homogeneous. Adjustment is relatively fast, implying that economic forces act rapidly and discrepancies in the equilibrium relationships are short-lived. We also find evidence of non-linear adjustment back to equilibrium; when prices are too high, adjustment takes place at a slower rate than when they are too low.     

Growth Effects of Bubbles in an Endogenous Growth Model

This paper examines the possibility of the existence of bubbles and their effects on the growth rate by using an endogenous growth model. A necessary and sufficient condition for the existence of steady-state equilibrium with bubbles is provided. If non-zero rates of the useless asset supply are allowed, a steady-state equilibrium with bubbles exists even if the growth rate of the bubbleless equilibrium is lower than the market interest rate. The growth rate in the steady state with bubbles depends positively on the supply rate of the useless asset. Dynamic properties of bubbles are also analysed.
JEL Classification Numbers: E52, O41, O42.     

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small. Received: April 1, 2000; revised version: January 10, 2001     

The Castle on the Hill

A simple example of a stochastic game with irreversibility is studied and it is shown that the folk theorem fails in a robust way. In this game of Castle on the Hill, for a broad range of discount factors, including those close to one, equilibrium is unique. Moreover, the equilibrium for large discount factors is Pareto dominated by the equilibrium for low discount factors. A unique cyclic equilibrium is also possible for intermediate ranges of discount factors. Journal of Economic Literature Classification Numbers: C7, C6.     

Ambiguity,uncertainty aversion and equilibrium welfare

Summary. In order to analyse the effect of ambiguity and uncertainty aversion on equilibrium welfare, a two period, pure exchange one good economy is considered. Agents are Choquet-expected-utility maximizers with same convex capacity and strictly concave utility index. It is proven that equilibrium is indeterminate whenever several probabilities in the core of the capacity minimize the expected value of aggregate endowment and not all agents have same expected endowments under those probabilities. It is further shown that small changes in aggregate endowment may have drastic welfare implications. A more general model is considered in the case of no aggregate uncertainty: agents have a set of priors and are uncertainty averse as modelled by Gilboa-Schmeidler [1989]. In the case of complete markets, it is shown that assets have a spread of equilibrium prices similar to the spread of no-arbitrage prices compatible with absence of arbitrage in markets with imperfections.Received: 2 June 2000, Revised: 27 March 2003, JEL Classification Numbers: D46, D59,D60, G12.I have benefited from conversations with L. Epstein, F. Magnien and J. M. Tallon.     

The role of lender behavior in international project finance

Summary. A sovereign borrower seeks to raise funds internationally to finance a fixed-size project, which no single lender can finance alone. Lenders cannot lend more than their endowments, which are private information. A coordination failure arises; therefore, some socially desirable projects may not be financed, even if ex post feasible. There are multiple equilibria, and a conflict exists between lenders about which equilibrium to coordinate on. When endowments are volatile, some lenders prefer an equilibrium in which the project is financed with probability , even if ex post feasible. The government eliminates such equilibria by offering a sufficiently high return, only if endowment volatility is small. Received: June 1, 1999; revised version: December 4, 2000     

Non-implementation of rational expectations as a perfect Bayesian equilibrium

Summary. We point out several conceptual difficulties of the rational expectations equilibrium concept. In particular we show that such an equilibrium need not be incentive compatible and need not be implementable as a perfect Bayesian equilibrium . A comparison of rational expectations equilibria with the private core is also provided. We conclude that the private core is a more appropriate concept to capture the idea of contracts under asymmetric information.Received: 15 December 2003, Revised: 18 November 2004, JEL Classification Numbers: C71, C72, D5, D82. Correspondence to: Nicholas C. YannelisWe wish to thank Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment.     

Exhaustible Resources,Non-Convexity and Competitive Equilibrium

Theoretical underpinnings of competitive equilibrium in an exhaustible-resource market with non-convex (u-shaped) costs are proposed. The analysis extends to intertemporal production Novshek and Sonnenschein’s approximation of static competitive equilibrium by limits of Cournot equilibria. A problem with using Novshek and Sonnenschein’s method is that oligopolistic equilibrium, even an open-loop equilibrium, to which limits might be applied, does not exist when there is a non-convex technology. Using epsilon equilibrium as the equilibrium concept finesses this problem. There are two types of limiting competitive equilibrium. A third type of competitive equilibrium that has been prominent in the literature is found to be inconsistent with limiting approximations.     

Strategic market games quantal response equilibria

Summary. The paper explores a model of boundedly rational traders who act strategically. The general framework of analysis is the sell all model of Shapley and Shubik [6] whereas the behavioral rule of traders is related to the bounded rationality of McKelvey and Palfrey [5] and the subsequent of Chen Friedman and Thisse [1]. A new equilibrium concept is introduced appropriate to integrate in the basic model market participants that may choose an inferior action with positive probability. Further, assuming that these market participants are engaged in an infinite repeated game and making them able to learn playing rationally, we demonstrate that in the limit the original equilibrium of Shapley and Shubik is attained and basically emerges as a special case of our equilibrium concept.Received: 20 September 2003, Revised: 11 December 2004, I am indebted to Yanis Varoufakis and especially to Dimitrios P. Tsomocos for their helpful comments.     

On Intersectoral allocations,factors substitutability and multiple long-run growth paths

Summary. This article considers a two-sector model of economic growth with “labour-augmenting” intersectoral external effects stemming from the aggregate capital stock. It is shown that equilibrium balanced growth paths with a non-trivial labour allocation scheme become available. A set of sufficient conditions for the existence of multiple equilibrium growth rays is provided and their determinacy properties are then characterised. Finally, examination of a parameterised C.E.S. economy illustrates the central role of non-unitary values for the elasticity of substitution in the multiplicity issue. Received: October 31, 2000; revised version: September 25, 2001     

Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions

Summary. The sequential equilibrium of an ascending-price auction of a single item is derived explicitly for the case of log-normal distributions and a multiplicative valuation model comprising both common and private factors, and allowing asymmetries. If the prior distribution on the common factors is diffuse, or of the form obtained by Bayesian updating from a diffuse prior distribution, then the equilibrium strategies are log-linear with coefficients obtained by solving a set of linear equations. A similar construction applies to normal distributions and additive terms in the valuation model. An example illustrates the predictions derived from the model. Received: December 11, 1996; revised version: July 15, 1997     

Imperfect recall and the relationships between solution concepts in extensive games

Summary. In a game of imperfect recall, a sequential equilibrium may not be a Nash equilibrium, and a perfect equilibrium may not be a sequential equilibrium. Sufficiency conditions weaker than perfect recall are given to ensure the standard relationships hold between perfect equilibrium, sequential equilibrium and Nash equilibrium.Received: 22 October 2003, Revised: 18 November 2003, JEL Classification Numbers: C72.     

International trade in genetically modified products

This paper investigates competition between two markets that sell close substitutes: a traditional product and a genetically modified (GM) product. Tightening an import quota on the GM product raises the prices of both goods and hurts consumers. Two scenarios are considered under free trade: Cournot–Nash equilibrium and Stackelberg equilibrium. A Stackelberg type monopolist produces more, and the competitive traditional firms produce less, than in Cournot–Nash equilibrium. In the long run, an import ban on the GM product does not help competitive producers of the genetically modified organism (GMO)-free products but benefits only the landowners in Europe.     

Comparing Sunspot Equilibrium And Lottery Equilibrium Allocations: The Finite Case*

Sunspot equilibrium and lottery equilibrium are two stochastic solution concepts for nonstochastic economies. We compare these concepts in a class of completely finite, (possibly) nonconvex exchange economies with perfect markets, which requires extending the lottery model to the finite case. Every equilibrium allocation of our lottery model is also a sunspot equilibrium allocation. The converse is almost always true. There are exceptions, however: For some economies, there exist sunspot equilibrium allocations with no lottery equilibrium counterpart.     

Internal and external exchange rate equilibrium in a cointegration framework. An application to the Spanish peseta

A simple cointegration methodology is used to compute the equilibrium real exchange rate for the peseta. The stock of foreign assets and the evolution of sectoral prices are considered to be the fundamentals for the real exchange rate. After testing for cointegration, we proceed to decompose the series into a permanent and a transitory component, following the method devised by Gonzalo and Granger. The permanent component of the real exchange rate corresponds to its (time-varying) equilibrium value, and the deviation of the actual real exchange rate from this equilibrium value gives an estimation of the degree of misalignment of the real exchange rate. By the end of the sample (1998:1), the peseta is estimated to be undervalued around 6%.     

The dynamics of inequality and social security in general equilibrium

This paper analyzes the dynamic politico-economic equilibrium of a model where repeated voting on social security and the evolution of household characteristics in general equilibrium are mutually affected over time. In particular, we incorporate within-cohort heterogeneity in a two-period Overlapping-Generation model to capture the intra-generational redistributive effect of social security transfers. Political decision-making is represented by a probabilistic voting à la Lindbeck and Weibull (1987). We analytically characterize the Markov perfect equilibrium, in which social security tax rates are shown to be increasing in wealth inequality. A dynamic interaction between inequality and social security leads to larger social security programs. In a model calibrated to the U.S. economy, the dynamic interaction is shown to be quantitatively important: It accounts for more than half of the social security growth in the dynamics. We also perform some normative analysis, showing that the politico-economic equilibrium outcomes can be fundamentally different from the Ramsey allocation.