Perfect competition in an oligopoly (including bilateral monopoly)

We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly.     

Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Nonconvex production sets, decreasing returns in the aggregate, and endogenous determination of the number of active firms are allowed. A Walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition (loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case) holds. The condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the Walrasian equilibrium.     

Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

Instability in the implementation of Walrasian allocations

The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well-known tatonnement instability emerges as a special case.     

Walras' Law and Keynesian Macroeconomics

This paper examines the claim that Keynesian models violate Walras' law. Walras' law is founded in the logic of exchange. Standard statements misrepresent it, as it pertains to a monetary economy. Keynesian models are consistent with Walras' law once this misrepresentation is corrected. The law holds for both notional and effective demands. It also holds in unconstrained Walrasian equilibria, constrained Walrasian equilibria, and constrained non-Walrasian equilibria. The latter corresponds to a Keynesian conception of equilibrium: markets need not clear, but agents expectations must be fulfilled.     

On persistent disequilibrium

Consider a standard model of a Walrasian economy where the time derivative of price change is a sign preserving function of excess demand. The only steady states of such a system are the Walrasian equilibria. For if the system is not at a Walrasian equilibrium then there must be excess demands or supplies in some market and thus those prices must be changing. Walras' law implies that all prices cannot change in the same direction, and thus relative prices must change.However, it seems that in real world economies there have been states of persistent disequilibrium. How can this be? How can there be stationary states of an economy that are not Walrasian equilibria?The answer presented in this paper goes something like this: the demands actually presented to the market, i.e., the demands that affect price movements, are not the Walrasian demands. Rather, these demands, the effective demands, are a function of both price and quantity signals. There is no reason why there cannot be equilibria of the effective demand system that are not equilibria of the Walrasian demand system.In this paper, I present a simple abstract model of effective demand systems and given a condition for this system to have non-Walrasian equilibria. I also present a simple example of this phenomena. Finally I discuss the real world implications of this model. Related concepts of effective demand are discussed in [A1H], [2], [3], [L5], and [L6].     

A note on Walrasian equilibria in non-Walrasian models

We demonstrate that equilibria termed ‘Walrasian’ in non-Walrasian models are generally not, but rather Hicksian Temporary Competitive Equilibria in expected virtual prices. They are only Walrasian when the expected virtual prices would clear all markets.     

Microeconomic uncertainty and macroeconomic indeterminacy

We propose a stylized intertemporal macroeconomic model wherein the combination of decentralized trading and microeconomic uncertainty (taking the form of privately observed and uninsured idiosyncratic shocks) creates an information problem between agents and generates indeterminacy of the macroeconomic equilibrium. For a given value of the economic fundamentals, the economy admits a continuum of equilibria that can be indexed by the sales expectations of firms at the time of investment. The Walrasian equilibrium is one of these possible equilibria but it is reached only if firms are optimistic enough. With a weaker degree of optimism, equilibrium output, employment and real wages will be lower than in the Walrasian equilibrium. Moreover, the range of possible equilibria will depend positively on the wage elasticity of the labour supply and on the magnitude of the information problem between buyers and sellers (in our case, the variance of the idiosyncratic shocks).Stochastic simulations performed on a calibrated version of the model show that pure demand expectation shocks may generate business cycle statistics that are not inconsistent with the observed ones.     

On Nash implementation of Walrasian equilibria in a market for pure indivisibles without money

This paper deals with the Walrasian property of Nash and strong equilibria of a specific strategic market game which refers to a pure exchange economy involving purely indivisible commodities and no money. The game is of sealed-bid auction type and it is shown that any Nash equilibrium at which no agent is in status quo is a strong equilibrium and implements a Walrasian equilibrium. Moreover, it appears that two modifications of the game's rules ensure that any strong equilibrium outcome is Walrasian. These results are identical to those obtained by Svensson for markets involving purely indivisible goods and money.     

The comparative statics of cumulative distribution function changes for the class of risk averse agents

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and the noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Following earlier work of Novshek and Sonnenschein we allow for set-up cost and permit a minimal form of mixed strategies. We depart from them by requiring that the aggregate production set exhibits some degree (however small) of decreasing returns. Contrasting with their results, it is shown that a (regular) Walrasian equilibrium of a limit economy can always be approximated by a sequence of noncooperative equilibria for the tail of the approximating (finite) economies. Thus, there is a surprising qualitative discontinuity when one passes from the Novshek-Sonnenschein case of aggregate constant returns to scale of the decreasing returns case of this paper.     

Ownership structure and efficiency in large economies

We analyze the limit behavior of sequences of oligopolistic equilibria in which firms follow objectives consistent with their shareholders?? interests. We show that convergence to a competitive outcome may fail for some distributions of firms?? shares across consumers and provide a characterization of the class of ownership structures that lead to Walrasian equilibrium allocations in the limit.     

Manifolds of golden rule and balanced steady state equilibria

Summary. We show that the set of balanced steady state (resp. golden rule) equilibria, parameterized by endowments, of stationary overlapping-generations economies are smooth manifolds diffeomorphic to Euclidean spaces. These properties extend similar properties of the Walrasian equilibria and enable one to apply the natural projection approach to the study of these equilibria. Received: October 30, 1995; revised version: October 10, 1996     

Walrasian versus quasi-competitive equilibrium and the core of a production economy

Summary. This paper presents very general conditions guaranteeing that a quasi-competitive equilibrium is a Walrasian equilibrium. We also develop a generalization (and a simplified proof) of Nikaidos and McKenzies extensions of the classic Debreu-Scarf theorem on core convergence, and apply the first result to obtain an equivalence between the set of Edgeworth equilibria and the set of Walrasian equilibria in a production economy.Received: 6 September 2002, Revised: 14 November 2003, JEL Classification Numbers: C71, D50, D51.     

Imperfectly competitive cycles with Keynesian and Walrasian features

We consider a multi-sector overlapping generations model with oligopolistic firms in the output markets and wage-setting trade unions in the labour markets. A coordination problem between firms creates multiple temporary equilibria which are either Walrasian or of the Keynesian unemployment type. There exist many deterministic and stochastic equilibrium cycles fluctuating between Keynesian recession and Walrasian boom periods with arbitrarily long phases in each regime. The cycles are in accordance with certain empirical regularities. Money is neutral and superneutral, but appropriate countercyclical fiscal policies stabilize the cycles in a textbook Keynesian way.     

Walrasian General Equilibrium Allocations and Dynamics in Two-Sector Growth Models

This paper analyzes and solves miniature Walrasian general equilibrium systems of momentary and moving equilibria. The Walrasian framework encompasses the fundamental neoclassical and classical two‐sector growth models; the families of solutions of steady‐state and persistent growth per capita in various competitive two‐sector economies are parametrically characterized. Moreover, the endogenous behavior of relative prices and the sectoral allocation of primary factors are analyzed in detail. The technology parameters of the capital good industry are decisive for obtaining long‐run per capita growth in closed (global) economies. A review of the literature complements the theorems on the general equilibrium allocations, dynamic systems, and the time paths of Walrasian two‐sector economies.     

More on economies with a finite set of Walrasian equilibria

Proposition. The graph of the Walrasian equilibrium correspondence is a piecewise continuously differentiable manifold. Furthermore, there exists an open dense set of economies, Ω, such that for all w in Ω (a) the number of equilibria of the economy w is finite; and (b) there exists a neighborhood V(w) on which the set of equilibria is represented by a finite family of piecewise continously differentiable functions.     

The Second Welfare Theorem in Economies with Non‐Walrasian Markets

The standard version of the second welfare theorem assumes that market operations produce Walrasian outcomes. Therefore, if there are individuals who can manipulate prices, the conclusion of the second welfare theorem is questionable. In this paper, we address the decentralization of a Pareto‐optimal allocation, when markets are non‐Walrasian. Our objective in this paper is to develop a game which can implement Pareto‐optimal allocations as Nash equilibria of strategic exchange in markets. In this way, we develop a version of the second welfare theorem for economies where markets are strategic.     

Walrasian analysis via two-player games

We associate to any pure exchange economy a game with only two players, regardless of the number of consumers. In this two-player game, each player represents a different role of the society, formed by all the individuals in the economy. Player 1 selects feasible allocations trying to make Pareto improvements. Player 2 chooses an alternative from the wider range of allocations that are feasible in the sense of Aubin. The set of Nash equilibria of our game is non-empty and our main result provides a characterization of Walrasian equilibria allocations as strong Nash equilibria of the associated society game.     

Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces

Summary. We consider a differential information economy with infinitely many commodities and analyze the veto power of the grand coalition with respect the ability of blocking non-Walrasian expectations equilibrium allocations. We provide two different Walrasian expectations equilibrium equivalence results. First by perturbing the initial endowments in a precise direction we show that an allocation is a Walrasian expectations equilibrium if and only if it is not privately dominated by the grand coalition. The second characterization deals with the fuzzy veto in the sense of Aubin but within a differential information setting. This second equivalence result provides a different characterization for the Walrasian expectations equilibrium and shows that the grand coalition privately blocks in the sense of Aubin any non Walrasian expectations equilibrium allocation with endowment participation rate arbitrarily close to the total initial endowment participation for every individual. Finally, we show that any no free disposal Walrasian expectations equilibria is coalitional Bayesian incentive compatible. Since the deterministic Arrow-Debreu-McKenzie model is a special case of the differential information economy model, one derives new characterizations of the Walrasian equilibria in economies with infinitely many commodities.Received: 29 October 2003, Revised: 24 February 2004, JEL Classification Numbers: D51, D82, D11. Correspondence to: Emma Moreno-GarcíaThe authors are grateful to an anonymous referee for his/her careful reading and helpful comments and suggestions.C. Hervés and E. Moreno acknowledge support by Research Grant BEC2000-1388-C04-01 (Ministerio de Ciencia y Tecnología and FEDER); and support by the Research Grant SA091/02 (Junta de Castilla y León).     

A simple auctioneerless mechanism with Walrasian properties

A simple mechanism for reallocating holdings is described, in which no auctioneer is required: outcomes are determined solely from traders' actions and without any requirement that the mechanism be in equilibrium. The mechanism is shown to exactly duplicate the performance of the Walrasian auctioneer (both in its equilibria and in its disequilibrium path) if individuals are price takers, and, if the number of individuals is large, to approximately duplicate the auctioneer's performance even when individuals behave strategically, each taking account of his own influence on prices.