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.     

NOMINAL BONDS AND INTEREST RATES*

In this article, I integrate the microfoundation of monetary theory with the model of limited participation to analyze the competition between nominal bonds and money. The market for government nominal bonds is centralized and Walrasian, whereas the goods market is modeled as random matches. The government imposes a legal restriction that requires all government goods to be purchased with money but not with bonds. By contrast, private agents can exchange between themselves with both money and bonds. I show that an arbitrarily small legal restriction is sufficient to prevent matured bonds from being a medium of exchange. I also analyze the effects of monetary policy with and without the legal restriction. Some of those effects differ significantly from traditional monetary models.     

Monetary policy and efficiency in over‐the‐counter financial trade

We develop a monetary model that incorporates over‐the‐counter (OTC) asset trade. After agents have made their money holding decisions, they receive an idiosyncratic shock that affects their valuation for consumption and, hence, for the unique liquid asset, namely money. Subsequently, agents can choose whether they want to enter the OTC market in order to sell assets and thus boost their liquidity or to buy assets and thus provide liquidity to other agents. In our model, inflation affects not only the money holding decisions of agents, as is standard in monetary theory, but also the entry decision of these agents in the financial market. We use our framework to study the effect of inflation on welfare, asset prices and OTC trade volume. In contrast to most monetary models, which predict a negative relationship between inflation and welfare, we find that inflation can be welfare improving within a certain range, because it mitigates a search externality that agents impose on one another when they make their OTC market entry decision. Also, an increase in the holding cost of money will lead to a decrease in asset prices, a regularity that is well documented in the data and often considered anomalous.     

Inefficiency caused by random matching and heterogeneity

I study an economy with sellers and buyers with unit supplies and unit demands. Both parties have valuations uniformly distributed on a unit interval. I quantify the inefficiency, compared to the Walrasian markets, when the agents meet randomly. There are several causes of inefficiency that I deal with separately. First, even if there is perfect information about valuations it makes a difference whether all agents participate in the markets or whether only those who would trade in the Walrasian market participate. The same applies when there is private information about valuations.     

COMPENSATION FOR QUALITY DIFFERENCE IN A SEARCH MODEL OF MONEY*

We study an economy in which there is always double coincidence of wants, agents have perfect information about qualities of goods, and there are no transaction costs. The hold‐up problem arises because efforts invested in improving quality prior to search may not be compensated in the market. Situations in which barter fails to motivate quality improvement are identified. With money, however, the extra effort in quality improvement will be compensated when high‐quality good producers trade with agents holding both the low‐quality good and money. Injection of money can induce almost all agents to produce the high‐quality good.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

An alternative measure of wage flexibility

Wage flexibility is usually defined as the responsiveness of wages to market disequilibrium. But market disequilibrium can be defined in different ways. One can accept a non-Walrasian definition of equilibrium, the market being in equilibrium when agents have no incentive to change their decisions, even if a change of wages can improve their position. To study the behavior of wages as an equilibrating variable, it is appropriate to consider Walrasian demand and supply functions, in which wages are allowed to move in each period in a direction to restore equilibrium between Walrasian demand and supply, even when agents experience restrictions and take notice of these restrictions when making decisions. The degree of wage flexibility is most often measured as the amount of equilibrating change that took place in a certain period. In most wage equations wage flexibility is measured by the coefficient of the unemployment variable, which links the equilibrating change in the wage variable to the degree of market disequilibrium. The equalization of market disequilibrium with unemployment poses some problems. The authors wish to thank Freddy Heylen of the University of Gent for helpful comments.     

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.     

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Search cost,trading strategies and optimal market structure

The theory of Walrasian equilibrium yields a set of prices at which the aggregate competitive demand for each commodity equals its aggregate competitive supply. However, even at equilibrium prices the theory of competitive equilibrium does not explicitly offer explanation regarding the manner in which trades are actually executed. This paper considers a model where trade takes place in a decentralized fashion and examines in a dynamic game-theoretic framework, the role of social institution of money and markets in facilitating exchange. The steady state Nash equilibrium derived in the paper demonstrates how, depending on the level of transaction costs associated with a market setup (synonymously, trading posts to exchange possible pairs of goods) appropriate monetary trade emerges, which like a hub and spoke network (Starr and Stinchcombe, 1999) makes some markets non-functioning and in equilibrium only the markets having trade through the medium of exchange continue to exist. However, despite the obvious advantages of a market setup in reducing search costs, pure random search for a complementary trading partner (as considered by Ostroy and Starr, 1974; Kiyotaki and Wright , 1989; and others) prevails in many economies, especially, in many developing economies. This paper models this feature of developing economies by introducing differences in transaction costs across agents and shows why sustainable equilibria might exist exhibiting random search for certain commodities even in the presence of established markets.     

Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust

A well-known result by Vega-Redondo (1997) [18] implies that in symmetric Cournot oligopolies, imitation leads to the Walrasian outcome. We show that this result is not robust to the slightest asymmetry in costs, since every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is a good predictor of market outcomes. Finally, we suggest a new theory based on a mix of imitation and other learning processes that explains subjects' behavior fairly well.     

Perpetual youth and endogenous labor supply: A problem and a possible solution

In the “perpetual youth” overlapping-generations model of Blanchard and Yaari, if leisure is a “normal” good then some agents will have negative labor supply. We suggest a solution to this problem by using a modified version of Greenwood, Hercowitz and Huffman’s utility function. The modification incorporates real money balances, so that the model may be used to analyze monetary as well as fiscal policy. In a Walrasian version of the economy, we show that increased government debt and increased government spending raise the interest rate and lower output, while an open-market operation to increase the money supply lowers the interest rate and raises output.     

The Marshallian Market and the Walrasian Economy. Two Incompatible Bedfellows

The aim of this paper is to question a view which is usually taken for granted, namely that the Marshallian partial equilibrium and Walrasian general equilibrium analysis stand in a relationship of continuity. It will be claimed that the contrary is true: the generalisation of the Marshallian market does not lead to a Walrasian economy or, conversely, the Walrasian economy is not composed of Marshallian markets. To bring this point home, the basic methodological choices underpinning the analysis of the Marshallian market and of the Walrasian economy will be compared. The issue of why no full-fledged Marshallian representation of the economy has arisen which might stand as an alternative to the Walrasian account will also be investigated and a series of reasons for this lack of generalisation of the Marshallian market will be considered. Finally, it will be claimed that if the Marshallian economy concept has no explicit existence, it has nonetheless an implicit one. It forms the background against which a series of reasoning about the working of the economy as a whole, which cannot fit the Walrasian economy framework, are developed. No less prestigious names than those of Keynes, Hicks, Patinkin, Friedman, Clower and Leijonhufvud will be adduced as witnesses.     

AN OVER‐THE‐COUNTER APPROACH TO THE FOREX MARKET

The foreign exchange (FOREX) market is an over‐the‐counter market characterized by intermediation and significant bid–ask spreads. However, most of the existing international macroeconomics literature models the FOREX as a standard Walrasian market. This article constructs a dynamic general equilibrium model of intermediation in the FOREX market. We use our framework to compute standard measures of FOREX liquidity, such as bid–ask spreads and trade volume, and study how they are affected by macroeconomic fundamentals and market microstructure. We also study how FOREX market microstructure affects the volume of international trade and, consequently, welfare. Our empirical exercise offers support to the models' main predictions.     

Sequential bargaining and competition

Summary This paper studies a sequential bargaining model of a decentralised market. A main objective is to explore the conditions under which the unique subgame perfect equilibrium outcome of the market game approximates the Walrasian outcome of the market. The three main messages that emerge from our results are as follows. First, contrary to conventional wisdom, frictionless markets need not be Walrasian. Second, the relative magnitudes of frictions can have a profound impact on the market outcome even in the limit as the absolute magnitudes of the frictions become negligible. And third, the relative magnitudes of certain types of frictions may have to be significantly large in order for markets to be Walrasian, reflecting that certain types of frictions are needed in the market in order to induce the Walrasian outcome.This paper is based on a chapter of my Ph.D. thesis. I would like to thank Ken Binmore, David Canning, Partha Dasgupta and Frank Hahn for their helpful comments. I owe special thanks to Ariel Rubinstein for his comments, remarks and encouragement. The comments and suggestions of an anonymous referee have significantly improved the exposition at several places.     

The workings of a commodity money system in an incomplete information macro model

This paper compares the properties of a token money system with that of a commodity money system in an uncertain environment. In an incomplete information world, relative prices are not known with certainty. However, a commodity money system provides some information because the nominal price of the monetary commodity is known. The benefits of this information-enhancing function may be offset, though by distortions in relative prices relative to their full information Walrasian equilibrium values. Because the two systems have vastly different structural parameters, we cannot unambiguously state which system is welfare superior.     

About market structure

I study an economy where sellers choose locations, and buyers choose which location to visit. All sellers in one location correspond to the Walrasian market while each seller in a separate location corresponds to the standard random matching model. Trades are consummated in auctions, and it turns out that the Walrasian market is not an equilibrium market structure. Rather, the sellers choose to distribute themselves in several locations endogenously creating the imperfectness of markets. I determine the number of sellers per location in equilibrium as a function of the ratio of buyers to sellers.     

Middle Men: The Visible Market‐Makers

This paper presents a framework in which middlemen emerge to intermediate between ex‐ante homogeneous buyers and sellers in the presence of search frictions. Middlemen announce prices, and hold an inventory to provide more sure services. Middlemen can mitigate trade imbalances with price competition. Using this framework I illustrate how the frictionless limit can emerge and how middlemen can implement the short‐side principle for the market price to be Walrasian. The recent progress in the literature on intermediation will also be discussed.     

Search, money, and inflation under private information

I study monetary exchange and inflation when buyers have private information about their willingness to pay for certain goods. Introducing imperfect information in the Lagos-Wright [A unified framework for monetary theory and policy analysis, J. Polit. Economy 113(3) (2005) 463-484] economy shows that the existence of monetary equilibrium is a more robust feature of the environment. In general, my model has a monetary steady state in which only a proportion of the agents hold money. Agents who do not hold money cannot participate in trade in the decentralized market. The proportion of agents holding money is endogenous and depends (negatively) on the level of expected inflation. As in Lagos and Wright's model, in equilibrium there is a positive welfare cost of expected inflation, but the origins of this cost are very different.     

Credit and inflation under borrower?s lack of commitment

In this paper we study the effects of monetary policy on privately supplied credit in model economies where money is needed for transaction purposes and agents who default on their loans cannot participate in the credit market but are allowed to accumulate money. In our deterministic benchmark economy where agents alternate in productivity, credit has the role of smoothing consumption. We show that deflation crowds out credit completely. The reason is that deflation increases the value of being excluded from the credit market and eliminates the incentive to repay loans. When inflation is positive but low, credit, consumption smoothing and welfare increase with inflation, until inflation reaches a threshold at which the allocation is efficient and money becomes superneutral.