DYNAMIC TRADING IN A DURABLE GOOD MARKET WITH ASYMMETRIC INFORMATION*

We analyze a dynamic version of the Akerlof–Wilson “lemons” market in a competitive durable good setting. There is a fixed set of sellers with private information about the quality of their wares. The price mechanism sorts sellers of different qualities into different time periods—prices and average quality of goods traded increase over time. Goods of all qualities are traded in finite time. Market failure arises because of the waiting involved—particularly for sellers of better quality. The equilibrium path may exhibit intermediate breaks in trading.     

Dynamic sorting in durable goods markets with buyer heterogeneity

In a competitive dynamic durable good market where sellers have private information about quality, I identify certain inefficiencies that arise due to heterogeneity in buyers' valuations. Even if the market induces dynamic sorting among sellers and all goods are eventually traded, inefficiency can arise because high valuation buyers buy early when low‐quality goods are sold, while high‐quality goods are allocated to low valuation buyers that buy later. This misallocation adds to the inefficiency caused by delay in trading. Under certain circumstances, high‐quality goods may never be traded as in a static market.     

Dynamic price competition

We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption.We characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an efficient equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.     

Bertrand price competition with differentiated commodities

This develops a general equilibrium, differentiated commodity version of Bertrand price competition. We study two, related market games in which buyers as well as sellers announce both quantities and prices. In the first game, buyers' strategies are artificially restricted. The Nash allocations of this game will be nearly competitive, provided that the commodities supplied by sellers are sufficiently similar. In the second game, the restriction on buyers' strategies is relaxed and a stronger solution criterion, called local perfection, is invoked. The locally perfect equilibria of the unrestricted game coincide the Nash equilibria of the restricted game.     

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length δ, and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as δ approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.     

The Stability of Price Dispersion under Seller and Consumer Learning*

In many markets, it is possible to find rival sellers charging different prices for the same good. Earlier research has attempted to explain this phenomenon by demonstrating the existence of dispersed price equilibria when consumers must make use of costly search to discover prices. We ask whether such equilibria can be learned when sellers adjust prices adaptively in response to current market conditions. With consumer behavior fixed, convergence to a dispersed price equilibrium is possible in some cases. However, once consumer learning is introduced, the monopoly outcome first found by Diamond (Journal of Economic Theory3 (1971), 156–68) is the only stable equilibrium.     

A Noncooperative Analysis of Hotelling's Location Game

We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremontet al.have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. We show that the location game possesses an infinity of mixed strategy Nash equilibria. In these equilibria coordination failure invalidates the principle of “maximum differentiation” and firms may even locate at the same point.Journal of Economic LiteratureClassification Numbers: C72, D43, L11.     

Strategic Buyers and Privately Observed Prices

A model of finitely repeated price competition between two sellers with differentiated goods and a large buyer is analyzed. The set of pure strategy sequential equilibria is investigated under public and private monitoring. With private monitoring, i.e., when prices are not observable to the competing sellers, all sales are made by the better seller and the set of repeated game equilibrium payoffs coincides with the stage game subgame perfect equilibrium payoffs. This is in sharp contrast to the game with perfect monitoring where the folk theorem obtains. Journal of Economic Literature Classification Numbers: C72, D43.     

Dynamics of International Debt Overhang with Two Lender Banks

This paper presents a dynamic formalization of the behaviour of creditor banks on the secondary market for debts. I formulate the problem as an infinite-horizon game with two banks as players where each bank decides in every period either to sell its loan exposure to the debtor country at the present secondary market price, or to wait and keep its exposure to the next period. There exist three types of subgame-perfect equilibria with the property called the time continuation. I consider the relation ship between our equilibria and those of the Kaneko–Prokop (1993) one-period approach to the same problem and show that their approach does not lose much of the dynamic nature of the problem. In any equilibrium of the game, each bank waits in every period with high probability. I discuss the implications of these results for the long-run behaviour of banks on the secondary market and the resolution of debt overhang
JEL Classification Number: F34     

Competitive search markets for durable goods

Summary. This paper considers a dynamic version of Akerlof's (1970) lemons problem where buyers and sellers must engage in search to find a trading partner. We show that if goods are durable, the market itself may provide a natural sorting mechanism. In equilibrium, high-quality goods sell at a higher price than low-quality goods but also circulate longer. This accords with the common wisdom that sellers who want to sell fast may have to accept a lower price. We then compare the equilibrium outcomes under private information with those under complete information. Surprisingly, we find that for a large range of parameter values the quilibrium outcomes under the two information regimes coincide, despite the fact that circulation time is used to achieve separation. Received: August 24, 2000; revised version: October 24, 2000     

Hangovers

This paper analyzes a process by which a market boom brought on by a temporary increase in the flow of buyers, can subsequently lead to a collapse of liquidity (speed of sale), prices and production to levels lower than before the onset of the boom. I consider a general model of markets subject to search frictions in the matching of buyers and sellers, where the entry of buyers and sellers (through production) are subject to adjustment costs. The resulting co-movement between unemployment, inventories and sales with the production cycle matches the stylized facts.     

Price discrimination of buyers with identical preferences and collusion in a model of advertising

A model of advertising and price distributions is investigated whereby each seller can contact different buyers, whose preferences are identical, with different probabilities. The model features a continuum of equilibria parametrized by the ratio of the buyers contacted by one seller—differing across “market segments”—and by the other sellers. In general, the sellers practice price discrimination across segments. More asymmetric equilibria correspond to higher volumes of transactions and higher expected transaction prices. This results in a lower expected utility for the buyers and higher expected profits; thus, identifying areas of influence can help the sellers to support collusion.     

Revisiting the Lemons Market

This article extends the standard competitive adverse selection model by allowing for qualitatively different information structures of agents on the informed side of the market. Using the stylized framework of the market for used cars, we examine the welfare properties of equilibria under the assumption that a fraction of the sellers remains uninformed about a parameter that is relevant for their own transaction. Whether market performance increases or decreases in the number of uninformed sellers is shown to depend on (1) the potential gains from trade in the market and (2) the average quality of the sellers' information structure.     

The Evolutionary Stability of Auctions over Bargaining

This paper considers equilibrium in transaction mechanisms. In an environment with homogeneous buyers and sellers, which eliminates the advantage auctions possess of matching buyers and sellers, both auctions and bargaining are equilibria. However, only auctions are evolutionarily stable. This identifies a new advantage of auctions over bargaining, arising from the division of the gains from trade.Journal of Economic LiteratureClassification Numbers: C78, C73, D44.     

Search costs and the severity of adverse selection

In view of some recent empirical evidence, I suggest a relationship between the magnitude of search costs and the severity of adverse selection in the context of a dynamic model with asymmetric information. In markets with small search costs sellers with low quality products misrepresent their quality and demand a high price. If search costs are not negligible, sellers׳ price offers are truthful and all product qualities are traded over time. In markets with small search costs, a budget balanced mechanism can mitigate adverse selection: sellers should pay a per period market participation tax and receive a rebate after trading.     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Implementing the Mortensen rule in a frictional labor market

We show that, in settings where meetings can be multilateral, the allocation rule proposed by Mortensen (1982) can be relatively straightforward to implement: as a local auction conducted by sellers. The implications of using this mechanism in a simple model of the labor market are then explored. We characterize the equilibrium properties of this model, which include wage dispersion, and examine its implied Beveridge curve. A dynamic version of the model is calibrated to the US labor market, and we show that the model can account for observed vacancy rates, given parameters that are chosen to match the average wages and the natural rate of unemployment, although the implied wage dispersion is quite small. Finally, in the limit, as the time between offer rounds in the model approaches zero, the equilibrium approaches the Walrasian competitive equilibrium.     

Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility

This paper presents a model of stochastic oligopoly with demand uncertainty where firms endogenously choose entry timing. We examine two extreme types of market structure and show that the equilibrium correspondence that connects them is continous. With two identically sized firms, there are symmetric, Cournot type equilibria where the probability of early entry declines with greater uncertainty, and for low uncertainty two asymmetric equilibria. With one large firm with a continuum of nonatomic firms, there is a unique Stackelberg equilibrium. We conclude that the behavior of a dominant firm with a finite fringe can be approximated by Stackelberg equilibrium.Journal of Economic LiteratureClassification Numbers?: D21, L11.     

Option to wait in a search model

We consider a standard search model with buyers and sellers. Upon meeting the buyers make a take-it-or-leave-it offer, but the sellers have an option not to trade immediately but wait for more agents to appear. If more buyers come, there is excess demand, and the buyers engage in auction to get the good. Analogously, if more sellers come, the sellers engage in a Bertrand-type pricing game to sell the object. The option to wait restricts the price offer of the buyer; in an equilibrium in which trades are consummated without delay there is a unique price offer for the buyer.JEL Classification: C78, D44, D831     

Bidding for Labor

We present a competing-auction theory of the labor market, where job candidates auction their labor services to employers. An equilibrium matching function emerges which has many of the features commonly assumed, including constant returns to scale in large economies. The auction mechanism also generates equilibrium wage dispersion among homogeneous workers and constrained-efficient entry of vacancies in large economies. In a dynamic version of the model, we generate implied numerical values for equilibrium unemployment and wage dispersion. The theory makes the novel prediction that wage dispersion is a decreasing function of the discount factor and labor market tightness. Journal of Economic Literature Classification Numbers: E24, J31, J41, J64, D44.