Competitive-search equilibrium in monetary economies

Competitive search was recently introduced in monetary economics by Rocheteau and Wright [Money in search equilibrium, in competitive equilibrium, and in competitive search equilibrium, Econometrica 73 (2005) 175-203]. We extend their work by eliminating the restriction that the fees market makers charge to enter a submarket must be either non-negative or identical for buyers and sellers. Without this restriction, buyers pay a positive fee to enter the submarket they visit and nothing else when they meet a seller. Sellers are remunerated by the market makers from the entry fees collected from the buyers. This trading arrangement allows buyers to perfectly predict their expenses, so the opportunity cost of holding idle money balances is eliminated.     

High profit equilibria in directed search models

We consider a model of directed search where the sellers are allowed to post mechanisms with entry fees. Regardless of the number of buyers and sellers, the sellers are able to extract all the surplus of the buyers by introducing entry fees and making price schedules positively sloped in the number of buyers arriving to their shops. This is in contrast to results that are achieved for large markets under the assumption that sellers cannot influence the utility of any particular buyer (market utility assumption), in which case buyers obtain strictly positive rents. If there is a bound on the prices or on the entry fees that can be charged, then the equilibrium with full rent extraction does not exist any more, and the market utility assumption is restored for large markets.     

A MARKET WITH FRICTIONS IN THE MATCHING PROCESS: AN EXPERIMENTAL STUDY*

We construct a laboratory market in which there is a friction in the matching between buyers and sellers. Sellers simultaneously post prices and then buyers simultaneously choose a seller. If more than one buyer chooses the same seller, the seller's single unit is randomly sold to one of them. Our results show a broad consistency with theoretical predictions, although price dispersion exists and is slow to decay. Prices also exceed the equilibrium level when there are only two sellers, and buyers' purchase probabilities are insufficiently responsive to price differences when there are two sellers.     

Low price signals high capacity

We study pricing in a model where buyers are homogeneous and sellers have either capacity one or two. We show that if buyers observe prices but not capacities then an equilibrium exists where sellers of capacity two post lower prices than sellers of capacity one. The equilibrium satisfies the intuitive criterion.     

Sorting versus screening: Search frictions and competing mechanisms

In a market where sellers compete by posting trading mechanisms, we allow for a general search technology and show that its features crucially affect the equilibrium mechanism. Price posting prevails when meetings are rival, i.e., when a meeting by one buyer reduces another buyer's meeting probability. Under price posting buyers reveal their type by sorting ex-ante. Only if the meeting technology is sufficiently non-rival, price posting is not an equilibrium. Multiple buyer types then visit the same sellers who screen ex-post through auctions.     

CONTINGENT PRICES AND MONEY*

Price posting with directed search is a widely used trading mechanism. Coles and Eeckhout showed that if sellers are allowed to post prices contingent on realized demand instead of one price, then there is real market indeterminacy. In this article, we fit this contingent price‐posting protocol into a monetary economy. We show that, as long as holding money is costly, there exists a unique equilibrium rather than a continuum. In this equilibrium sellers post a low price for when the buyer is alone, a high price for when several buyers show up, and buyers randomize between sellers and money holdings.     

Seller competition by mechanism design

This paper analyzes a market game in which sellers offer trading mechanisms to buyers and buyers decide which seller to go to depending on the trading mechanisms offered. In a (subgame perfect) equilibrium of this market, sellers hold auctions with an efficient reserve price but charge an entry fee. The entry fee depends on the number of buyers and sellers, the distribution of buyer valuations, and the buyer cost of entering the market. As the size of the market increases, the entry fee decreases and converges to zero in the limit. We study how the surplus of buyers and sellers depends on the number of agents on each side of the market in this decentralized trading environment.     

Remain silent and ye shall suffer: seller exploitation of reticent buyers in an experimental reputation system

By providing incentives for sellers to act in a trustworthy manner, reputation mechanisms can mitigate moral-hazard problems when particular buyers and sellers interact infrequently. However, these mechanisms rely on buyers sharing their private information about sellers, and thus may suffer from too little feedback when provision is costly. We experimentally compare a standard feedback mechanism to one in which sellers can inspect a buyer’s feedback-provision history, thus providing incentives to share private information even when costly. We find fairly high trust and trustworthiness in all markets, with buyers providing costly feedback, especially negative, sufficient to induce trustworthiness. However, feedback-provision histories did not improve outcomes, and at least weakly decreased trustworthiness with experienced participants, as this information enabled sellers to discriminate and ship less frequently to buyers lacking a reputation for information sharing.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

Evolutionary stability of bargaining and price posting: implications for formal and informal activities

In this paper we study the co-existence of two well known trading protocols, bargaining and price-posting. To do so we consider a frictional environment where buyers and sellers play price-posting and bargaining games infinitely many times. Sellers switch from one market to the other at a rate that is proportional to their payoff differentials. Given the different informational requirements associated with these two trading mechanisms, we examine their possible co-existence in the context of informal and formal markets. Other than having different trading protocols, we also consider other distinguishing features. We find a unique stable equilibrium where price-posting (formal markets) and bargaining (informal markets) co-exist. In a richer environment where both sellers and buyers can move across markets, we show that there exists a unique stable dynamic equilibrium where formal and informal activities also co-exist whenever sellers’ and buyers’ net costs of trading in the formal market have opposite signs.     

The Demand for Information Services and the Market Structure

Uninformed buyers' demand for statistical screening between privately informed sellers is studied in a fixed price market. A single buyer will screen more extensively than would two or more buyers, since in the latter case buyers realize that sellers will be attracted to buyers with the most favorable screening policy (i.e., not to screen at all). This result is robust to some but not all types of modifications in the model. For instance, information quality differences in the sense of Blackwell will reinforce this effect. Furthermore, in equilibrium only the best information service will be used. Received April 17, 2001; revised version received January 24, 2002 Published online: November 11, 2002     

Search and endogenous concentration of liquidity in asset markets

We develop a search-based model of asset trading, in which investors of different horizons can invest in two assets with identical payoffs. The asset markets are partially segmented: buyers can search for only one asset, but can decide which one. We show the existence of a “clientele’’ equilibrium where all short-horizon investors search for the same asset. This asset has more buyers and sellers, lower search times, and trades at a higher price relative to its identical-payoff counterpart. The clientele equilibrium dominates the one where all investor types split equally across assets, implying that the concentration of liquidity is socially desirable.     

Optimality versus practicality in market design: A comparison of two double auctions

We consider a market for indivisible items with m buyers and m sellers. Traders privately know their values/costs, which are statistically dependent. Two mechanisms are considered. The buyer's bid double auction collects bids and asks from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders' beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.     

An experimental comparison of two search models

Summary. We report an experiment designed to investigate markets with consumer search costs. In markets where buyers are matched with one seller at a time, sellers are predicted to sell at prices equal to buyers' valuations. However, we find sellers post prices that offer a more equal division of the surplus, and these prices tend to be accepted, while prices closer to the equilibrium prediction are rejected. At the other extreme, sellers are predicted to sell at a price equal to marginal cost when buyers are matched with two sellers at a time. Here, we find prices are closer to, but still significantly different from, the equilibrium prediction. Thus, our results support theoretical comparative static, but not point, predictions.     

Buyer groups as strategic commitments

Buyer cooperatives, buyer alliances, and horizontal mergers are often perceived as attempts to increase buyer power. In contrast to prior research emphasizing group size, I show that even small buyer groups composed of buyers with heterogeneous preferences can increase price competition among rival sellers by committing to purchase exclusively from one seller. Without transfer payments, at least one buyer group exists for each pair of sellers and buyer groups membership is chosen to achieve indifference between the two sellers. With transfer payments, and just two sellers, the grand coalition is a coalition-proof subgame perfect equilibrium (CP-SPNE), though equilibria with arbitrarily many buyer groups also exist. With three sellers (and with more sellers when the distribution of buyers is symmetric), a CP-SPNE always exists, all coalition-proof equilibria are payoff equivalent and have at least one buyer group for each pair of firms, so the grand coalition is not an equilibrium.     

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.     

WHO SEARCHES?*

We consider a directed search model with buyers and sellers and determine whether buyers look for sellers or vice versa. The buyers and sellers can choose to search or wait; what they do in equilibrium depends on the relative size of the two populations and the price formation mechanism. We study bargaining and auctions and find that when one population is much larger than the other the former searches and the latter waits. Under auction with roughly equal populations some buyers and sellers search and some wait. Our results challenge the practice of postulating who searches and who waits.     

Surplus Extraction and Competition

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have correlated private information about their valuations. In contrast to the monopoly case where sellers charge entry fees and extract all buyers' surplus, it is shown that in the unique symmetric equilibrium with competition, sellers hold second price auctions with reserve prices set equal to their cost. Most important, it is a best reply for sellers not to charge entry fees of the kind normally used to extract surplus, even though it is feasible for them to do so.     

Uniqueness of equilibrium in sealed high-bid auctions

For the case of two buyers we show that equilibrium in the sealed high-bid auction is unique when (i) buyers' reservations prices are drawn independently from distributions with finite support and positive mass at the lower endpoint; (ii) buyers have private values; and (iii) buyers' preferences are log supermodular. For more than two buyers, we obtain the same result under the additional assumptions that (iv) buyers with the same reservation price have the same preferences; (v) buyers are risk neutral or risk averse with non-increasing absolute risk aversion; and (vi) the supports of the different buyers' distributions of reservation prices have the same upper endpoint.     

Does risk aversion explain behavior in a lemon market?

Siegenthaler proposes an ingenious solution to the lemon market adverse selection problem. He incorporates ‘‘cheap talk’’ in which sellers send out costless and nonbinding messages informing potential buyers of the quality of their goods; these messages could be true or false. This segments the market into several submarkets. Potential buyers need to decide which submarket to enter and what price to bid for the goods. Sellers then decide whether to accept the bid or not. He experimentally tests his model and finds that the comparative static results align with his theory, although the data do not exactly fit the model. Indeed, he does not fit the model to the data. His theory assumes risk-neutral decision-makers (DMs). Two reasons why the fit is not perfect may be that the DMs are not risk neutral and not perfectly rational. In this note, we report the results of fitting an asymmetric risk averse quantal response equilibrium (QRE) extension of his model to his data, and we find that the extension fits well. We show that the results are consistent with the market evidence and shed light on future research on lemon markets.