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     

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.     

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.     

Imperfect Competition in Auction Designs

We study the competition between two owners of identical goods who wish to sell them to a pool of potential buyers. The sellers compete simultaneously setting reserve prices for their second price sealed bid auctions. Upon observing the set reserve prices, the buyers decide simultaneously in which auction to bid. We show that this game has (at least) one equilibrium and that all equilibria are inefficient: reserve prices are not driven to zero (cost). We also discuss where and why the parallel between optimal auction design and optimal pricing in the case of monopoly breaks down for oligopoly.     

Mechanisms for a spatially distributed market

We consider the problem of a spatially distributed market with strategic agents. A single good is traded in a set of independent markets, where shipment between markets is possible but costly. The problem has previously been studied in the non-strategic case, in which it can be analyzed and solved as a min-cost-flow problem. We consider the case where buyers and sellers are strategic. Our first result gives a double characterization of the VCG prices, first as distances in a certain residue graph and second as the minimal (for buyers) and maximal (for sellers) equilibrium prices. This provides a computationally efficient, individually rational and incentive compatible welfare maximizing mechanism. This mechanism is, necessarily, not budget balanced and we also provide a budget-balanced mechanism (which is also computationally efficient, incentive compatible and individually rational) that achieves high welfare. Finally, we present results for some extensions of the model.     

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.     

Dissertation abstract: Essays on pricing in experimental duopoly markets

This dissertation comprises three independent essays that analyze pricing behavior in experimental duopoly markets. The first essay examines whether the content of buyer information and the timing of its dissemination affects seller market power. We construct laboratory markets with differentiated goods and costly buyer search in which sellers simultaneously post prices. The experiment varies the information on price or product characteristics that buyers learn under different timing assumptions (pre- and post-search), generating four information treatments. Theory predicts that price information lowers the equilibrium price, but information about product characteristics increases the equilibrium price. That is, contrary to simple intuition, presence of informed buyers may impart a negative externality on other uninformed buyers. The data support the model's negative externality result when sellers face a large number of robot buyers that are programmed to search optimally. Observed prices conform to the model's comparative statics and are broadly consistent with predicted levels. With human buyers, however, excessive search instigates increased price competition and sellers post prices that are significantly lower than predicted. The second essay uses experimental methods to demonstrate the anti-competitive potential of price-matching guarantees in both symmetric and asymmetric cost duopolies. When costs are symmetric, price-matching guarantees increase the posted prices to the collusive level. With asymmetric costs, guaranteed prices remain high relative to prices without the use of guarantees, but the overall ability of guarantees to act as a collusion facilitating device depends on the relative cost difference. Fewer guarantees, combined with lower average prices, suggest that cost asymmetries may discourage collusion. The third essay investigates the effect of firm size asymmetry on the emergence of price leadership in a homogeneous good duopoly. With discounting, the unique subgame-perfect equilibrium predicts that the large firm will emerge as the endogenous price leader. Independent of the level of size asymmetry, the laboratory data indicates that price leadership by the large firm is one of the most frequently observed timings of price announcement. In most cases, however, it comes second to simultaneous price-setting. This tendency to wait for the other firm to announce its price is especially strong when the level of size asymmetry between firms is low. We attribute the lower than expected frequency of price leadership to coordination failure, which is further compounded by elements of inequity aversion. JEL Classification C91, D43, D83, L11 Dissertation Committee: Timothy Cason (Chair), Department of Economics, Purdue University Dan Kovenock, Department of Economics, Purdue University Stephen Martin, Department of Economics, Purdue University Marco Casari, Department of Economics, Purdue University     

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.     

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     

Equilibrium in Auction and Bargaining Markets When Agents Can Wait and Search

The paper studies two market structures and two modes of trade. The agents, buyers and sellers, can choose whether to stay or search. The meetings take place randomly, and trades are consummated by auction or by bargaining. There are altogether four possible markets but in equilibrium at most two markets are active simultaneously. There is almost always a unique evolutionary stable equilibrium which consists of an auction market when the numbers of buyers and sellers differ greatly, and two simultaneous auction markets when the numbers are relatively close.     

Randomized double auctions: gains from trade,trader roles,and price discovery

Experimental double-auction commodity markets are known to exhibit robust convergence to competitive equilibria under stable or cyclical supply and demand conditions, but little is known about their performance in truly random environments. We provide a comprehensive study of double auctions in a stochastic setting where the equilibrium prices, trading volumes and gains from trade are highly variable across periods, and with commodity traders who may buy or sell their goods depending on market conditions and their individual outcomes. We find that performance in this stochastic environment is sensitive to underlying market conditions. Efficiency is higher and convergence to the competitive equilibrium stronger when the potential gains from trade are high and when the equilibrium spans a wide range of quantities, implying a large number of marginal trades. Speculative re-trading is prevalent, especially among those who have little to gain under equilibrium pricing. Those with the largest expected gains typically earn far less than predicted, while those with little or no predicted earnings gain modestly from speculation, leading to some redistribution of gains from high to low expected earners. Excessive trading volumes are associated with negative efficiencies in markets with low gains from trade, but not in the high-gains markets, where zero-sum trading and re-trading appear to enforce efficiency and near-equilibrium pricing. Buyers earn more relative to their competitive equilibrium benchmark than sellers do. Introducing trader specialization leads to fewer trading errors and higher market efficiency, but it does not eliminate zero-sum trading and re-trading.

     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

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.     

A structural model of competing sellers: Auctions and posted prices

In an original data set of goods listed for sale online, I observe that both auctions and posted prices are popular with buyers and sellers in the compact-disc market. To explain why these two mechanisms coexist, I estimate a structural model of competing sellers who differ in the value of their outside options. Buyers are allowed to value auctioned and posted-price goods differently but the estimated value distributions suggest that differences across buyers do not explain the mechanism coexistence that I observe. In contrast, differences across sellers' outside options are important: the value of the outside option segments the market with high outside-option sellers choosing to post a fixed price. There are two key forces at work that drive this empirical result. First, competition between sellers favors coexistence over an auction-only or a posted-price-only marketplace because sellers prefer to be in a market with fewer rivals. Second, sellers with more valuable outside options prefer the posted-price mechanism because posted-price goods sell less often than auctioned goods but at a higher price. As a result, a larger outside option reduces the loss from not selling and favors the posted-price mechanism.     

Farmers’ performance and subject pool effect in decentralized bargaining markets

We report results from a decentralized bargaining market experiment conducted with farmers and students. Our results indicate that despite its bad reputation, performance is highly efficient (although not as efficient as the competitive equilibrium prediction). Farmers and students perform similarly regarding quantities, prices, and allocative efficiencies, but not regarding payoff allocations between buyers and sellers.     

Confusopoly: competition and obfuscation in markets

This paper examines the effects of competition in experimental posted-offer markets where sellers can confuse buyers. I report two studies. In one, the sellers offering heterogeneous goods can obfuscate buyers by means of spurious product differentiation. In the other study, sellers offer identical goods and make their prices unnecessarily complex by having multi-part tariffs. I vary the level of competition by having treatments with two and three- sellers in both studies, and having an additional treatment with five-sellers in one study. The results show that average complexity created by a seller is not different for the treatments with two, three and five sellers. In addition, market prices are highest and buyer surplus is lowest when there are two sellers in a market.     

MEETINGS AND MECHANISMS

This article shows how meeting frictions affect equilibrium trading mechanisms and allocations in an environment where identical sellers post mechanisms to compete for buyers with ex ante heterogeneous private valuations. Multiple submarkets can emerge, each consisting of all sellers posting a particular mechanism and the buyers who visit those sellers. Under mild conditions, high-valuation buyers are all located in the same submarket, and low valuation buyers can be in: (i) the same submarket, (ii) a different submarket, and (iii) a mixture of (i) and (ii). The decentralized equilibrium is efficient when sellers can post auctions with reserve prices or entry fees.     

COMPETITIVE PRICING AND EFFICIENCY IN SEARCH EQUILIBRIUM*

We consolidate and generalize some results on price determination and efficiency in search equilibrium. Extending models by Rubinstein and Wolinsky and by Gale, heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition. When the discount rate r and search costs converge to 0, we show that prices in all exchanges are the same and equal the competitive, market clearing, price. Given positive search costs, efficiency obtains iff bargaining satisfies Hosios' condition and r=0. When prices are set by third‐party market makers, however, we show that search equilibrium is necessarily efficient.     

EXPERIMENTAL WORK ON SUBSIDIES,MORAL HAZARD,AND MARKET POWER IN AGRICULTURAL MARKETS

Laboratory markets are created to capture the important features of agricultural commodity markets. Sellers make production decisions and hold inventories before goods are sold. In a posted‐bid auction environment, price supports create a moral hazard for sellers. Part of the price‐support subsidy is transferred to buyers in the form of lower prices, which are close to those predicted by the buyers' Cournot level. The subsidy program is expensive for this reason. Lump‐sum payments correct the moral hazard problem and are better at transferring income to sellers. However, transfers made at the beginning of each production period cause a decline in production levels. (JEL D44, C92)     

COMPETITIVE MARKET BEHAVIOR: CONVERGENCE AND ASYMMETRY IN THE EXPERIMENTAL DOUBLE AUCTION

We conducted a large number of controlled continuous double auction experiments to reproduce and stress-test the phenomenon of convergence to competitive equilibrium under private information with decentralized trading feedback. Our main finding is that across a total of 104 markets (involving over 1,700 subjects), convergence occurs after a handful of trading periods. Initially, however, there is an inherent asymmetry that favors buyers, typically resulting in prices below equilibrium levels. Analysis of over 80,000 observations of individual bids and asks helps identify empirical ingredients contributing to the observed phenomena including higher levels of aggressiveness initially among buyers than sellers.