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.     

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.     

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.     

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     

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.     

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.     

Sequential Procurement With Subcontracting

Two symmetric sellers are approached sequentially by fragmented buyers. Each buyer conducts a second-price auction and purchases from the seller who offers the lower price. Winning an auction affects bidding for future contracts because the sellers have nonconstant marginal costs. We assume that the sellers are completely informed, and we study the unique equilibrium that survives iterated elimination of weakly dominated strategies. If subcontracting between the sellers is impossible, the final allocation of contracts is generally inefficient. If postauction subcontracting is possible, the sellers can be worse off, ex ante , than when subcontracting is impossible.     

A choice of auction format in seller cheating: a signaling game analysis

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values. We thank an anonymous referee for useful comments that have improved the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) 15310023 and (C) 18530139.     

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.     

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.     

Turnover Externalities with Marketplace Trading

This article considers equilibrium decentralized trade when there is a marketplace where buyers and sellers meet costlessly. Since buyers have idiosyncratic match payoffs for each seller's good, some buyers, rather than trade with the current stock of sellers, wait for new sellers to enter the marketplace to obtain a good they like. A turnover externality exists where all traders are better off with higher entry rates of new traders. Furthermore, this turnover externality supports multiple Pareto-rankable equilibria. This provides new insights into similar results obtained in the random-matching literature.     

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.     

Equilibrium reserve prices in sequential ascending auctions

We study a model where bidders have perfectly correlated valuations for two goods sold sequentially in two ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Despite the lack of commitment by the seller, we characterize an equilibrium and study its properties. Strategic non-disclosure of information takes the form of non-participation in the early auction by low-valuation bidders, while high-valuation bidders bid up to their true valuations. Some buyers who would profitably buy at the reserve price refrain from participating in order to decrease the second-auction reserve price.     

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.     

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.     

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.     

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.     

基于买方市场的劳工标准移植研究

市场的竞争促使越来越多发展中国家的企业成为劳工认证供应链的一部分。本文基于买方主导型市场结构,运用信息租模型分析劳工标准在中国移植状况。研究表明,高劳工标准的存在,是供应商追求信息租金和采购商追求真实剩余博弈的均衡;当供应商类型分布不满足单调风险率性质时,会出现低标准混同均衡,也是采购商借助买方市场势力极大化真实剩余的结果;当采购商风险偏好属于规避型时,最后均衡劳工标准较之风险中性时要高,同时买卖双方福利都会提高。     

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.     

Market behavior in bid,offer, and double auctions: A Reexmination

This study examines the robustness of the previously observed [Smith (1964)] differences in market behavior between double auctions (both buyers and sellers may enter price quotes), bid auctions (only buyers may enter price quotes), and offer auctions (only sellers may enter price quotes). Based on the results of twenty-one market experiments, we find little support for the a priori hypothesis that bid auction prices tend to be greater than double auction prices which tend to be greater than offer auction prices.