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.     

Trade mechanism selection in markets with frictions

We endogenize the trade mechanism in a search economy with many homogeneous sellers and many heterogeneous buyers of unobservable type. We study how heterogeneity and the traders' continuation values—which are endogenous—influence the sellers' choice of trade mechanism. Sellers trade off the probability of an immediate sale against the surplus expected from it, choosing whether to trade with everyone and how quickly. In equilibrium sellers may simply target one buyer type via non-negotiable offers (price posting), or may price discriminate (haggling). We also study when haggling generates trading delays. A price setting externality arises because of a strategic complementarity in the sellers' pricing choices.     

STRATEGIC ADVERTISING AND DIRECTED SEARCH

Imperfect observability and costly informative advertising are introduced into a standard directed search framework. Capacity‐constrained sellers send costly advertisements to direct buyers' uncoordinated search by specifying their location and terms of trade. We show that the equilibrium advertising intensity is nonmonotonic in the buyer–seller ratio. In addition, we also find that price posting dominates auctions since both mechanisms yield the same expected revenue, but the latter results in higher advertising expense. Finally, we find a positive comovement between market transparency and price for low market tightness when the measure of informed buyers is endogenous.     

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     

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.     

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.     

Indeterminacy and directed search

The directed search approach assumes each seller posts a fixed price and, ex post, randomly allocates the good should more than one buyer desire the good. This paper assumes sellers can post prices which are contingent on ex post realized demand; e.g. an advertisement might state the Bertrand price should there be more than one buyer, which corresponds to an auction outcome. Competition in fixed prices and ex post rationing describes equilibrium behavior. There is also real market indeterminacy: a continuum of equilibria exists which are not payoff equivalent. Sellers prefer the equilibrium in auctions.     

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.     

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.     

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.     

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.     

THE HIDDEN COST OF BARGAINING: EVIDENCE FROM A CHEATING-PRONE MARKETPLACE

It is widely believed that successful bargaining helps consumers increase their surplus. We present evidence from a field experiment showing that bargaining over price reduces buyer surplus in a marketplace where sellers cheat on the weight whose value may more than offset the price discount. Our results show that bargaining entails hidden costs since sellers cheat significantly more when buyers bargain than not and they cheat significantly more when bargaining succeeds than fails. Overall bargaining reduces buyer surplus than not bargaining. Our result is relevant for credence goods markets where bargaining over prices may induce sellers to “undertreat” more.     

A Walrasian Rubinstein and Wolinsky model

We provide a full dynamic analysis of a continuous-time variant of Rubinstein and Wolinsky (1985) matching and bargaining model with unbalanced flows of buyers and sellers. The focus is on the price limit as the frictions of search are removed. It is found that a necessary and sufficient condition for the limit price to be Walrasian at all times is the alignment of the initial buyer and seller stocks with the flows.     

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.     

Bundling as an optimal selling mechanism for a multiple-good monopolist

Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price-bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n-object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.     

DYNAMIC PRICE COMPETITION WITH CAPACITY CONSTRAINTS AND A STRATEGIC BUYER

We analyze a simple dynamic durable good model. Two incumbent sellers and potential entrants choose their capacities at the start of the game. We solve for equilibrium capacity choices and the (necessarily mixed) pricing strategies. In equilibrium, the buyer splits the order with positive probability to preserve competition, making it possible that a high and low price seller both have sales. Sellers command a rent above the value of unmet demand by the other seller. A buyer benefits from either a commitment not to make future purchases or by hiring an agent to always buy from the lowest priced seller.     

Asymmetric first-price menu auctions under intricate uncertainty

This paper studies asymmetric first-price menu auctions in the procurement environment where the buyer does not commit to a decision rule and asymmetric sellers have interdependent costs and statistically affiliated signals. Sellers compete in bidding a menu of contracts, where a contract specifies a vector of characteristics and a payment required from the buyer for delivering these characteristics. The buyer does not commit ex-ante to a decision rule but rather upon observing all the menus offered by sellers chooses the best contract. This paper establishes the existence of a continuum of separating monotone equilibria in this game bounded above by the jointly ex-post efficient outcome and below by the jointly interim efficient outcome. It shows that the jointly ex-post efficient equilibrium outcome is the only ex-post renegotiation-proof outcome and it is also ex-ante robust to all continuation equilibria.     

Sunk costs and fairness in incomplete information bargaining

We study a bilateral trading relationship in which one agent, the seller, can make a nonrecoverable investment in order to generate potential gains from trade. Afterwards, the seller makes a price offer that the buyer can either accept or reject. If agents are fairminded, sellers who are known by the buyer to have high investment costs are predicted to charge higher prices. If the investment cost is private information, low-cost sellers should price more aggressively and high-cost sellers less aggressively than under complete information, giving rise to disagreement and/or underinvestment. Our experiment support these predictions.     

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.     

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.