Search, common knowledge, and competition

This paper analyzes the effects of buyer search costs and seller private and common knowledge on seller competition. It shows that lack of common knowledge results in the equilibrium price continuously decreasing to the perfectly competitive one as buyer search costs for price decrease from positive for all buyers to zero for all buyers, even if each market agent's uncertainty (in the private knowledge) is small. At the same time, if the uncertainty of each seller about buyer valuations is small, the effects of a small change in the search costs or of information structure on pricing may be large (but continuous).     

Price and information disclosure in the private art market: A signalling game

In this paper, we model private art market agents’ strategic interactions in presence of two types of asymmetric information, about artwork quality and buyer’s knowledge, assuming the seller does not know how informed is the buyer while the buyer does not know the quality of the artwork before purchase. If the seller can choose either a high or a low price and the buyer can signal his type to the seller, we identify the conditions for both equilibria with pooling buyer signalling strategy and with separating strategy, as well as conditions for equilibria where the seller fixes the price according to the actual quality and where he posts prices trying to take advantage of buyer’s limited information. Finally, we identify the condition for the emergence of a “counter-lemon” result, where low-quality artworks and uninformed collectors exit the market, suggesting that seller uncertainty does not directly benefit the buyers, but it can impact the quality traded in the market.     

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.     

Sequential selling mechanisms

Summary In this paper we attempt to formalize the idea that a mechanism that involves multilateral communication between buyers and sellers may be dominated by one that involves simple bilateral communication. To do this we consider the well known problem in which a seller tries to sell a single unit of output to a group ofN buyers who have independently distributed private valuations. Our arguments hinge on two considerations. First, buyers communicate their willingness to negotiate with the seller sequentially, and second, buyers have the option of purchasing the good from some alternative supplier. It is shown that the seller cannot improve upon a procedure in which she offers the good to each buyer in turn at a fixed price. The seller reverts to multilateral communication if possible, only when no buyer is willing to pay the fixed price. In reasonable environments buyers will be too impatient to wait for the outcome of a multilateral negotiation and all communications will be bilateral.In many problems in mechanism design, informed traders have no alternative to participation in the mechanism that is offered by its designer. The best mechanism from the designer's point of view is then the one that is most efficient at extracting informational rents, that is, a simple auction. In a competitive environment it is likely to be costly for buyers to participate in an auction or any other multilateral selling scheme in which the seller must process information from many different buyers because alternative trading opportunities will be disappearing during the time that the seller is collecting this information. Buyers might be willing to participate in an auction, but only if they could be guaranteed that the competition that they face will not eliminate too much of their surplus.At the other extreme to the auction is a simple fixed price selling scheme 1. The seller simply waits until he meets a buyer whose valuation is high enough, given the opportunities that exist in the rest of the market, for him to be willing to pay this price. The seller extracts the minimum of the buyer's informational rents since the price that a buyer pays is independent of his valuation. Yet the seller might like this scheme if adding a second bidder to the process makes it very difficult for him to find a buyer with a valuation high enough to want to participate.In the presence of opportunity costs, the seller faces a trade-off between his ability to extract buyers informational rents and his ability to find buyers who are willing to participate in any competitive process. In practice this trade-off will impose structure on the method that is used to determine a price. In markets where there are auctions, limits are put on buyer participation. In tobacco auctions bids are submitted at a distinct point in time from buyers who are present at that time. In real estate auctions time limits are put on the amount of time the seller will wait before making a decision. These restrictions on participation are presumably endogenously selected by the seller (possibly in competition with other mechanism designers) with this trade-off in mind.On the other hand, markets in which objects appear to trade at a fixed price are rarely so simple. A baker with a fixed supply of fresh bagels is unlikely to collect bids from buyers and award the bagels to the high bidder at the end of the day. Buyers are unlikely to be willing to participate in such a scheme since they can buy fresh bagels from a competitor down the street. Yet despite the fact that bagels sell at a fixed price throughout the day, most bakers are more than willing to let it be known that they will discount price at the end of the day on any bagels that they have not yet sold. Selling used cars presents a similar problem. Each potential buyer for the used car is likely to have inspected a number of alternatives, and is likely to know the prices at which these alternative can be obtained. A seller who suggests that buyers submit a bid, then wait until the seller is sure that no higher offer will be submitted is asking buyers to forgo these alternative opportunities with no gain to themselves. To avoid the rigidity of the pure fixed price scheme most used cars are sold for a fixed price or best offer. These examples suggest that the best selling mechanism may involve a complex interplay between participation and surplus extraction considerations.The purpose of this paper is to provide a simple formalism within which the factors that determine the best contract can be evaluated. We consider the best known environment from the point of view of auction design in which there are a large number of buyers with independent private valuations for a unit of an indivisible commodity that is being sold by a single supplier who acts as the mechanism designer. We modify this standard problem in two critical ways. First, we assume that the seller meets the potential buyers sequentially rather than all at once. Secondly we assume that buyers have a valuable alternative that yields them a sure surplus. This creates a simple bidding cost that is effectively the expected loss in surplus (created by the disappearance of outside alternatives) that the buyer faces during the time that he spends negotiating with the seller.These simple assumptions allow us to calculate the impact of competition and communication costs using completely standard arguments from the mechanism design literature. We are able to show that with these assumptions the seller's expected surplus will be highest if the object is sold according to the following modified fixed price scheme: the seller contacts each of the potential buyers in turn and either offers to negotiate or announces that he no longer wishes to trade. If he offers to negotiate and the buyer agrees, the buyer immediately has the option of trading for sure with the seller at a fixed price set ex ante. If the buyer does not wish to pay this fixed price, he may submit an alternative bid. The seller will then continue to contact new buyers, returning to trade with the buyer only if no buyer wishes to pay the fixed price and no higher bid is submitted.It will be clear that in our environment, both the simple fixed price scheme and the simple auction are feasible. The simple auction prevails when the fixed price is set equal to the maximum possible valuation, while the simple fixed price scheme occurs when the fixed price is set so that buyers are willing to participate if and only if they are willing to pay the fixed price. Our results will show that a simple auction in never optimal for the seller. The seller can always strictly improve his payoff by moving to a scheme in which there is some strictly positive probability that trade will occur at the fixed price. On the other hand, there are reasonable circumstances in which the seller cannot achieve a higher payoff than the one she gets by selling at a fixed price. It is shown that for any positive participation cost, there is a large, but finite, number of potential buyers so that the seller cannot achieve a higher payoff than what she gets by selling at a fixed price. Two simple, but important continuity results are also illustrated. As the cost of participation in the mechanism increases (decreases), the probability with which the seller's unit of output is sold at a fixed price goes to one (zero) in the best modified fixed price mechanism for the seller.Our paper is not the first to generate such a modified fixed price scheme. Both McAfee and McMillan (1988) and Riley and Zeckhauser (1983) come up with similar schemes for the case in which the seller must bear a fixed cost for each new buyer that she contacts. There are two essential differences between our model and theirs. First, as the cost is interpreted as the opportunity cost of participation in the mechanism, it is reasonable to imagine that the seller advertises the mechanism ex ante. Another way of putting this is that the seller pays a fixed rather than a variable cost to communicate the mechanism to buyers. This makes it possible to assume that the mechanism is common knowledge to the seller and all the buyers at the beginning of the communication process. For this reason we can make our case using completely standard arguments. Secondly, the mechanism in the opportunity cost case plays a different allocative role than it does in the case when the seller bears a cost. The mechanism must decide whether buyers should communicate with the seller or pursue their alternative activities, as well as who should trade and at what price. It is this allocative role that makes bilateral communication superior to multilateral communication in a competitive environment. These differences allow us to show, for example, that a simple fixed price scheme is undominated for the seller when the number of buyers is finite. As shown by McAfee and McMillan, this is only possible when the number of potential buyers is infinite when the seller bears the cost of communication.Remarkably, the existence of opportunity costs to buyer participation is not, by itself, sufficient to explain why sellers might prefer bilateral communications mechanisms. Samuelson (1983) and McAfee and McMillan (1987) show that when buyers must pay a fixed cost to submit a bid, which is equivalent to giving up a valuable alternative, a seller cannot expect to earn more than she does in a second price auction (though Samuelson shows that the reserve price may depend on the number of potential buyers). One of the contributions of this paper is to show that the assumption that buyers make their participation decisions simultaneously is critical to this result. Simultaneous entry decisions means that whether or not any particular buyer is assigned to the alternative activity is independent of any other buyer's valuation. With sequential communication the seller is able to relax this constraint. It is precisely the enlargement of the class of feasible mechanism that breaks down the optimality of the simple auction.The second author acknowledges the support of the Social Sciences and Humanities Research Council of Canada and the CRDE at the Université de Montreal.     

Equilibrium Partner Switching in a Bargaining Model With Asymmetric Information

We study a model in which the seller of an indivisible object faces two potential buyers and makes an offer to either of them in each period. We find that the seller's ability to extract surplus from them depends crucially on the value of the cost of switching from one buyer to the next. If the seller is pessimistic about the buyers' valuations and there is a switching cost, however small, then the market is a natural bilateral monopoly; the second buyer is never called on. If the switching cost is zero, or if the seller is optimistic, then switching, and possibly recall of the original buyer, may occur.     

Intertemporal pricing in laboratory posted offer markets with differential information

Summary. This paper analyzes intertemporal seller pricing and buyer purchasing behavior in a laboratory retail market with differential information. A seller posts one price each period that a buyer either accepts or rejects. Trade occurs over a sequence of "market periods" with a random termination date. The buyer and seller are differentially informed: The seller's cost of producing a unit of a fictitious good is known and constant in all periods, but the buyer's value for the good (demand) is a random variable governed by a Markov Process whose structure is common knowledge. At the beginning of each period the unit's value is determined by "nature" and is privately revealed only to the buyer. The market termination rule is a binary random variable. We conduct 32 laboratory experiments designed to study intertemporal pricing by human subjects in the Posted Offer Institution when demand follows a stochastic process. There are four series of experiments: 8 with simulated buyers, 8 with inexperienced subjects, 8 with once experienced subjects, and 8 with twice experienced subjects.     

Prices for cash and cash for prices? Theory and evidence on convenient pricing

A transaction between a seller and a buyer incurs a payment cost. The payment cost is borne by the seller, depending on the payment instrument the buyer chooses, cash or card. Card payment is more costly than cash payment, so the seller prefers that the buyer pays cash. In this article, we study the strategy of the seller setting a convenient price, which simplifies transactions and pushes the buyer to pay cash. The theoretical analysis, which models both the seller and the buyer in a game setting, derives two propositions: (1) the seller is more likely to set a more convenient price and (2) the buyer is more likely to pay cash a more convenient price. The empirical analysis supports both propositions. Thus, sellers adopt a convenience pricing strategy – prices for cash – and this strategy pushes buyers to pay cash – cash for prices.     

DIRECTED SEARCH,COORDINATION FAILURE,AND SELLER PROFITS: AN EXPERIMENTAL COMPARISON OF POSTED PRICING WITH SINGLE AND MULTIPLE PRICES

We experimentally examine posted pricing and directed search. In one treatment, capacity‐constrained sellers post fixed prices, which buyers observe before choosing whom to visit. In the other, firms post both “single‐buyer” (applied when one buyer visits) and “multibuyer” (when multiple buyers visit) prices. We find, based on a 2 × 2 (two buyers and two sellers) market and a follow‐up experiment with 3 and 2 × 3 markets, that multibuyer prices can be lower than single‐buyer prices or prices in the one‐price treatment. Also, allowing the multibuyer price does not affect seller profits and increases market frictions.     

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.     

Word-Of-Mouth Communication and Community Enforcement

We study a repeated game where a seller, who has a short-term incentive to supply low quality, is periodically matched with a randomly selected buyer. Buyers observe only the outcomes of their neighbors' games and may receive signals from them. When the buyer population is large, the seller may sell high quality even when each buyer observes her action in any given period with an arbitrarily small probability. When networking among buyers is costly, low quality is always supplied with a positive probability. For this case, we characterize an equilibrium where the seller randomizes between high and low quality.     

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.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

SEARCH,ADVERSE SELECTION,AND MARKET CLEARING

We examine a dynamic decentralized trading model with infinitesimal sellers and buyers to investigate whether or not the market fails to clear in the limit of search friction vanishing. A seller, who has private information about product quality, and a buyer are matched to bargain over price. They form a long‐term relationship if they reach agreement. They return to the matching pool if they fail to agree or the existing relationship is dissolved. The market fails to clear if and only if the ratio of agents' patience over the dissolution rate exceeds a threshold.     

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.     

Asymmetric information in bilateral trade and in markets: An inversion result

I consider bilateral trade between a seller and a buyer with private valuations. The seller makes a take-it-or-leave-it price offer. If the seller observes the buyer?s valuation (symmetric information), bilateral trade is trivially efficient. If the seller cannot observe the valuation (asymmetric information), bilateral trade is inefficient. This bilateral trading game is embedded into a large matching market. In the steady-state equilibrium of the market game, the relation between the informational regime and efficiency is inverted: With small frictions efficiency obtains if information is asymmetric. If information is symmetric, however, the trading outcome can be very inefficient—even if frictions vanish.     

Multidimensional Bargaining Under Asymmetric Information

A buyer with private information regarding marginal valuation bargains with a seller to determine price and quantity of trade. Depending on parameter values, a high‐valuation buyer wants either to reveal information to create value or to conceal it to capture value. In the first case, equilibrium trades are efficient. In the second case, the low‐valuation buyer purchases less than her efficient quantity, and there can be a one‐period delay in trade. The quantity distortion is the only inefficiency that persists when time between offers approaches zero. There exist equilibria that are independent of the seller's prior beliefs.     

Dynamic Monopoly with Nondurable Goods

A nondurable good monopolist who posts a single price will generally achieve an inefficient outcome. But is it possible that the monopolist would achieve efficiency by repeatedly posting prices before delivery? If buyers recognize the effect of current purchases on future prices, then, under complementary ideal conditions, the answer is yes. On the other hand, traditional concerns about monopoly are viable if the seller bears a small cost per buyer of market reopening.Journal of Economic LiteratureClassification Numbers: D42, L12.     

The asymptotic shapley value for a simple market game

We consider the game in which b buyers each seek to purchase 1 unit of an indivisible good from s sellers, each of whom has k units to sell. The good is worth 0 to each seller and 1 to each buyer. Using the central limit theorem, and implicitly convergence to tied down Brownian motion, we find a closed form solution for the limiting Shapley value as s and b increase without bound. This asymptotic value depends upon the seller size k, the limiting ratio b/ks of buyers to items for sale, and the limiting ratio of the excess supply relative to the square root of the number of market participants. This work was sponsered in part by NSF Grant DMS-03-01795.     

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.     

Buyer behavior under the Best Offer mechanism: A theoretical model and empirical evidence from eBay Motors

We use data from eBay Best Offer listings to analyze haggling over prices in transactions with one seller and a series of potential buyers for a limited-supply product. We characterize this transaction mechanism as a sequential-move game to investigate buyer behavior. Our model suggests that a buyer's offer price increases in relations to the number of buyers who have previously made an offer on the item and the Buy-It-Now price chosen by the seller. On the other hand, the offer price decreases for items which have been listed on eBay for a longer period of time. We empirically test our theoretical predictions using data on the sales of Toyota Camry cars on eBay Motors. The empirical evidence is consistent with our model.