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.     

Optimal selling strategies when buyers may have hard information

Consider a revenue-maximizing seller who can sell an object to one of n potential buyers. Each buyer either has hard information about his valuation (i.e., evidence that cannot be forged) or is ignorant. The optimal mechanism is characterized. It turns out that more ignorance can increase the expected total surplus. Even when the buyers are ex ante symmetric, the object may be sold to a buyer who does not have the largest willingness-to-pay. Nevertheless, an additional buyer increases the expected total surplus in the symmetric case, whereas more competition can be harmful if there are ex ante asymmetries.     

On Bargaining for an Indivisible Good

This note studies contracts involving lotteries for the purpose of trading an indivisible good. Lottery contracts allow players to reach agreements for trading the good even if the reservation price of the potential buyer is below that of the potential seller. When certainty exchanges are possible, lottery contracts often dominate them. An interesting feature of the contracts is that the probability of trading the good depends on the players' bargaining powers, but the payments do not.Journal of Economic LiteratureClassification Numbers: C78.     

Bilateral bargaining, unverifiable quality, and options to return

Summary. The paper investigates an alternating-offers bargaining game between a buyer and a seller who face several trading opportunities. These items (goods or services) differ in their non-verifiable quality characteristics which gives rise to a moral hazard problem on the seller's part. For the special case of two goods, we completely characterize the set of subgame-perfect equilibria. We find that the seller always extends an option to return the good, while the buyer may suffer from this warranty. Also, qualitatively different types of equilibrium outcomes occur depending on the parameters of the model: (a) the seller may obtain a larger share of the surplus although the parties ex ante have symmetric bargaining positions, (b) the subgame-perfect equilibrium may entail inefficient trade, and (c) multiple equilibria may exist including equilibria with delay in negotiations. Finally, we analyze a situation where bargaining proceeds after the good was returned which is shown to reestablish uniqueness and efficiency of equilibrium.Received: 23 August 2001, Revised: 3 April 2003, JEL Classification Numbers: C78, L14, L15, D82. Correspondence to: Christoph LülfesmannThis paper has greatly benefitted from discussions with Avner Shaked and Timothy von Zandt. We also wish to thank Wolfgang Leininger, Zvika Neeman, Clemens Puppe, Wolfram Richter, Karl Schlag, Ilya Segal, and seminar participants in Dortmund, Bonn and Berkeley for helpful comments and discussions. Financial support by Deutsche Forschungsgemeinschaft, SFB 303 at the University of Bonn is gratefully acknowledged.     

Bargaining and Search with Incomplete Information about Outside Options

This paper considers a model of bargaining in which the seller makes offers and the buyer can search (at a cost) for an outside option; the outside option cannot be credibly communicated, and the seller's offer is recallable by the buyer for one period. There are essentially two equilibrium regimes. For sufficiently high search cost, the game ends immediately; otherwise the search occurs in equilibrium. Compared to the case where the buyer can communicate his outside option, the seller is worse off, and the game results in search for a smaller set of values of the search cost, i.e., less equilibrium delay.C72.     

Mechanism design with a liquidity constrained buyer: The 2×2 case

This paper studies the implications of buyers' liquidity constraints for the optimal selling strategy. The possibility that a buyer faces a binding liquidity constraint affects the seller's strategy in a nontrivial way. Specifically, when a seller has one unit of a good to sell to a buyer with a quasilinear utility function, the `no-haggling' result indicates that textbook monopoly pricing is optimal, absent liquidity constraints. Introducing a potentially binding liquidity constraint vitiates the no-haggling result, and can make it strictly beneficial for the seller to use nonlinear pricing, to commit to a declining price sequence, or to require the buyer to post a cash bond.     

Optimal Information Disclosure in Auctions and the Handicap Auction

We analyse a situation where a monopolist is selling an indivisible good to risk-neutral buyers who only have an estimate of their private valuations. The seller can release, without observing, certain additional signals that affect the buyers' valuations. Our main result is that in the expected revenue-maximizing mechanism, the seller makes available all the information that she can, and her expected revenue is the same as it would be if she could observe the part of the information that is "new" to the buyers. We also show that this mechanism can be implemented by what we call a handicap auction in interesting applications. In the first round of this auction, each buyer picks a price premium from a menu offered by the seller (a smaller premium costs more). Then the seller releases the additional signals. In the second round, the buyers bid in a second-price auction where the winner pays the sum of his premium and the second highest non-negative bid. In the case of a single buyer, this mechanism simplifies to a menu of European call options.     

Pairwise trade and coexistence of money and higher-return assets

A new theory of coexistence of money and higher-return assets is set out. It applies to any setting in which some trade involves an exchange of goods for assets and occurs between two people—a buyer and a seller. We show that there exists a function mapping the portfolios of the buyer and the seller to the trade that occurs such that (i) the trade is in the buyer-seller core and (ii) some people are induced to enter the buyer-seller meeting with money.     

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.     

Paying not to sell

In this paper we show that, in the presence of buyer and seller power, a monopolist can enter into a costly contractual relationship with a low-quality supplier with the sole intention of improving its bargaining position relative to a high-quality supplier, without ever selling the good produced by that firm.     

Simultaneous Price And Quantity Determination In A Joint Profit Maximizing Bilateral Monopoly Under Dynamic Optimization

A long standing controversial issue in the literature surrounding the bilateral monopoly is the determinacy of equilibrium price and quantity when the seller and buyer maximize their joint profits. This controversy led to incorrect presentation of bilateral monopoly solutions in the literature. In this study, we employ a dynamic optimization model to simultaneously determine the equilibrium price and quantity transacted between the buyer and seller. We also show that for the bilateral monopoly to achieve equilibrium they must transact the intermediate product at the hint profit maximizing level. Any deviation from this level will result in one party exercising greater control than the other, and thus, will lead to a situation of either pure monopsony or monopoly, or nonexistence of both parties. [D43, C78,C61]     

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.     

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length δ, and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as δ approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.     

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.     

Strategic delay and endogenous offers in bargaining games with private information

This paperendogenously determines the order of offers and the duration of delay in reaching agreement between buyers and sellers in a continuous-time bargaining game in which a seller wishes to vend an object of known cost to a buyer, to whom the value of the good is private information, and in which each player can choose to strategically delay a response to a previous offer or to interrupt the delay of his rival. Both buyers and sellers are shown to prefer to move first in a model of bargaining in which: (1) either player can make the first offer; (2) after the minimum time has elapsed from the previous offer, either player can make an offer; and (3) players can choose to strategically delay and refrain from making an offer after the previous offer. When the buyer moves first, the equilibrium response for the seller is to accept the offer immediately. When the seller moves first the equilibrium is characterized by the seller making all but the last offer, with minimal feasible delay between successive offers. Observable endogenous delay in reaching an agreement in such equilibria approaches zero as the minimal feasible delay between offers approaches zero. This indicates that in noncooperative bargaining models with private information, where players can strategically delay their offers, endogenizing the order in which players make offers removes the ability of informational asymmetries to generate equilibria exhibiting endogenous delay in reaching an agreement.     

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.     

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.     

Monopolistic screening and uninformed buyers

In the standard monopolistic screening problem, buyers obtain information rent as a result of possessing private information; if a contract can be offered before the buyer knows his valuation, the seller can extract the full (expected) surplus. I consider a situation where the buyer may or may not have private information about his valuation at the time the contract is offered. Is the seller (strictly) better off as compared to the standard situation? The answer depends crucially on the specific model. In the 2-types model, unless the probability (that the buyer is uninformed) reaches a critical threshold, the seller is unable to benefit from the buyer's ignorance. In the continuum-types model, on the other hand, optimal expected profit is strictly higher than in the standard model whenever this probability is positive.     

Selling an asset to a competitor

A seller decides whether to allocate an item among two potential buyers. The seller and buyer 1 interact ex post in such a way that each of them suffers a negative externality if the other possesses the item. We show that the optimal allocation rule favors buyer 2, who does not interact ex post with the seller, and in particular bidder 1 may not obtain the good even if his valuation is highest. The auction is therefore subject to resale. When resale is possible, the seller must distort the original auction. We show that the mechanism depends crucially on the way resale is organized ex post. The seller may decide to always allocate the good to the agent with the highest valuation when rents are fully extracted by an intermediary on the resale market. However, she may resort to a stochastic mechanism when the winner of the primary auction has full bargaining power in the resale stage.     

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).