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.     

Auction design by an informed seller: A foundation of reserve price signalling

This paper studies mechanism design by a seller privately informed of the (continuous) quality of an indivisible object. An important solution to this informed-principal problem, the Rothschild–Stiglitz–Wilson mechanisms, which correspond to the least-cost separating allocations in the signalling literature, is characterized. The characterization reveals that reserve prices are the least costly device to separate sellers of different qualities: In the RSW mechanisms, the lowest-quality seller adopts her public-information optimal selling procedure, and each higher-quality seller adopts a selling procedure that differs from her public-information optimal one only in that the reserve prices are higher. This finding provides a mechanism-design foundation for reserve-price signalling studied in the literature.     

Optimal mechanism design with resale via bargaining

In this paper, we examine the optimal mechanism design of selling an indivisible object to one regular buyer and one publicly known buyer, where inter-buyer resale cannot be prohibited. The resale market is modeled as a stochastic ultimatum bargaining game between the two buyers. We fully characterize an optimal mechanism under general conditions. Surprisingly, in this optimal mechanism, the seller never allocates the object to the regular buyer regardless of his bargaining power in the resale market. The seller sells only to the publicly known buyer, and reveals no additional information to the resale market. The possibility of resale causes the seller to sometimes hold back the object, which under our setup is never optimal if resale is prohibited. We find that the seller?s revenue is increasing in the publicly known buyer?s bargaining power in the resale market. When the publicly known buyer has full bargaining power, Myerson?s optimal revenue is achieved; when the publicly known buyer has no bargaining power, a conditionally efficient mechanism prevails.     

Creating competition out of thin air: An experimental study of right-to-choose auctions

This paper presents an experimental study of a mechanism that is commonly used to sell multiple heterogeneous goods. The novel feature of this procedure is that instead of selling each good in a separate auction, the seller executes a single auction in which buyers, who may be interested in completely different goods, compete for the right to choose a good. We provide experimental evidence that a Right-to-Choose (RTC) auction can generate more revenue than the theoretically optimal auction. Moreover, in contrast to the “optimal” auction, the RTC auction is approximately efficient in the sense that the surplus it generates is close to the maximal one. Furthermore, a seller who would like to retain some of his goods can generate more revenue with a restricted RTC auction in which not all rights-to-choose are sold, than with the theoretically optimal auction.     

On the Evaluation of Options on Lotteries: An Experimental Study

We present the results of a comparative experimental study of the evaluation of simple lotteries and call/put/insurance options on these lotteries. The main findings and conclusions are:

(a) The observed bidding patterns depend on the type of asset under evaluation. In particular, subject behavior when buying or selling a basic lottery seems much more cautious than their behavior when buying or selling options on that lottery.

(b) The observed bidding patterns also depend on subject positions with respect to the underlying asset. In particular, the bids for buying lotteries and options long are statistically uncorrelated with the bids for selling the same lotteries and options short.

(c) Subjects with extreme risk attitudes are more inclined to violate basic no-arbitrage conditions (like the call-put parity) when bidding for the different lotteries.

We demonstrate that it is difficult to reconcile the experimental evidence with mainstream theories on individual decision and choice (although we find strong support for prospect theory in some parts of the data). We conclude that the evaluation of options on lotteries is context-dependent and subtler than perceived by existing theories.     

Optimal sale across venues and auctions with a buy-now option

We characterize the optimal selling mechanism for a seller who faces demand demarcated by a high and a low end and who can access an (online) auction site (by paying an access cost) in addition to using his own store that can be used as a posted price selling venue. We first solve for the optimal mechanism of a direct revelation game in which there is no venue-restriction constraint. We find that the direct optimal mechanism must necessarily incorporate a certain kind of pooling. We then show that even with the venue constraint, the seller can use a two stage indirect mechanism that implements the allocation rule from the optimal direct mechanism, and uses the venues in an optimal fashion. The first stage of the indirect mechanism is a posted price at the store. If the object is not sold, we move to stage two, which involves an auction at the auction site. A feature of this auction is a buy-now option which is essential for implementing the pooling feature of the optimal direct mechanism. We also show that the buy-now option in the optimal mechanism is of a “temporary” variety, and that a “permanent” buy-now option, in contrast, cannot implement the optimal mechanism. Auctions with a temporary buy-now option are in widespread use on eBay. We thank the Associate Editor, George Deltas, for his insightful comments. We also thank seminar participants at the University of Basel and the SAET conference 2007.     

Auction design with endogenously correlated buyer types

This paper studies optimal auction design when the seller can affect the buyers? valuations through an unobservable ex ante investment. The key insight is that the optimal mechanism may have the seller play a mixed investment strategy so as to create correlation between the buyers? otherwise (conditionally) independent valuations. Assuming that the seller announces the mechanism before investing, the paper establishes conditions on the investment technology so that a mechanism exists which leaves buyers no information rent and leaves the seller indifferent between his investments. Under these conditions, the seller can, in fact, extract the first best surplus almost fully.     

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.     

消费者谈判能力与厂商标价策略-模型及基于实验经济学的检验

本文建立的理论模型研究了消费者谈判能力、谈判成本和对商品的偏好程度等几方面对厂商最优标价决策的影响。当消费者谈判能力较弱时,厂商可能策略性地不对商品标价,以获取更大利润,利润大小与消费者的谈判能力呈倒U形关系;而当消费者谈判能力较强时,厂商会选择对商品进行标价以最大化利润;但若消费者谈判能力很弱,消费者很可能因无利可图而放弃购买,这时厂商就会选择标价销售。通过对模型进行模拟实验,模型的结果得到了进一步验证。本文同时证明,在一定条件下,厂商选择策略性不标价可能不是社会最优的,因此需要通过政府强制标价来实现市场有效性。     

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.     

Learning about the arrival of sales

We analyse optimal stopping when the economic environment changes because of learning. A primary application is optimal selling of an asset when demand is uncertain. The seller learns about the arrival rate of buyers. As time passes without a sale, the seller becomes more pessimistic about the arrival rate. When the arrival of buyers is not observed, the rate at which the seller revises her beliefs is affected by the price she sets. Learning leads to a higher posted price by the seller. When the seller does observe the arrival of buyers, she sets an even higher price.     

Information structures in optimal auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. We show that an optimal information structure exists.     

Experiments on lotteries for shrouded and bundled goods: Investigating the economics of fukubukuro

Fukubukuro (or lucky bag) is a familiar institution in Japan and elsewhere in which the exact contents of a New Year sales item are hidden from the consumer before purchase. Motivated by the fukubukuro example and the lack of evidence on risk attitudes in lotteries involving goods, we conduct a laboratory experiment in which the outcomes are bundled or unbundled goods. The implied gains to a monopoly seller for marketing goods in lottery form rather than separately are only clearly positive for lotteries where there is a higher probability of obtaining the more highly valued good.     

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.     

Asking questions

We examine a model of limited communication in which the seller is selling a single good to two potential buyers. In each of the finite number of periods the seller asks one of the two buyers a binary question. After the final answer, the allocation and the transfers are executed. The model sheds light on the communication protocols that arise in welfare maximizing mechanisms.     

Intertemporal self-selection with multiple buyers

Summary We consider a monopolist selling durable goods to consumers with unit demands but different preferences for quality. The seller can offer items of different quality at the same time to induce buyers to self-select, as in Mussa-Rosen (1978), but is not artificially constrained to offer only one such menu. Instead the seller can offer without precommitment asequence of menus over time. In the two-buyer case where the seller has complete information about each buyer's marginal valuation for quality, the seller's profits exceed what can be obtained from a single menu and sometimes approximate the profits of a perfectly discriminating monopolist. In companion papers (Bagnoli et al., 1990, 1992), we show that these conclusions continue to hold (1) in the infinite-horizon case with any finite number of buyers and (2) in two-period examples where the seller has incomplete information about buyer preferences.     

RETESTING THE UNCERTAINTY EFFECT USING LOTTERIES WITH REAL PRODUCTS AND MONEY

In the current study, several experiments re‐examine the uncertainty effect using lotteries that include real products, monetary outcomes and electronic gift cards in a between‐subjects design. The study also takes the selling position into consideration, in addition to the buying position considered by all previous works on the uncertainty effect. The results indicate that for all types of lotteries, the bids are higher than the bids for the worst possible realization. These findings are consistent with the internality axiom and do not support the uncertainty effect.     

Reputation and Survival: Learning in a Dynamic Signalling Model

We consider the impact of reputation on the survival of a monopolist selling single units in discrete time periods, whose quality is learned slowly. If the seller learns her own quality at the same rate as customers, a sufficiently bad run of luck could induce her to stop selling. When she knows her quality, a good seller never stops selling though at low reputations a bad seller does with some probability. Furthermore, a seller with positive, though imperfect, information sells for the same number of periods whether her information is private or public. We further consider the robustness of the central result when the seller's opportunities for strategic behaviour are limited.     

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.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000