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.     

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.     

技术冲击和劳动供给对经济波动的影响分析--基于可分劳动RBC模型的实证检验

文章根据国内外经济波动的不同特征,构建了用于研究中国经济波动的可分劳动RBC模型,并对改革开放以来的中国经济进行了实证检验,从供给角度考察技术冲击对中国经济波动的影响,并在RBC模型框架下分析了技术进步对中国劳动市场的影响。研究发现,一是在固定劳动和可分劳动RBC模型中,技术冲击可以解释中国经济波动的主要部分;二是可分劳动RBC模型的实证结果表明,劳动供给变动对经济波动的影响较小,技术进步对改革后的产出、居民消费和就业都产生了正向冲击效应。技术进步对就业增长效应较小,致使我国的劳动需求增长率明显小于劳动供给增长率,劳动市场供需严重不平衡,这也是导致就业波动较为平缓、失业问题日趋严峻的一个重要原因。     

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.     

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     

SELLING A LEMON UNDER DEMAND UNCERTAINTY

We consider a seller who has private information about the quality of her good but is uncertain about buyer arrivals. Assuming that the high‐quality seller insists on a price, we show that the low‐quality seller's surplus and pricing strategy crucially depend on buyers' knowledge about the demand state. If they are also uncertain about demand, then demand uncertainty increases the low‐quality seller's expected payoff, and her optimal strategy is to lower the price after some time. If buyers know the demand state, then demand uncertainty does not affect the low‐quality seller's payoff, but she must employ a sophisticated pricing strategy.     

Strategy-proof and nonbossy allocation of indivisible goods and money

Summary. Which strategy-proof nonbossy mechanisms exist in a model with a finite number of indivisible goods (houses, jobs, positions) and a perfectly divisible good (money)? The main finding is that only a finite number of distributions of the divisible good is consistent with strategy-proofness and nonbossiness. Under various additional assumptions - neutrality, individual rationality, object efficiency, weak decentralization - the distribution of the divisible good is further restricted. For instance, under neutrality the outcome of the mechanism can have only one distribution, which is hence independent of individual preferences. In this case the mechanism becomes serially dictatorial. On the other hand, individual rationality leads to a fixed price equilibrium with a well-defined rationing method (Gale's top-trading cycle procedure). Received: October 3, 2000; revised version: August 10, 2001     

Direct sale of information when precision is unobservable

Abstract.  This paper studies the incentives of an information seller to provide precise information when precision is not observable and investors with rational expectations can extract information from the equilibrium asset price. I show that the seller can verify her precision by employing a non‐linear contract. I derive the equilibrium fee for information as a function of the seller's incentives, the sales volume, and buyers' trading intensity. I also analyse the implications of allowing the seller to trade on her own account for truthfulness and precision choice. JEL Classification: G11, G14, D42     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.     

Haggling over substitutes

Using a model of substitutable goods I determine generic conditions on tastes which guarantee that fixed prices are not optimal: the fully optimal tariff includes lotteries. That is, a profit maximising seller would employ a haggling strategy. We show that the fully optimal selling strategy in a class of cases requires a seller to not allow themselves to focus on one good but to remain haggling over more than one good. This throws new light on the selling strategies used in diverse industries. These insights are used to provide a counter-example to the no lotteries result of McAfee and McMillan (J. Econ. Theory 46 (1988) 335).     

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.     

The multiple unit auction with variable supply

Summary. The theory of multiple unit auctions traditionally assumes that the offered quantity is fixed. I argue that this assumption is not appropriate for many applications because the seller may be able and willing to adjust the supply as a function of the bidding. In this paper I address this shortcoming by analyzing a multi-unit auction game between a monopolistic seller who can produce arbitrary quantities at constant unit cost, and oligopolistic bidders. I establish the existence of a subgame-perfect equilibrium for price discriminating and for uniform price auctions. I also show that bidders have an incentive to misreport their true demand in both auction formats, but they do that in different ways and for different reasons. Furthermore, both auction formats are inefficient, but there is no unambiguous ordering among them. Finally, the more competitive the bidders are, the more likely the seller is to prefer uniform pricing over price discrimination, yet increased competition among bidders may or may not enhance efficiency. Received: June 18, 1998; revised version: January 13, 1999     

Co-learning patterns as emergent market phenomena: An electricity market illustration

The definition of emergence remains problematic, particularly for systems with purposeful human interactions. This study explores the practical import of this concept within a specific market context: namely, a double-auction market for wholesale electric power that operates over a transmission grid with spatially located buyers and sellers. Each profit-seeking seller is a learning agent that attempts to adjust its daily supply offers to its best advantage. The sellers are co-learners in the sense that their supply offer adjustments are in response to past market outcomes that reflect the past supply offer choices of all sellers. Attention is focused on the emergence of co-learning patterns, that is, global market patterns that arise and persist over time as a result of seller co-learning. Examples of co-learning patterns include correlated seller supply offer behaviors and correlated seller net earnings outcomes. Heat maps are used to display and interpret co-learning pattern findings. One key finding is that co-learning strongly matters in this auction market environment. Sellers that behave as Gode-Sunder budget-constrained zero-intelligence agents, randomly selecting their supply offers subject only to a break-even constraint, tend to realize substantially lower net earnings than sellers that tacitly co-learn to correlate their supply offers for market power advantages.     

On the Interplay of Hidden Action and Hidden Information in Simple Bilateral Trading Problems

A buyer and a seller can exchange one unit of an indivisible good. While producing the good, the seller can exert unobservable effort (hidden action). Then the buyer realizes whether his or her valuation is high or low, which stochastically depends upon the seller's effort level (hidden information). The parties are risk neutral—they can rule out renegotiation and write complete contracts. It is shown that the first best cannot be achieved whenever the ex post efficient trade decision is trivial. The second-best contract is characterized and an application of the model to the choice of risky projects is briefly discussed. Journal of Economic Literature Classification Numbers: C72, C78, D23, D82.     

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.     

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.     

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.     

A Characterization for Dominant Strategy Implementation

We introduce a perfect price discriminating mechanism for allocation problems with private information. A perfect price discriminating mechanism treats a seller, for example, as a perfect price discriminating monopolist who faces a price schedule that does not depend on her report. In any perfect price discriminating mechanism, every player has a dominant strategy to truthfully report her private information.We establish a characterization for dominant strategy implementation: Any outcome that can be dominant strategy implemented can also be dominant strategy implemented using a perfect price discriminating mechanism. We apply this characterization to derive the optimal, budget-balanced, dominant strategy mechanisms for public good provision and bilateral bargaining.     

THE OPTIMAL LISTING STRATEGIES IN ONLINE AUCTIONS

This article proposes a unified framework to completely characterize the seller's optimal listing strategy in the online auction as a function of her rate of time impatience. Specifically, the fixed‐price listing, the regular auction, and the buy‐it‐now (BIN) auction are each a solution of the seller's single optimization problem under different values of the rate of intertemporal discount: The perfectly patient seller adopts the regular auction, the sellers with a medium range of time impatience adopt the BIN auction, and the most impatient of sellers adopt the fixed‐price listing. Moreover, under mild conditions, the reverse price is inversely related to the value of the seller's discount factor, either within or across formats. This in turn implies that the posted price in the fixed‐price sale is greater than the reserve price of the BIN auction, followed by that of the regular auction. These predictions offer clear empirical implications.     

Contract enforcement in sellers' markets

I present an infinitely repeated game model where a monopolist seller has a contractual obligation with several buyers in each period. If a contract is violated the buyer can collect some compensation and impose a penalty on the seller. There are an infinite number of subgame perfect equilibria in this model, but I employ the concept of e-validated equilibrium to pick out a unique equilibrium outcome for the game where the seller is able to dominate the buyers. This model is clearly applicable to supply problems of Soviet-type economies, but it can explain certain phenomena of Western economies as well.