The sale of small firms: a multidimensional analysis

Summary. This paper endogeneizes the security voting structure in an auction mechanism used to sell a small firm. The design of security voting structure allows the seller to choose between two objectives which are not mutually consistent. If the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. At the opposite, if he wants to sell his firm to the most efficient candidate, he should sell all the shares. Received: July 4, 2001; revised version: October 31, 2002 RID="*" ID="*" The paper has benefited from a number of comments from the anonymous referees. Correspondence to: C. At     

Strategic behavior in dynamic auctions

Summary In this paper, we study a two-period common-value auction model in which the seller possesses some private information about the value of the object being sold. Assuming that buyers possess no private information in the first period, we characterize a set of equilibria in which the strategy of the seller is equivalent to a decision of whether to sell the object in the first or the second period with no reserve price. The seller sells in the second period if and only if the information is favorable enough. We also show that revealing private information increases the seller's profit in some equilibria, but not in others. One implication is that the seller's ability to sell on more occasions reduces his expected revenue under certain conditions.This is a revised version of Chapter 4 of my Ph.D. dissertation. I am very grateful to my advisor, Robert Rosenthal, for his extremely valuable advice. I would like to thank him, Dan Bernhardt, Jacob Glazer, Ronald Harstad, Albert Ma, Michael Manove, Michael Peters, Philip Reny, Doug Tattrie, Andrew Weiss, and especially the anonymous referee for their very helpful comments, Marilyn Banting for her editorial assistance, and the National Science Foundation for financial support under Grant #SES-8808362.     

A monopolistic market for information

We analyze a model where traders buy information from a monopolistic seller, which is subsequently used in a speculative market. In order to overcome the dilution in the value of information due to its leakage through informative prices, the seller of information may prefer to sell noisier versions of the information he actually has. Moreover, to obtain higher profits, it is desirable for the seller to sell different signals to different traders, so that the added noise realizations do not affect equilibrium prices. One way of doing so, which does not require discrimination, is to sell identically distributed personalized signals to each of a large number of traders.     

Bundle and separate sales in auctions with entry

A seller sells dissimilar objects while taking the auction rule as given. Should the seller sell the objects separately or as a bundle? Generally, when the number of bidders is small bundling helps to stimulate the competition and raise revenue. In this paper, we show that if entry is costly enough the process of endogenous participation generates sufficient competition to make bundling unnecessary in auctions. Thus whether a bundle auction generates a higher or a lower revenue ultimately depends first on the level of the entry costs and then, possibly, on the number of potential bidders.     

Strategic vote manipulation in a simple democracy

In both the Employee Stock Ownership Plan (ESOP) and employee buyouts, the common and crucial phenomenon is that some workers have two sources of income, namely wages and shares of profit. We analyze that phenomenon in an economy where workers are nonunionized and wages are determined by voting. If the employers sell a certain amount of shares of the capital stock to some non-risk-loving workers, these workers vote for the lowest possible wage along with the employers. As a result, all workers become equally worse off because of the competition among workers to buy those shares.     

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.     

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.     

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.     

Bargaining with a possibly committed seller

We consider negotiations with an open time horizon where a buyer has private information about his valuation and does not know whether the seller is committed to the advertised price. This setting combines two common specifications made in the non-cooperative bargaining literature: one side is privately informed about its valuation, which is drawn from a continuum, and the other side is possibly committed to a fixed offer. We analyze the game both in discrete and in continuous time and show convergence of the two settings, which extends results from Abreu and Gul [2000. Bargaining and reputation. Econometrica 68, 85–117]. One interesting result is that as time proceeds, the non-committed seller becomes less likely to concede in a given period, i.e., it appears as if he becomes more “stubborn.” We further show that a seller may prefer to negotiate with a “worse” buyer as this enhances the value of his possible commitment.     

Sequentially Optimal Auctions

In auctions where a seller can post a reserve price but if the object fails to sell cannot commit never to attempt to resell it, revenue equivalence between repeated first price and second price auctions without commitment results. When the time between auctions goes to zero, seller expected revenues converge to those of a static auction with no reserve price. With many bidders, the seller equilibrium reserve price approaches the reserve price in an optimal static auction. An auction in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers is computed.Journal of Economic LiteratureClassification Numbers: C78, D44, D82.     

Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.     

Exclusive Versus Non-exclusive Dealing in Auctions with Resale

We consider a seller who can either sell exclusively through resellers, or allow potential consumers to purchase directly from him. The consumers’ willingness to pay is private information. All transactions are in the form of second-price sealed bid auctions. We show that, if the resellers can gain access to a substantially bigger portion of the market than the seller himself, the seller obtains a higher revenue by dealing exclusively through them, i.e., by committing to not sell to any consumer. The result is due to a “winner’s curse” effect: the resellers win only if the consumers that they compete against submit lower bids, i.e., if part of their customer base has low valuations. This depresses the resellers’ willingness to pay relative to what they would be willing to pay under an exclusive resale contract. Our results do not depend on the presence of transaction costs: exclusive dealing yields strictly higher revenue even when the resellers can market the item at zero cost. We would like to thank Richard Engelbrecht-Wiggans, Michael Rothkopf and seminar participants at Iowa State University, the Midwest Mathematical Economics meetings, the Milken Institute, Rutgers University, SUNY at Stony Brook Summer Workshop on Game Theory, for helpful comments and suggestions.     

Manipulation and the Allocational Role of Prices

It is commonly believed that prices in secondary financial markets play an important allocational role because they contain information that facilitates the efficient allocation of resources. This paper identifies a limitation inherent in this role of prices. It shows that the presence of a feedback effect from the financial market to the real value of a firm creates an incentive for an uninformed trader to sell the firm's stock. When this happens the informativeness of the stock price decreases, and the beneficial allocational role of the financial market weakens. The trader profits from this trading strategy, partly because his trading distorts the firm's investment. We therefore refer to this strategy as manipulation . We show that trading without information is profitable only with sell orders, driving a wedge between the allocational implications of buyer and seller initiated speculation, and providing justification for restrictions on short sales.     

Endogenous Firm Objectives

We analyze the behavior of a monopolistic firm in general equilibrium when the firm's decisions are taken through shareholder voting. We show that, depending on the underlying distribution, rational voting may imply overproduction as well as underproduction, relative to the efficient level. Any initial distribution of shares is an equilibrium, if individuals do not recognize their influence on voting when trading shares. However, when they do, and there are no short–selling constraints, the only equilibrium is the efficient one. With short–selling constraints typically underproduction occurs. It is not market power itself causing underproduction, but the inability to perfectly trade the rights to market power.     

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.     

How do selling mechanisms affect profits,surplus, capacity and prices with unknown demand?

I analyze a model in which a seller wishes to sell multiple homogeneous goods to a large group of buyers with unknown demand. The seller may either sell objects via a posted‐price mechanism, a discriminatory‐price auction, a uniform‐price auction, their open‐bid analogs, or a revelation mechanism in which the seller first asks all potential buyers to report their valuations and then sets a reserve price. I show that the revelation mechanism leads to the greatest profits, the auction mechanisms result in identical expected profits and the posted‐price mechanism results in the smallest profits. However, the more profitable mechanisms impose stronger informational requirements that may make these mechanisms infeasible in practice, and the posted‐price mechanism also results in the greatest total surplus. I also find the seller chooses a lower capacity and reserve price in an auction than in the posted‐price mechanism.     

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.     

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.     

高新技术产品出口管制对一国产品创新的影响

基于Grossman和Helpman的水平创新理论,构建了一国的高新技术产品出口管制影响其产品创新的模型。结果表明:在企业不改变产品价格的情况下,适度的出口管制有利于本国的产品创新,但过于严格的出口管制会妨碍本国的产品创新;在消费者支出不变的情况下,如果企业提升产品价格,则出口管制会加快创新速度。