Sequential auctions with randomly arriving buyers

We analyze a dynamic market in which buyers compete in a sequence of private-value auctions for differentiated goods. New buyers and new objects may arrive at random times. Since objects are imperfect substitutes, buyers? values are not persistent. Instead, each buyer?s private value for a new object is a new independent draw from the same distribution.We consider the use of second-price auctions for selling these objects, and show that there exists a unique symmetric Markov equilibrium in this market. In equilibrium, buyers shade their bids down by their continuation value, which is the (endogenous) option value of participating in future auctions. We characterize this option value and show that it depends not only on the number of buyers currently present on the market and the distribution of their values, but also on anticipated market dynamics.     

An optimal auction with correlated values and risk aversion

We consider an auction setting where the buyers are risk averse with correlated private valuations (CARA preferences, binary types), and characterize the optimal mechanism for a risk-neutral seller. We show that the optimal auction extracts all buyer surplus whenever the correlation is sufficiently strong (greater than 1/3 in absolute value), no matter how risk averse the buyers are. In contrast, we note that a sufficiently risk-averse seller would not use a full rent extracting mechanism for any positive correlation of the valuations even if the buyers were risk neutral.     

How private is private information? The ability to spot deception in an economic game

We provide experimental evidence on the ability to detect deceit in a buyer–seller game with asymmetric information. Sellers have private information about the value of a good and sometimes have incentives to mislead buyers. We examine if buyers can spot deception in face-to-face encounters. We vary whether buyers can interrogate the seller and the contextual richness. The buyers’ prediction accuracy is above chance, and is substantial for confident buyers. There is no evidence that the option to interrogate is important and only weak support that contextual richness matters. These results show that the information asymmetry is partly eliminated by people’s ability to spot deception.     

Agreement theorem for neo-additive beliefs

In this paper, we extend Aumann’s (Ann Stat 4:1236–1239, 1976) probabilistic agreement theorem to situations in which agents’ prior beliefs are represented by a common neo-additive capacity. In particular, we characterize the family of updating rules for neo-additive capacities, which are necessary and sufficient for the impossibility of “agreeing to disagree” on the values of posterior capacities as well as on the values of posterior Choquet expectations for binary acts. Furthermore, we show that generalizations of this result to more general acts are impossible.     

Bilateral monopoly on a market for an intermediate good

In this paper we analyze a procedure through which price and quantity could be determined on a bilateral monopoly market for an intermediate good. The proposed solution concept is of a non-cooperative Nash equilibrium type. A dynamic process in which the bilateral monopolists repeatedly announce prices and quantities is studied. It is shown that, under particular assumptions, this process must converge to the proposed equilibrium solution. Finally, our solution concept leads to the competitive equilibrium if both sides of the market are ‘fractionated’ into a large number of ‘small’ buyers and ‘small’ sellers.     

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.     

Monopoly and demand uncertainty

We develop a formal framework to analyse a monopoly’s problem when demand is determined by a Poisson-distribution and the valuations of the buyers are draws from a common distribution. The buyers have unit demand, and the good in question is discrete. The monopoly has to make its quantity and pricing decisions before demand is realised. We determine sufficient conditions for the monopoly’s pricing decision to be unique, and we demonstrate the difference to the planner’s problem by numerical examples. We also study an economy with a fixed number of buyers assuming that the valuations are draws from the uniform distribution. When the economy grows in the limit one recovers the standard case of a monopoly with linear demand and constant marginal costs.     

Optimality versus practicality in market design: A comparison of two double auctions

We consider a market for indivisible items with m buyers and m sellers. Traders privately know their values/costs, which are statistically dependent. Two mechanisms are considered. The buyer's bid double auction collects bids and asks from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders' beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

Investors’ heterogeneity and tranching

The article presents a theoretic model of tranching in asset securitization. When potential buyers are heterogeneous in the constraint on their portfolios, we find that senior tranche, which is less risky and created by tranching, will introduce more investors and thus reduce risk exposure to investors. Thus, tranching helps improve the sale’s revenue. We also find that the portfolio constraints of investors are always binding at optimum, which is called marginal rating.     

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.     

Overconfidence in the Markets for Lemons

We extend Akerlof's “Market for Lemons” (1970, Quarterly Journal of Economics 84, 488–500) by assuming that some buyers are overconfident. Buyers in our model receive a noisy signal about the quality of the good that is on display for sale. Overconfident buyers do not update according to Bayes' rule but take the noisy signal at face value. We show that the presence of overconfident buyers can stabilize the market outcome by preventing total adverse selection. However, this stabilization comes at a cost: rational buyers are crowded out of the market.     

Are auction revenues affected by rising art buyers’ premia? The case of early American art

The steady rise in the premiums charged to art buyers at auction (above hammer price) has been underway since 1992. This article, using a stable and bounded sample of repeat purchase of American works created before 1950, reveals that this tact has reduced hammer prices for that art. However, renewed and hyper-competitive efforts to bring more and higher quality art to market by the two main houses, Sotheby’s and Christie’s, have resulted in general profitability. Nevertheless, we calculate that a rise in buyers’ premia at Sotheby’s, a publically traded company, has reduced revenues and profits below their potential in the absence of such increases.     

Disapproval aversion or inflated inequity acceptance? The impact of expressing emotions in ultimatum bargaining

Past experimental research has shown that when rating systems are available, buyers are more generous in accepting unfair offers in ultimatum bargaining. However, it also suggests that, under these conditions, sellers behave more fairly to avoid receiving negative feedback. This paper experimentally investigates which effect is stronger with the use of a rating system: buyers’ inflated inequity acceptance or sellers’ disapproval aversion. We explore this question by varying the information condition on the buyers’ side. Our experiment shows that in a setup where the size of the pie is common knowledge for both buyers and sellers, when a rating system is present, the sellers exhibit disapproval aversion but the buyers do not display greater acceptance of inequity. By contrast, when only sellers are aware of the size of the pie, sellers behave aggressively to exploit buyers and their behavior does not change in the presence of a rating system; however, buyers display greater acceptance of inequity when a rating system is present. We discuss how these results can be explained by a theoretical model that includes sellers’ social disapproval aversion and buyers’ disappointment aversion in addition to the players’ inequality aversion.     

Social norms, information, and trust among strangers: theory and evidence

Can a social norm of trust and reciprocity emerge among strangers? We investigate this question by examining behavior in an experiment where subjects repeatedly play a two-player binary “trust” game. Players are randomly and anonymously paired with one another in each period. The main questions addressed are whether a social norm of trust and reciprocity emerges under the most extreme information restriction (anonymous community-wide enforcement) or whether trust and reciprocity require additional, individual-specific information about a player’s past history of play and whether that information must be provided freely or at some cost. In the absence of such reputational information, we find that a social norm of trust and reciprocity is difficult to sustain. The provision of reputational information on past individual decisions significantly increases trust and reciprocity, with longer histories yielding the best outcomes. Importantly, we find that making reputational information available at a small cost may also lead to a significant improvement in trust and reciprocity, despite the fact that most subjects do not choose to purchase this information.     

The effect of heterogeneous beliefs on mergers and acquisitions

This article investigates the effect of heterogeneous beliefs on firms’ mergers and acquisitions (M&A) decisions. Using data of China’s financial market, which is featured with great heterogeneity of belief, we find that heterogeneous beliefs are positively associated with the occurrence of M&A transactions, and firms with greater heterogeneous beliefs are more likely to pay the transactions with stock. Moreover, we show that government intervention, measured by state ownership, weakens the effect of heterogeneous beliefs on firms’ M&A decisions.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

The asymptotic shapley value for a simple market game

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

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.     

Evolutionary stability of bargaining and price posting: implications for formal and informal activities

In this paper we study the co-existence of two well known trading protocols, bargaining and price-posting. To do so we consider a frictional environment where buyers and sellers play price-posting and bargaining games infinitely many times. Sellers switch from one market to the other at a rate that is proportional to their payoff differentials. Given the different informational requirements associated with these two trading mechanisms, we examine their possible co-existence in the context of informal and formal markets. Other than having different trading protocols, we also consider other distinguishing features. We find a unique stable equilibrium where price-posting (formal markets) and bargaining (informal markets) co-exist. In a richer environment where both sellers and buyers can move across markets, we show that there exists a unique stable dynamic equilibrium where formal and informal activities also co-exist whenever sellers’ and buyers’ net costs of trading in the formal market have opposite signs.