Australian National University

Synergies and Price Trends in Sequential Auctions

Email address: flavio.menezes@anu.edu.au

Abstract:
Weber (1983) considers a sequential auction of identical objects and shows that expected prices follow a martingale i.e., bidders expect prices will remain constant on average throughout the sequence of auctions within a sale. In Weber's model, bidders only purchase one of a fixed number of objects. That is, the marginal value for a bidder of a second object is zero. The essence of Weber's result is that there are two opposite and exactly offsetting effects on price as the auction proceeds; a reduction in competition with fewer buyers puts downward pressure on price, while increased competition with fewer objects put upward pressure on price. There is, however, empirical evidence that prices are not constant throughout sequential auction sales. Ashenfelter (1989) reports that identical cases of wine fetch different prices at sequential auctions in three auction houses from 1985 to 1987. Although the most common pattern was for prices to remain constant, prices were at least twice as likely to decline as to increase. Ashenfelter refers to this phenomenon as the\ ``price decline anomaly.'' McAfee and Vincent (1993) adopted a similar approach to Ashenfelter and examined data from Christie's wine auctions at Chicago in 1987. In addition to pairwise comparisons, they examined triples of identical wine sold in the same auction sale. Their results are very similar to those of Ashenfelter. Similar empirical findings were identified in a number of other markets; cable television licenses (Gandal (1995); condominiums (Ashenfelter and Genesove (1992), and Vanderporten (1992-a,b); dairy cattle (Engelbrecht-Wiggans and Kahn (1992)); stamps (Taylor (1991) and Thiel and Petry (1990)) and wool (Jones, Menezes and Vella (1998)). Gandal provides evidence that prices increased in the sale of cable-TV licences in Israel. Gandal attributes the price increases to the interdependencies among licenses, which may increase competition in the later rounds of the sale. Jones, Menezes and Vella indicate that prices may increase or decrease in sequential auctions of wool (adjusting prices to estimate wool of homogeneous quality). Most theoretical explanations for price variation in sequential auctions have concentrated on explaining the price decline anomaly. In a two-object model, Black and de Meza (1992) explain the price decline anomaly by the existence of an option that gives the winner of the first auction the rights to purchase the second object at the same price. In particular, for the case where the value of a second object for a player is equal to a fraction of the value of a first object, they show the existence of an equilibrium in which expected prices increase in the absence of an option to buy and may decrease when the option is present. We will characterize price trends in a more general setting and determine the effect of the option on the seller's revenue. McAfee and Vincent explain the anomaly by considering the effects of risk aversion on bidding strategies. For identical objects they show how bids in the first round are equal to the expected prices in the second round plus a risk premium associated with the risky future price. They assume buyers have nondecreasing risk aversion and can only buy one object. Von der Fehr (1994) uses participation costs to obtain different net valuations for identical objects. When bidders face a cost of participating in each auction of two identical objects sold sequentially, price is lower in the second auction than it is in the first. This follows because the number of buyers who stay for the second auction falls by more than the successful bidder in the first auction. Once again, buyers only buy one object. Engelbrecht-Wiggans (1994) and Bernhardt and Scoones (1994) show how expected prices decline when the objects are statistically identical (i.e., where bidders' valuations for the objects are independent draws from a fixed distribution) and the distribution of values is bounded. Menezes and Monteiro (1997) replicate these results for the case when buyers are allowed to buy more than one object but participation is endogenous as bidders face participation costs. Finally, there are also explanations for the price decline in the context of sequential common value auctions. For example, Gale and Hausch (1994) examine a two-object two-bidder first-price sequential auction, where each bidder wants only one object. They show that a bidder may submit a low bid for the first object even if it is not her preferred item. She might do that in order to hedge against the possibility that she might lose the second auction in case she skips the first auction and her opponent also prefers the second object. This "bottom-fishing" behavior may imply decreasing expected prices because although it has a nonnegative effect on the first auction's revenue, it has a negative effect on the second auction's revenue. Frutos and Rosenthal (1998) provide an example for a special case where signals can take on only two values. There are two bidders who know the value of the objects and two who do not. Each bidder wants one object. In this setting they show that expected prices are decreasing in sequential second-price auctions of identical common-valued objects. The reason is that there is information being revealed in the first auction and that might imply a reduction in competition in the second auction; there will be only one informed and two uninformed bidders in the last auction. In contrast, we examine sequential auctions of identical objects where individuals demand more than one object. An individual's value for a bundle of objects is either greater than the sum of the values attributed to the separate objects (positive synergy) or less than the sum (negative synergy) --- Black and de Meza consider a special case of negative synergies. Thus, in this paper we explore the type of interdependencies described, for example, by Gandal (1997) in reference to the cable-TV auctions in Israel. Rosenthal and Krishna (1996) also consider the effects of synergies on bidding behavior. However, they concentrate on simultaneous auctions and consider only a very special type of positive synergy; where a bidder's value for two objects is simply equal to twice his value for an individual object plus a positive constant. (For example, for a player with a value close to zero, the marginal synergy is infinite). In contrast, we consider synergies of a general form, allowing for positive and negative synergies. We show that the existence of positive synergies implies declining expected prices. When two objects are worth more as a bundle than as separate objects, whoever buys the first object has the opportunity to realize the synergy. Therefore, the price in the first period includes a premium to reflect such opportunity. For the case of negative synergies, expected prices increase. There are several corollaries. First, the seller is indifferent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the simultaneous auction may yield higher or smaller expected revenue than the sequential auction. Third, when the synergy is positive an option to buy the additional object at the price of the first object is never exercised in the symmetric equilibrium. In contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net effect on the seller's revenue of the introduction of an option is ambiguous. This conforms to the results of Black and de Meza for the case of constant negative average synergies. Finally, we provide an example where one player has positive synergies and the other has negative synergies. In this case it is still possible for expected prices to decline.

PDF file of paper: menezes.pdf

Session: Industrial Organization Theory I

Time: Saturday, 7 July, 8am - 9:30am

Room: D