An Empirical Comparison of Three Auction Strategies for Multiple Products

ABSTRACTThis study investigates bidders' bidding strategies and the relative profitability of three auction strategies, one auction for the bundle, two simultaneous separate auctions, and two sequential separate auctions under a controlled environment. The results suggest that when there is high variation and no asymmetry among product values, the three selling mechanisms are equally profitable. When there is high asymmetry but no variation among product values, one auction for the bundle is more profitable than two separate auctions when there are two bidders, but less profitable than when there are ten bidders. Generally, selling products simultaneously or sequentially generates the same revenue.JEL Classifications: M31, D01, D03, D44, C91Keywords: multiple-product auction; bundlingI. INTRODUCTIONAuctioneers often have multiple complementary products to auction off. Complementarity is present when bidders' value for the bundle is higher than the sum of individual values for these products. Complementarity may be due to savings in transaction costs when one wins multiple products. For example, a winner of two eBay auctions run by the same auctioneer may save on shipping costs if the shipment can be combined. Complementarity may also be a consequence of extra utility from consuming the products together. A typical example is a set of antique furniture for which people usually are willing to pay more to have the complete set. An additional reason for people to pay more than the sum of the individual values is that it will take tremendous effort (if possible at all) to find all the individual pieces from different sellers.Let us consider an auctioneer selling two different products using second price sealed-bid auctions (also called Vickery auctions)1. An auctioneer, selling one unit each of two products, A and B, typically has three alternative selling strategies: (1) one auction for the bundle consisting of A and B, (2) two simultaneous separate auctions for A and B, and (3) two sequential separate auctions for A and B.For the seller, each of the three strategies has its advantages and disadvantages. When complementary is not present, separate auctions are efficient because winners are always the bidders with the highest values for the individual products. This efficiency minimizes the consumer surplus the winners have and therefore increases the revenues of separate auctions.The following numerical example demonstrates the inefficiency of an auction for the bundle. Let's suppose there are three bidders bidding on the two products, A and B. Table 1(a) shows the values for A, B, and the bundle of A and B together, which is the sum of the values for A and B. In a Vickery auction, it is an incentive-compatible strategy for each bidder to bid her true value. As Table 1(b) shows, when A and B are auctioned off as a bundle, that price will be equal to the second highest value for and the bid for the bundle, which is $140. When A and B are auctioned off separately, the individual prices will be $80 and $80, respectively, and the total revenue will then be $160. Also note that two simultaneous and sequential separate auctions should generate the same revenue, since the outcome of one auction will not affect the bidders' strategies for the other auction.However, when complementarity is present, bidders in separate auctions find themselves facing a so called exposure risk (Ausubel et al., 1997; Rothkopf et al., 1998; Bykowsky et al., 2000; Chakraborty, 2004; Popkowski Leszczyc and Haubl, 2010). This is the risk of winning only one of the products at a price higher than its individual value, or winning both products at a price higher than the value for the bundle, as bidders may bid above their value(s) in an attempt to win both auctions and receive the extra complementarity.The exposure risk affects bidders differently in simultaneous and sequential auctions for two complements, say product A and product B. …