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Bidding with Securities: Auctions and Security Design

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Bidding with Securities: Auctions and Security Design Bidding with Securities: Auctions and Security Design By PETER M. DEMARZO,ILAN KREMER, AND ANDRZEJ SKRZYPACZ* We study security-bid auctions in which bidders compete for an asset by bidding with securities whose payments are contingent on the asset’s realized value. In formal security-bid auctions, the seller restricts the security design to an ordered set and uses a standard auction format (e.g., first- or second-price). In informal settings, bidders offer arbitrary securities and the seller chooses the most attractive bid, based on his beliefs, ex post. We characterize equilibrium and show that steeper securities yield higher revenues, that auction formats can be ranked based on the security design, and that informal auctions lead to the lowest possible revenues. (JEL D44, G32, G34) Auction theory and its applications have be- bid auction, and provide an extensive charac- come increasingly important as an area of eco- terization of such auctions. nomic research over the last 20 years. As a Formal auctions of this type are commonly result, we now have a better understanding of used in government sales of oil leases, wireless how the structure of an auction affects its out- spectrum, highway building contracts, and lead- come. Almost all the existing literature studies plaintiff auctions. Informal auctions of this type the case when bidders use cash payments, so (in the sense that formal auction rules are not set that the value of a bid is not contingent on future forth in advance) are common in the private events. sector. Examples include authors selling pub- In a few cases, such as art auctions, the real- lishing rights, entrepreneurs selling their firm to ized value is subjective and cannot be used as a an acquirer or soliciting venture capital, and basis for payment; however, this is the excep- sports associations selling broadcasting rights.1 tion. In many important applications, the real- The major difference between a formal and ization of the future cash flow generated by the an informal mechanism is the level of commit- auctioned asset or project can be used in deter- ment by the seller. In an informal mechanism, mining the actual payment. That is, the bids can bidders choose which securities to offer, and the be securities whose values are derived from the seller selects the most attractive offer ex post. In future cash flow. We call this setting a security- this case, the auction contains the elements of a signaling game because the seller may infer bidders’ private information from their security choices when evaluating their offers. In a for- * Stanford Graduate School of Business, 518 Memorial mal mechanism the seller restricts bidders to use Way, Stanford, CA 94305 (e-mails: DeMarzo: pdemarzo@ stanford.edu; Kremer: [email protected]; Skrzypacz: [email protected]). We thank two anonymous refer- 1 See Kenneth Hendricks and Robert H. Porter (1988) for ees, Kerry Back, Simon Board, Sandro Brusco, Nicolae a discussion of oil lease auctions, in which royalty rates are Garleanu, Burton Hollifield, John Morgan, and seminar commonly used. In wireless spectrum auctions, the bids are participants at Harvard University, Hebrew University, Uni- effectively debt securities (leading in some cases to default). versity of Iowa, Massachusetts Institute of Technology, Highway building contracts are often awarded through New York University, Stanford University, University of “build, operate, and transfer” agreements to the bidder that New York at Stony Brook, Technion, Tel Aviv University, offers to charge the lowest toll for a pre-specified period. UC Berkeley, UC Davis, UC San Diego, USC, Washington See Jill E. Fisch (2001) for the use of contingency-fee University, Yale University, WFA 2003, ASSA 2004, the auctions in the selection of the lead plaintiff in class action Stony Brook International Conference on Game Theory suits. In mergers, acquisitions, and venture capital agree- 2004, and the Utah Winter Finance Conference 2004 for ments, equity and other securities are commonly used (see useful comments. This material is based upon work sup- Kenneth J. Martin, 1996). John McMillan (1991) describes ported by the National Science Foundation under Grant the auction of the broadcast rights to the Olympic games, 0318476. We also acknowledge the financial support of the where bids contained revenue-sharing clauses. Similarly, Center for Electronic Business and Commerce. publishing contracts include advance and royalty payments. 936 VOL. 95 NO. 4 DEMARZO ET AL.: AUCTIONS AND SECURITY DESIGN 937 securities from a pre-specified ordered set, such reservation values. As a result, Alice as an equity share or royalty rate. The seller is would bid 4 Ϫ 1 ϭ $3M and win the committed to disqualify any offer outside this auction, paying Bob’s bid of 3 Ϫ 1 ϭ set. The seller also commits to an auction for- $2M. mat, such as a first- or second-price auction. One of our main results is that the revenues Now suppose that rather than bidding from an informal mechanism are the lowest with cash, the bidders compete by offer- ing a fraction of the future revenues. As across a large set of possible mechanisms. In we discuss later, it is again a dominant other words, the seller benefits from any form of strategy for bidders to bid their reserva- commitment. Moreover, we show how to rank tion values. Alice offers 3⁄4 of future cash security designs and auction formats in terms of flows while Bob offers 2⁄3. As a result, their impact on the seller’s revenues, and that Alice wins the auction and pays according the design of the securities can be more impor- to Bob’s bid; that is, she gives up 2⁄3 of the tant than design of the auction itself. future revenues. This yields a higher pay- off for the auctioneer; (2⁄3) ϫ $4M ϭ In our model, several agents compete for an Ͼ asset or project that requires an upfront invest- $2.67M $2M (in addition to any up- front payment). ment. This investment may correspond to an amount of cash that the seller needs to raise, or the resources required to run the project. Bid- This example is based on Robert G. Hansen ders observe private signals regarding the value (1985), who was the first to examine the use of they can expect if they acquire the asset. Our securities in an auction setting. Hansen showed initial structure is similar to an independent that a second-price equity auction yields higher private values model, so that different bidders expected revenues than a cash-based auction. In expect different payoffs upon winning, although a related paper, John G. Riley (1988) considers we also consider correlated and common val- first-price auctions where bids include royalty ues. The model differs from standard auction payments in addition to cash. He shows that models in that bids are securities. Bidders offer adding the royalty increases expected revenues. derivatives in which the underlying value is the The intuition in both cases is that adding an future payoff of the asset. Because the winner equity component to the bid lowers the differ- may make investments or take other actions that ence between the winner’s valuation and that of affect this payoff, we also discuss the possibility the second highest bidder. Because this differ- of moral hazard. ence is the rent captured by the winner, reduc- One might conjecture that the results from ing it benefits the seller. standard auction theory carry over to security- In this paper, we generalize this insight along bid auctions by simply replacing each security several dimensions. First, we consider a general with its cash value. Unlike cash bids, however, class of securities that includes debt, equity or the value of a security bid depends upon the royalty rates, options, and hybrids of these. Sec- bidder’s private information. This difference ond, we consider alternative auction formats can have important consequences as the follow- (e.g., first-price versus second-price). Third, we ing simple example demonstrates: consider informal auctions, in which the seller cannot commit to an auction mechanism in Consider an auction in which two bidders, advance. Alice and Bob, compete for a project. The The structure of the paper is as follows. The project requires an initial fixed investment basic model is described in Section I. We begin that is equivalent to $1M (we can inter- our analysis in Section II by examining formal pret some or all of this amount as a min- mechanisms, which consist of both an auction imum up-front cash payment required by format and a security design. There we establish the seller). Alice expects that if she un- dertakes the project, then on average it the following results: would yield cash flows of $4M; Bob ex- pects future cash flows of only $3M. As- ● We characterize super-modularity conditions suming these estimates are private values, under which a monotone—and hence effi- in a standard second-price auction it is a cient—equilibrium is the unique outcome for dominant strategy for bidders to bid their the first- and second-price auctions. 938 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005 ● First we compare security designs holding ● In the unique equilibrium satisfying standard fixed the auction format (first- or second- refinements of off-equilibrium beliefs, bid- price). We show that for either format, the ders use the “flattest” securities available, seller’s expected revenues are positively re- e.g., cash or debt. Moreover, the outcome is lated to the “steepness” (a notion that we equivalent to a first-price auction. As a result, define) of the securities. As a result, debt we conclude that this ex post maximization contracts minimize the seller’s expected pay- yields the worst possible outcome for the offs while call options maximize it.
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