Bidding with Securities: Auctions and Security Design

TLDR: Equilibrium is characterized and it is shown 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.

Abstract: We study security-bid auctions in which bidders compete for an asset by bidding with securities. That is, they offer payments that are contingent on the realized value of the asset being sold. The value depends on investment by the winner, thus creating the possibility of moral hazard. Such auctions are commonly used, both formally and informally. In formal auctions, the seller generally restricts bids to an ordered set, such as an equity share or royalty rate. By restricting the bids, standard auction formats such as first and second-price auctions can be used. In informal settings with competing buyers, the seller does not commit to a mechanism upfront. Rather, bidders offer securities and the seller chooses the most attractive bid, based on his beliefs, ex-post. We characterize equilibrium payoffs and bidding strategies in this setting, and show that an informal mechanism yields the lowest possible revenues across all mechanisms. We also determine the optimal formal mechanism, and show that the security design is more important than the auction format. We show that the revenue equivalence principle (that expected revenues are independent of the auction format) holds if the set of permissible securities is ordered and convex (such as equity). Otherwise, it need not hold. For example, when bidders offer standard debt securities, a second-price auction is superior. On the other hand, if bidders compete on the conversion ratio of convertible debt, a first- price auction yields higher revenues. Finally, we examine how different forms of moral hazard impact our results.