Bidding with Securities: Auctions and Security Design

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. Standard auction mechanisms (such as first-price and second-price auctions) are not well defined unless the set of securities is restricted to an ordered set. For example, the seller may require a bidto be exclusively an equity share, or exclusively a debt payment. Given such a restriction, we first ask whether revenue equivalence holds, i.e. whether expected revenues depend upon the auction format. We show that this principle holds if the set of permissible securities is convex. Otherwise, this need not be true. 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. We then consider the joint problem of choosing both the security and auction design. We show that the optimal mechanism yielding the highest possible expected revenues for the seller is a first-price auction with levered equity. On the other hand, a first-price auction with debt contracts is the worst possible mechanism for the seller. Finally, we examine the case in which the seller cannot commit to a formal mechanism. Instead, he chooses the most attractive bid ex post, based on his beliefs. We show that this procedure yields the lowest possible revenues across all mechanisms