Spiteful Bidding in Sealed-Bid Auctions

Abstract

We study the bidding behavior of spiteful agents who, contrary to
the common assumption of self-interest, maximize the weighted
difference of their own profit and their competitors' profit. This
assumption is motivated by inherent spitefulness, or, for example,
by competitive scenarios such as in closed markets where the loss of
a competitor will likely result in future gains for oneself. We
derive symmetric Bayes Nash equilibria for spiteful agents in
first-price and second-price sealed-bid auctions. In first-price
auctions, bidders become "more truthful" the more spiteful they
are. Surprisingly, the equilibrium strategy in second-price
auctions does not depend on the number of bidders. Based on these
equilibria, we compare revenue in both auction types. It turns out
that expected revenue in second-price auctions is higher than
expected revenue in first-price auctions whenever agents have the
slightest interest in reducing others' profit as long as they still
care for their own profit. In other words, revenue equivalence only
holds for auctions in which all agents are either self-interested or
completely malicious.