The Spite Motive and Equilibrium Behavior in Auctions

Abstract

We study auctions where bidders have independent private values but attach a disutility to the surplus of rivals, and derive symmetric equilibria for first-price, second-price, English, and Dutch auctions. We find that equilibrium bidding is more aggressive than standard predictions. Indeed, in second-price auctions it is optimal to bid above one's valuation; that is, bidding "frenzies" can arise in equilibrium. Further, revenue equivalence between second-price and first-price auctions breaks down, with second-price outperforming first-price. We also find that strategic equivalence between second-price and English auctions no longer holds, although they remain revenue equivalent. We conclude that spiteful bidding rationalizes anomalies observed in laboratory experiments across the four auction forms better than the leading alternatives.