Asymmetric Spite in Auctions

Abstract

In many auctions, agents bid more aggressively than self-interest would prescribe. This can be explained by spite, where the agent's utility not only increases in the agent's surplus but also decreases as the other bidders' surpluses increase. Spite can stem from long-term benefits from making competitors worse off and from inherent psychological effects. There have been important recent game-theoretic analyses of spiteful bidding assuming all agents are equally spiteful. We present, to our knowledge, the first auction analysis in the more realistic setting where bidders may be spiteful to different extents. We show that the equilibrium bidding function can still be written in the same form — except that the spite factor is replaced by an expressed spite factor. This leads to bidders expressing spites that are higher or lower than their true spite depending on others' spite. Perhaps surprisingly, in the two-bidder case, the mapping from true spite to expressed spite is the same across all common auction mechanisms. Furthermore, even with two bidders, important properties of symmetric-spite settings cease to hold: the allocation can be inefficient and the revenue ranking may reverse between first- and second-price auctions. We also show that in sealed-bid auctions under asymmetric valuation distributions, there can be a "bargaining problem" in selecting bids. Finally, we study the generalization where agents can have different extents of spite toward different other bidders.