A tractable theory of value-dependent spite in first- and second-price auctions

I propose a model of value-dependent spite in first- and second-price auctions. My central innovation is that bidders are more spiteful the greater their value for the object. I show that equilibrium bids are increasing and, in contrast to models of value-independent spite, non-linear in bidders’ values. Due to how the marginal benefit of increasing one’s bid changes as one’s value increases, bids are convex in first-price auctions and concave in second-price auctions. I confirm that value-dependent spite leads to overbidding in both auction formats, and that second-price auctions yield greater expected revenue for the seller. Unlike the standard model, however, bidders with the lowest value in second-price auctions no longer submit positive bids. My modelling approach provides new, testable insights on spiteful bidding behaviour and generalises existing findings.