Value-dependent spite in first-price all-pay auctions

I introduce value-dependent spite into first-price all-pay auctions and demonstrate that it leads to overbidding. Unlike in first- and second-price winner-pay auctions, value-dependent spite does not change the basic curvature of equilibrium bids: they remain convex. Nonetheless, value-dependent spite predicts different overbidding patterns from those predicted by value-independent spite. My main result highlights that, for low values, equilibrium bids when spite is value-dependent are closer to the non-spiteful benchmark than when spite is value-independent. Using approximations, I show that this result is strengthened when the relationship between a bidder’s value and her degree of spite is convex and weakened when it is concave.