All-pay auctions with interdependent valuations: The highly competitive case1

We analyze symmetric, two-player all-pay auctions with interdependent valuations and general discrete signal structures. We extend the previous literature by being able to analyze auctions in which an increase in a bidder’s posterior expected value for winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are “highly competitive” in the sense that the bidder’s higher valuation also signals that the other bidder has an incentive to bid aggressively. We present a construction which computes all symmetric equilibria, and show how, in highly competitive environments, the search problem this construction faces can be complex. In equilibrium, randomization can take place over disjoint ranges of bids, with equilibrium supports having a potentially rich structure. JEL Classifications: D44; D82; D72.