All-pay auctions with affiliated binary signals

Abstract

We analyze all-pay auctions with affiliated values and binary signals. We analyze the unique symmetric equilibrium with any number of bidders and show that the bidders earn positive rents only if the equilibrium is monotone. We also characterize the symmetric equilibrium of the closely related two-player war of attrition.We compare expected revenues across these formats. All-pay auctions result in lower expected rents to the bidders than standard auctions, but they also induce inefficient allocations in some models with affiliated private values. With two bidders, the effect on rent extraction dominates, and the all-pay auctions outperform standard auctions in terms of expected revenue. With many bidders, standard auctions may result in higher expected revenue. The war of attrition outperforms the standard auctions in terms of revenue, but its ranking relative to all-pay auctions is ambiguous.