War of Attrition with Affiliated Values

Abstract

We study the war of attrition between two players when the players’ signals are binary and affiliated. Our model covers both the case of common values and affiliated private values. We characterize the unique symmetric equilibrium and demonstrate the possibility of nonmonotonic symmetric equilibria, i.e. equilibria where the player with a lower signal wins with positive probability. Such an outcome is inefficient in the case of private valuations. We compare the war of attrition to other related mechanisms, the all-pay auction and standard first and second-price auctions. The war of attrition dissipates the bidders’ rents more effectively but at the same time distorts the allocation more severely than the other mechanisms. In terms of expected revenues, the war of attrition dominates the standard auctions, but the ranking against the all-pay auction is ambiguous.

Keywords: War of Attrition, affiliated signals

JEL Classification: D44, D82