Correlated Equilibria and Communication Equilibria in All-pay Auctions

We study cheap-talk pre-play communication in the static all-pay auctions. For the case of two bidders, all correlated and communication equilibria are payoff equivalent to the Nash equilibrium if there is no reserve price, or if it is commonly known that one bidder has a strictly higher value. Hence, in such environments the Nash equilibrium predictions are robust to preplay communication between the bidders. If there are three or more symmetric bidders, or two symmetric bidders and a positive reserve price, then there may exist correlated and communication equilibria such that the bidders’ payoffs are higher than in the Nash equilibrium. In these cases, pre-play cheap talk may affect the outcomes of the game, since the bidders have an incentive to coordinate on such equilibria.