Correlated equilibria and communication equilibria in all-pay auctions *

Abstract We study cheap-talk pre-play communication in the static all-pay auctions. For the case of two bidders we show that 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 pre-play communication between the bidders. If there are three or more symmetric bidders, or two symmetric bidders and a positive reserve price, then we show that there 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. JEL classification: C72; D44; D82; D83; L4