In many situations an auctioneer is able to prevent bidders from organizing an explicit cartel that enforces coordinated behavior of the bidders and facilitates exchange of side payments. However it may be very difficult to prevent the bidders from simply engaging in cheap talk before the auction, and such communication can affect the outcomes of the auction. For example, in the second-price auctions pre-play communication allows to sustain the following ‘phases-of-the-moon’ rotation scheme. Before the auction a designated winner is randomly chosen; during the auction the bidders coordinate on the equilibrium where the designated winner obtains the good for free by submitting a very high bid while the other bidders submit zero bids. In the first-price and the all-pay auctions such scheme would not work, because (under standard assumptions) there is only one equilibrium for any given prior beliefs, but there may exist other communication equilibria. In this paper I investigate how communication before the auction can affect the outcomes of the sealed bid all-pay auctions.

By the revelation principle (Myerson (1982)) the outcome of any communication protocol can be replicated by the procedure whereby the bidders first secretly report their valuations to a neutral trustworthy mediator, who then makes private non-binding recommendations on how to bid to each bidder. Thus a communication equilibrium is a joint probability distribution over the valuations and the bids of the bidders, subject to the constraints that the bidders should find it optimal first to report their true valuations, and then submit the recommended bids. For each communication equilibrium there is an associated outcome function that maps profiles of the bidders’ valuations into their probabilities of winning and their expected bids.

I show that in the case of symmetric bidders there is a unique communication equilibrium which is outcome equivalent to the Nash equilibrium of this game. To prove this I consider the constraints on the equilibrium outcomes imposed by one particular kind of deviation strategies available to each bidder. At the reporting stage the bidder randomizes over all possible valuations according to the prior probability distribution of her valuations; at the bidding stage the bidder ignores the recommended bids and uses a particular deviational bidding strategy. Such behavior at the reporting stage assures that at the bidding stage the deviating bidder is bidding against an ex ante distribution of the bids of the opponents. Hence, in the equilibrium each type of each bidder should do at least as well as she would do if she was just facing the ex ante distribution of the bids of the opponents. This observation allows to derive a bound on the ex ante distribution function of bids and thus on the expected profits from each bidder, that in turn yields a set of constraints on the equilibrium outcomes. For one specifically constructed deviational bidding strategy there is only a single equilibrium outcome that satisfies these constraints.

I conjecture that the communication equilibrium is unique also in the case of asymmetric bidders. I believe that similar approaches can be used to analyze communication equilibria of other related games like all-pay contests with asymmetric  information, as well as first-price auctions.