Disclosure Policies in All-Pay Auctions with Bid Caps

Abstract

In this paper, we study the optimal disclosure of bidders’ types in a two-bidder all-pay auction in the presence of a common and exogenously given bid cap. We focus on the set of disclosure policies that are contingent on realizations of bidders’ types and fully characterize the unique symmetric equilibrium under each of them. We find that, allowing only for full disclosure and full concealment, the ex ante expected revenue is higher under full disclosure only for intermediate levels of the bid cap. Allowing also for partial disclosure policies: (i) the ex ante expected revenue under full disclosure is higher than under partial disclosure to low-type bidders but lower than under partial disclosure to high-type bidders, regardless of the bid cap; (ii) full concealment could rank from the highest to the third highest, depending on the bid cap, the prior type distribution, and the type values. These results are due to the different sensitivities of bidders’ bids across bidders’ types and disclosure policies.