On Disclosure Policies in All-pay Auctions with Stochastic Entry

The contest entails one prize and n potential bidders. Each bidder receives a signal about the value of the prize and has a signal-dependent probability of participation. All bidders bear a cost of bidding that is an increasing function of their bids. It is shown that the contest organizer prefers fully concealing (disclosing) the information about the number of participating bidders when the cost functions are convex (concave). This result is applied to various cases with endogenous entry. However, it does not extend to the cases in which bidders have heterogeneous participation probabilities