On the reserve price in all-pay auctions with complete information and lobbying games

We study the equilibrium of the all-pay auction with complete information and a reserve price, and compare it with that of standard auctions. The seller should set a reserve price even when she faces incomplete information. In the latter setting, ex-ante asymmetry among bidders appears necessary to re-produce some (if any) of the interesting results derived assuming a fully-informed seller in the literature on the application of all-pay auction to lobbying games, while they appear to rely crucially on the implicit assumption of a weak (in terms of bargaining power) seller if she is fully informed.