On The Effects of Bid Caps in All-Pay Auctions

This note analyzes the effects of a bid cap in an all-pay auction with incomplete information. I find that a non-trivial bid cap affects an agent's expected payment in three ways: An "anti-competition effect" which is associated with this agent's own signal, a pro-competition "good news effect" which is associated with her opponents' signals and which alleviates the winner's curse, and an "inference effect" caused by affiliation of signals. Unlike the former two effects, the "inference effect'' is a double-edged sword. It is anti-competitive when the cap is relatively low and pro-competitive when a cap is relatively high