Three Bidders, All Pay
Three risk-neutral bidders have independent private values uniform on [0, 1]. In a sealed-bid all-pay auction, every bidder pays their own bid and the highest bid wins the object. In the symmetric equilibrium the bid is a strictly increasing function of the value. What does a bidder with value 3/4 bid? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Values That Lean High 4.0/10
Source: Standard all-pay auction equilibrium from auction theory (e.g. Krishna, Auction Theory). Statement written for AxiomIQ.