 Sequential private-value all-pay contest

Two players pay their invested efforts regardless of outcome. A leader invests first, and a follower observes that effort before deciding. With ties favoring the follower and unit costs, a follower of value $u$ matches leader effort $b$ when $u>b$, and otherwise declines. For a continuous follower cumulative distribution function $F$, the leader wins with probability $F(b)$ and has payoff $vF(b)-b$.