= All-pay indifference equation with random entry
{title2=$wG(b)^{n-1}-b=u$}
For a prize of value $w$, let $G(b)$ be the probability that a rival is absent or enters with effort at most $b$. When rivals act independently and have no atoms at positive efforts, effort $b>0$ wins with probability $G(b)^{n-1}$. If a player mixes over an interval of <best responses>, its payoff on that interval is constant, so $G(b)=((b+u)/w)^{1/(n-1)}$. If the absence probability is $q$ and the active <effort support> starts at zero, then $u=wq^{n-1}$.
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