= Ranked winning probabilities in an undiscounted elimination contest
{title2=$x_i=1-2^{-(m-i+2)}v_{m+1}/v_i\quad(2\leq i\leq m)$}
For $m<n$ prizes and ordered distinct valuations, the discounted-equilibrium limit gives $x_1=1-2^{-m}v_{m+1}/v_1$ and $x_i=1-2^{-(m-i+2)}v_{m+1}/v_i$ for $2\leq i\leq m$. A player must lose its successive fair nonfinal contests and then the asymmetric final contest to receive no prize. The marginal player's probability is $m-\sum_{i=1}^m x_i$, and lower players have probability zero.
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