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I am tasked with using the Revenue equivalence theorem to find the solution to the all-pay auction with $N$ players and $v_i \sim^{iid} U[0,1]$ values.

I understand the solution can be found as

$$ \beta(v_i) = F^{N-1}(v_i)v_i - \int_0^{v_i}F(z)dz = \frac{N-1}{N}v_i^N $$

but I don't understand how the theorem is helpful in figuring this out.

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  • $\begingroup$ Do you know the statement of the Revenue Equivalence theorem? If yes, could you please edit it into to your question? $\endgroup$
    – Giskard
    Apr 3 at 5:26

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