  Any social choice function (e.g the efficient allocation) can be implemented
using different payment rules: first price, second price, all-pay, etc. All of
these payment rules are guaranteed to have the same expected revenue by the
revenue equivalence theorem, but have different distributions of revenue,
leading to a question of which one is best. We prove that among all possible
payment rules, winner-pays-bid minimizes the variance in revenue and, in fact,
minimizes any convex risk measure.
