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Mechanism Redesign

This paper develops the theory of mechanism redesign by which an auctioneer can reoptimize an auction based on bid data collected from previous iterations of the auction on bidders from the same market. We give a direct method for estimation of the revenue of a counterfactual auction from the bids in the current auction. The estimator is a simple weighted order statistic of the bids and has the optimal error rate. Two applications of our estimator are A/B testing (a.k.a., randomized controlled trials) and instrumented optimization (i.e., revenue optimization subject to being able to do accurate inference of any counterfactual auction revenue).