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On the competitive ratio of online sampling auctions
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We study the problem of designing seller-optimal auctions, i.e. auctions where the objective is to maximize revenue. Prior to this work, the only auctions known to be approximately optimal in the worst case employed randomization. Our main result is the existence of deterministic auctions that approximately match the performance guarantees of these randomized auctions. We give a fairly general derandomization technique for turning any randomized mechanism into an asymmetric deterministic one with approximately the same revenue. In doing so, we bypass the impossibility result for symmetric deterministic auctions and show that asymmetry is nearly as powerful as randomization for solving optimal mechanism design problems. Our general construction involves solving an exponential-sized flow problem and thus is not polynomial-time computable. To complete the picture, we give an explicit polynomial-time construction for derandomizing a specific auction with good worst-case revenue. Our results are based on toy problems that have a flavor similar to the hat problem from [3].