Approximately Optimal Auctions
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چکیده
While Myerson’s theorem provides an elegant solution to the optimal auction design problem for k-good auctions, his auction is rather complicated, and is consequently not widely used in practice. On the other hand, posted-price mechanisms are widely used in practice. We have derived an optimal posted-price mechanism for an auction with a single bidder.1 What about for multiple bidders? What is the opti1 buyer, I suppose mal posted-price then? We can answer this question by taking derivatives, etc.,2 but the answer will ultimately depend on distributional 2 sounds like a good homework exercise assumptions. We will take an alternative approach in this lecture, analyzing not the optimal mechanism, but a randomized posted-price mechanism instead. Perhaps surprisingly, the guarantees we derive will be independent of any distributional assumptions. The mechanism we will analyze is “posting a random price”. We will analyze this mechanism in some detail, first assuming only one bidder. We will then generalize to n symmetric bidders’, where all bidders’ values are drawn from the same distribution, assuming digital goods, or equivalently, goods in infinite supply.
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