Simple Economies are Almost Optimal

06/02/2021
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by   Amir Ban, et al.
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Consider a seller that intends to auction some item. The seller can invest money and effort in advertising in different market segments in order to recruit n bidders to the auction. Alternatively, the seller can have a much cheaper and focused marketing operation and recruit the same number of bidders from a single market segment. Which marketing operation should the seller choose? More formally, let D={๐’Ÿ_1,โ€ฆ, ๐’Ÿ_n} be a set of distributions. Our main result shows that there is always ๐’Ÿ_iโˆˆ D such that the revenue that can be extracted from n bidders, where the value of each is independently drawn from ๐’Ÿ_i, is at least 1/2ยท (1-1/e) of the revenue that can be obtained by any possible mix of bidders, where the value of each bidder is drawn from some (possibly different) distribution that belongs to D. We next consider situations in which the auctioneer cannot use the optimal auction and is required to use a second price auction. We show that there is always ๐’Ÿ_iโˆˆ D such that if the value of all bidders is independently drawn from ๐’Ÿ_i then running a second price auction guarantees a constant fraction of the revenue that can be obtained by a second-price auction by any possible mix of bidders. Finally, we show that for any ฮต>0 there exists a function f that depends only on ฮต (in particular, the function does not depend on n or on the set D), such that recruiting n bidders which have at most f(ฮต) different distributions, all from D, guarantees (1-ฮต)-fraction of the revenue that can be obtained by a second-price auction by any possible mix of bidders.

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