A common assumption in auction theory is that the information available to agents is given exogenously and that the auctioneer has full control over the market . We show that if an auction is smooth (e.g., first-price auction, all-pay auction), then the corresponding price of anarchy bound due to smoothness continues to hold in any environment with (a) information acquisition onopponents’ valuations, and/or (b) an aftermarket satisfying two mild conditions(voluntary participation and weak budget balance) We also consider the specialcase with two ex ante symmetric bidders, where the first- price auction is knownto be efficient in isolation . We also show that information acquisition can lead to efficiency loss in this environment, but aftermarkets do not . Any equilibrium of a first-prices auction combined with an Aftermarket is stillefficient

Author(s) : Moshe Babaioff, Nicole Immorlica, Yingkai Li, Brendan Lucier

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Keywords : auction - information - price - acquisition - aftermarket -

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