Sequentially Optimal Auctions
We examine equlibria in sequential auctions where a seller can post a reserve price but, if the auction fails to result in a sale, can commit keeping the object off the market only for an exogenously fixed period of time. We restrict attention to enviornments where bidders have independent private values and where the support of the bidder types lies strictly above the valuation of the seller. In the case where the seller sells by second price auction in each period, there is a unique perfect Bayesian equilbrium. A form of revenue equivalence is shown. There exists a perfect Bayesian equilibrium of repeated first price auctions with the feature that in every period, the seller's expected revenue from the continuation is the same in either auction mechanism. As the length of time the seller can commit to keeping the object off the market goes to zero, seller expected revenues converge to those of a static auction with no reserve price. As the number of bidders becomes large, the seller expected revenue approaches the revenue from an optimal static auction. We also characterize a parametrized auction game in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers.
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