Auctions with Dynamic Populations: Efficiency and Revenue Maximization

Maher Said

MPRA Paper from University Library of Munich, Germany

Abstract: We examine an environment where goods and privately informed buyers arrive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both with and without a reserve price. We construct memoryless equilibrium bidding strategies in this indirect mechanism. Bidders reveal their private information in every period, yielding the same outcomes as the direct mechanisms. Thus, the sequential ascending auction is a natural institution for achieving either efficient or optimal outcomes. Interestingly, this is not the case for sequential second-price auctions, as the bids in a second-price auction do not reveal sufficient information to realize either the efficient or optimal allocation.

Keywords: Dynamic mechanism design; Random arrivals; Revenue equivalence; Indirect mechanisms; Sequential ascending auctions (search for similar items in EconPapers)
JEL-codes: C73 D44 D82 D83 (search for similar items in EconPapers)
Date: 2008-11-19
New Economics Papers: this item is included in nep-cta, nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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https://mpra.ub.uni-muenchen.de/14924/1/MPRA_paper_14924.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/14988/1/MPRA_paper_14988.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/16895/1/MPRA_paper_16895.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/23852/2/MPRA_paper_23852.pdf revised version (application/pdf)

Related works:
Journal Article: Auctions with dynamic populations: Efficiency and revenue maximization (2012)
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