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Auctions with Dynamic Populations: Efficiency and Revenue Maximization

Said, Maher (2010): Auctions with Dynamic Populations: Efficiency and Revenue Maximization.

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We study indirect mechanisms in a setting where both objects and privately-informed buyers arrive stochastically to a market. The seller in this setting faces a sequential allocation problem, and must elicit the private information of the dynamic population of buyers in order to achieve her desired outcome -- either an efficient or a revenue-maximizing allocation. We propose a simple indirect mechanism, the sequential ascending auction, which yields outcomes identical to those of an efficient dynamic Vickrey-Clarke-Groves mechanism. We construct equilibria in memoryless strategies where strategic bidders are able to reach the efficient outcome by revealing all private information in every period, inducing behavior that is symmetric across both incumbent and newly entered buyers. In contrast to settings with a static population, a sequence of second-price auctions cannot yield this outcome, as these auctions do not reveal sufficient information to symmetrize different cohorts. We also extend our results to revenue-maximization, showing that the sequential ascending auction with a reserve price is optimal.

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