On approximating optimal auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A new approach to auctions and resilient mechanism design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Simple versus optimal mechanisms
Proceedings of the 10th ACM conference on Electronic commerce
Multi-parameter mechanism design and sequential posted pricing
Proceedings of the forty-second ACM symposium on Theory of computing
Revenue maximization with a single sample
Proceedings of the 11th ACM conference on Electronic commerce
On optimal single-item auctions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal auctions with correlated bidders are easy
Proceedings of the forty-third annual ACM symposium on Theory of computing
Mechanism Design with Set-Theoretic Beliefs
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Prior-free auctions with ordered bidders
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We investigate the problem of optimal mechanism design, where an auctioneer wants to sell a set of goods to buyers, in order to maximize revenue. In a Bayesian setting the buyers' valuations for the goods are drawn from a prior distribution D, which is often assumed to be known by the seller. In this work, we focus on cases where the seller has no knowledge at all, and "the buyers know each other better than the seller knows them". In our model, D is not necessarily common knowledge. Instead, each buyer individually knows a posterior distribution associated with D. Since the seller relies on the buyers' knowledge to help him set a price, we call these types of auctions crowdsourced Bayesian auctions. For this crowdsourced Bayesian model and many environments of interest, we show that, for arbitrary valuation distributions D (in particular, correlated ones), it is possible to design mechanisms matching to a significant extent the performance of the optimal dominant-strategy-truthful mechanisms where the seller knows D. To obtain our results, we use two techniques: (1) proper scoring rules to elicit information from the players; and (2) a reverse version of the classical Bulow-Klemperer inequality. The first lets us build mechanisms with a unique equilibrium and good revenue guarantees, even when the players' second and higher-order beliefs about each other are wrong. The second allows us to upper bound the revenue of an optimal mechanism with n players by an n/n--1 fraction of the revenue of the optimal mechanism with n -- 1 players. We believe that both techniques are new to Bayesian optimal auctions and of independent interest for future work.