Beauty contests are auction mechanisms used to buy or sell differentiated products where the auctioneer does not specify a decision rule to pick the winning bidder. Beauty contests are widely used in procuring welfare-to-work projects, freelance services, selling online ads, real estate transactions, and hiring, dating/marriage decisions. Unlike price-only auctions, beauty contests have no closed-form bidding strategies and suffer from nonmultiplicatively separable unobserved auction heterogeneity, which makes their estimation challenging. To address these challenges, we formulate beauty contests as incomplete information games and present a two-step estimator. A key contribution of our method is its ability to account for common-knowledge auction-specific unobservables using finite unobserved types. We show that unobserved auction types and distributions of bids are nonparametrically identified and recoverable in the first step using a nonparametric Expectation-Maximization (EM)-like algorithm, and that these can then be used in the second step to recover cost distributions. We present an application of our method in the online freelancing context. We find that seller margins in this marketplace are around 15% of the bid, and that not accounting for unobserved heterogeneity can significantly bias cost estimates in this setting. Based on our estimates, we run counterfactual simulations and provide guidelines to managers of freelance firms.
