Lecture by Alex Suzdaltsev on "An Optimal Distributionally Robust Auction"

On Wednesday, June 17 the all-Russian seminar "Mathematical methods of decision analysis in economics, finance and politics" was held. A. Suzdaltsev gave a lecture on "An Optimal Distributionally Robust Auction"

Moderators:
-  Fuad Aleskerov,
-  Vladislav Podinovskiy,
-  Boris Mirkin


Author: Alex Suzdaltsev (Stanford Graduate School of Business)

Abstract: 

An indivisible object may be sold to one of n agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the values’ distribution is scarce: she knows only the means (which may be different) an upper bound for valuations. Valuations may be correlated.Using a constructive approach based on duality, we prove that a mechanism that maximizes the worst-case expected revenue among all deterministic dominant-strategy incentive compatible, ex post individually rational mechanisms takes the following form: (1) the bidders submit bids; (2) for each bidder, a linear score is calculated with fixed parameters; (3) the object is awarded to the agent with the highest score, provided it’s nonnegative; (4) the winning bidder pays the minimal amount he would need to bid to still win in the auction. The set of optimal mechanisms includes other mechanisms but all those have to be close to the optimal linear score auction in a certain sense. When means are high, all optimal mechanisms share the linearity property. Second-price auction without a reserve is an optimal mechanism when the number of symmetric bidders is sufficiently high.