Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions

88 Pages Posted: 22 Mar 2018 Last revised: 28 Jun 2019

See all articles by Negin Golrezaei

Negin Golrezaei

Massachusetts Institute of Technology (MIT) - Sloan School of Management; Massachusetts Institute of Technology - MIT Sloan School of Management; Massachusetts Institute of Technology (MIT) - Sloan School of Management

Adel Javanmard

University of Southern California

Vahab Mirrokni

Google Inc.

Date Written: March 19, 2018

Abstract

Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers’ valuations for an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers’ valuations, i.e., buyers’ preferences. The seller’s goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy that knows buyers’ heterogeneous preferences. Given the seller’s goal, utility-maximizing buyers have the incentive to bid untruthfully in order to manipulate the seller’s learning policy. We propose learning policies that are robust to such strategic behavior. These policies use the outcomes of the auctions, rather than the submitted bids, to estimate the preferences while controlling the long-term effect of the outcome of each auction on the future reserve prices. When the market noise distribution is known to the seller, we propose a policy called Contextual Robust Pricing (CORP) that achieves a T-period regret of O(d log(Td)log(T)), where d is the dimension of the contextual information. When the market noise distribution is unknown to the seller, we propose two policies whose regrets are sublinear in T.

Keywords: pricing, robust learning, strategic buyers repeated second-price auctions, online advertising

Suggested Citation

Golrezaei, Negin and Javanmard, Adel and Mirrokni, Vahab, Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions (March 19, 2018). Available at SSRN: https://ssrn.com/abstract=3144034 or http://dx.doi.org/10.2139/ssrn.3144034

Negin Golrezaei (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Massachusetts Institute of Technology - MIT Sloan School of Management ( email )

100 Main Street
Building E62-577
Cambridge, MA 02142
United States

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Adel Javanmard

University of Southern California ( email )

2250 Alcazar Street
Los Angeles, CA 90089
United States

Vahab Mirrokni

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

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