Watch and learn: Optimizing from revealed preferences feedback

Aaron Roth, Jonathan Ullman, Zhiwei Steven Wu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

33 Scopus citations


A Stackelberg game is played between a leader and a follower. The leader first chooses an action, then the follower plays his best response. The goal of the leader is to pick the action that will maximize his payoff given the follower's best response. In this paper we present an approach to solving for the leader's optimal strategy in certain Stackelberg games where the follower's utility function (and thus the subsequent best response of the follower) is unknown. Stackelberg games capture, for example, the following interaction between a producer and a consumer. The producer chooses the prices of the goods he produces, and then a consumer chooses to buy a utility maximizing bundle of goods. The goal of the seller here is to set prices to maximize his profit-his revenue, minus the production cost of the purchased bundle. It is quite natural that the seller in this example should not know the buyer's utility function. However, he does have access to revealed preference feedback-he can set prices, and then observe the purchased bundle and his own profit. We give algorithms for efficiently solving, in terms of both computational and query complexity, a broad class of Stackelberg games in which the follower's utility function is unknown, using only "revealed preference" access to it. This class includes in particular the profit maximization problem, as well as the optimal tolling problem in nonatomic congestion games, when the latency functions are unknown. Surprisingly, we are able to solve these problems even though the optimization problems are non-convex in the leader's actions.

Original languageEnglish (US)
Title of host publicationSTOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
EditorsYishay Mansour, Daniel Wichs
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Electronic)9781450341325
StatePublished - Jun 19 2016
Externally publishedYes
Event48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States
Duration: Jun 19 2016Jun 21 2016

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Other48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
Country/TerritoryUnited States

Bibliographical note

Funding Information:
Partially supported by an NSF CAREER award, NSF Grants CCF-1101389 and CNS-1065060, and a Google Focused Research Award.


  • Game theory
  • Learning
  • Optimization
  • Revealed preferences


Dive into the research topics of 'Watch and learn: Optimizing from revealed preferences feedback'. Together they form a unique fingerprint.

Cite this