TY - GEN

T1 - Watch and learn

T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016

AU - Roth, Aaron

AU - Ullman, Jonathan

AU - Wu, Zhiwei Steven

PY - 2016/6/19

Y1 - 2016/6/19

N2 - 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.

AB - 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.

KW - Game theory

KW - Learning

KW - Optimization

KW - Revealed preferences

UR - http://www.scopus.com/inward/record.url?scp=84979222072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979222072&partnerID=8YFLogxK

U2 - 10.1145/2897518.2897579

DO - 10.1145/2897518.2897579

M3 - Conference contribution

AN - SCOPUS:84979222072

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 949

EP - 962

BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Mansour, Yishay

A2 - Wichs, Daniel

PB - Association for Computing Machinery

Y2 - 19 June 2016 through 21 June 2016

ER -