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 language||English (US)|
|Title of host publication||STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing|
|Editors||Yishay Mansour, Daniel Wichs|
|Publisher||Association for Computing Machinery|
|Number of pages||14|
|State||Published - Jun 19 2016|
|Event||48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States|
Duration: Jun 19 2016 → Jun 21 2016
|Name||Proceedings of the Annual ACM Symposium on Theory of Computing|
|Other||48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016|
|Period||6/19/16 → 6/21/16|
Bibliographical noteFunding Information:
Partially supported by an NSF CAREER award, NSF Grants CCF-1101389 and CNS-1065060, and a Google Focused Research Award.
- Game theory
- Revealed preferences