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Mathematics > Optimization and Control
Title: Follower Agnostic Methods for Stackelberg Games
(Submitted on 2 Feb 2023 (v1), last revised 27 Mar 2024 (this version, v3))
Abstract: In this paper, we present an efficient algorithm to solve online Stackelberg games, featuring multiple followers, in a follower-agnostic manner. Unlike previous works, our approach works even when leader has no knowledge about the followers' utility functions or strategy space. Our algorithm introduces a unique gradient estimator, leveraging specially designed strategies to probe followers. In a departure from traditional assumptions of optimal play, we model followers' responses using a convergent adaptation rule, allowing for realistic and dynamic interactions. The leader constructs the gradient estimator solely based on observations of followers' actions. We provide both non-asymptotic convergence rates to stationary points of the leader's objective and demonstrate asymptotic convergence to a \emph{local Stackelberg equilibrium}. To validate the effectiveness of our algorithm, we use this algorithm to solve the problem of incentive design on a large-scale transportation network, showcasing its robustness even when the leader lacks access to followers' demand.
Submission history
From: Chinmay Maheshwari [view email][v1] Thu, 2 Feb 2023 21:21:14 GMT (24kb)
[v2] Wed, 24 May 2023 17:43:37 GMT (31kb)
[v3] Wed, 27 Mar 2024 00:38:33 GMT (627kb,D)
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