Follower Agnostic Methods for Stackelberg Games

TL;DR

This paper introduces a follower-agnostic algorithm for online Stackelberg games with multiple followers, capable of operating without knowledge of followers' utilities or strategies, and demonstrates its effectiveness in large-scale transportation networks.

Contribution

The paper proposes a novel gradient estimator and convergence analysis for leader strategies in Stackelberg games without follower utility knowledge, extending applicability to dynamic, real-world scenarios.

Findings

Algorithm converges to stationary points of the leader's objective.

Demonstrates asymptotic convergence to local Stackelberg equilibrium.

Effective in large-scale transportation network incentive design.

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.