Steer a Crowd: Learning to Persuade a Population in a Stackelberg Game

Yuanxin Liu, Siyu Chen, Chuanhao Li, Zhuoran Yang

Keywords: information design, stackelberg game, reinforcement learning, markov games, multi-agent system

Abstract:

Multi-agent systems are prevalent across various domains, characterized by misaligned objectives and information asymmetry, which facilitate the study of incentive design and information design. Existing research often assumes known models and static environments. Motivated by this, we propose a Dynamic Incentive and Information Design (DIID) framework for finite-horizon Markov games, involving a principal and multiple agents.
Our focus is on how the principal learns their optimal policy based on data generated through interactions with agents.
The main challenge lies in balancing the principal's regret and violations of agents' incentive compatibility constraints during interactions. We establish a lower bound characterizing the trade-off between the two objectives and propose an algorithm attaining the optimal trade-off, i.e. $\tilde{\mathcal{O}}(T^{2/3})$ regret and constraint violation. Additionally, with access to additional unilateral deviation information of the agents, we propose an algorithm attaining improved guarantees that achieve $\tilde{\mathcal{O}}(T^{1/2})$ for both regret and constraint violation simultaneously.

Primary Area: reinforcement learning

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Submission Number: 5425