Learning Stackelberg Equilibria and Applications to Economic Design Games

Gianluca Brero, Darshan Chakrabarti, Alon Eden, Matthias Gerstgrasser, Vincent Li, David C. Parkes

Keywords: Multi-agent Systems, Reinforcement Learning, Economic Design

Abstract: We study the use of reinforcement learning to learn the optimal leader's strategy in Stackelberg games. Learning a leader’s strategy has an innate stationarity problem---when optimizing the leader’s strategy, the followers’ strategies might shift. To circumvent this problem, we model the followers via no-regret dynamics to converge to a Bayesian Coarse-Correlated Equilibrium (B-CCE) of the game induced by the leader. We then embed the followers' no-regret dynamics in the leader's learning environment, which allows us to formulate our learning problem as a standard POMDP. We prove that the optimal policy of this POMDP achieves the same utility as the optimal leader's strategy in our Stackelberg game. We solve this POMDP using actor-critic methods, where the critic is given access to the joint information of all the agents. Finally, we show that our methods are able to learn optimal leader strategies in a variety of settings of increasing complexity, including indirect mechanisms where the leader’s strategy is setting up the mechanism’s rules.

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