Stackelberg POMDP: A Reinforcement Learning Approach for Economic Design

TL;DR

This paper presents a reinforcement learning framework for economic design modeled as a Stackelberg game, formulating the leader's problem as a POMDP and demonstrating its effectiveness through complex scenarios and convergence analysis.

Contribution

It introduces the Stackelberg POMDP framework, connecting POMDP solutions with Stackelberg game strategies and applying it to economic design with strategic followers.

Findings

Optimal leader strategies correspond to POMDP policies.

Effective training framework demonstrated through ablation studies.

Proven convergence to Bayesian coarse-correlated equilibrium.

Abstract

We introduce a reinforcement learning framework for economic design where the interaction between the environment designer and the participants is modeled as a Stackelberg game. In this game, the designer (leader) sets up the rules of the economic system, while the participants (followers) respond strategically. We integrate algorithms for determining followers' response strategies into the leader's learning environment, providing a formulation of the leader's learning problem as a POMDP that we call the Stackelberg POMDP. We prove that the optimal leader's strategy in the Stackelberg game is the optimal policy in our Stackelberg POMDP under a limited set of possible policies, establishing a connection between solving POMDPs and Stackelberg games. We solve our POMDP under a limited set of policy options via the centralized training with decentralized execution framework. For the specific case of followers that are modeled as no-regret learners, we solve an array of increasingly complex settings, including problems of indirect mechanism design where there is turn-taking and limited communication by agents. We demonstrate the effectiveness of our training framework through ablation studies. We also give convergence results for no-regret learners to a Bayesian version of a coarse-correlated equilibrium, extending known results to correlated types.