  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.
