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 the case of correlated types.

翻译：我们提出了一种面向经济设计的强化学习框架，其中环境设计者与参与者之间的交互被建模为Stackelberg博弈。在该博弈中，设计者（领导者）制定经济系统的规则，而参与者（追随者）做出策略性响应。我们将确定追随者响应策略的算法整合到领导者的学习环境中，从而将领导者的学习问题表述为一个部分可观测马尔可夫决策过程（POMDP），并称之为Stackelberg POMDP。我们证明，在有限策略集条件下，Stackelberg博弈中的最优领导者策略对应于我们提出的Stackelberg POMDP中的最优策略，由此建立了求解POMDP与Stackelberg博弈之间的联系。我们通过集中训练与分散执行的框架，在有限策略选项下求解该POMDP。针对追随者被建模为无遗憾学习者的特定情形，我们求解了一系列复杂度递增的设置，包括存在轮替通信与受限通信的间接机制设计问题。通过消融实验验证了训练框架的有效性。此外，我们给出了无遗憾学习者收敛至贝叶斯版本粗糙相关均衡的结论，将现有结果扩展至类型相关的情形。