Game dynamics, which describe how agents' strategies evolve over time based on past interactions, can exhibit a variety of undesirable behaviours including convergence to suboptimal equilibria, cycling, and chaos. While central planners can employ incentives to mitigate such behaviors and steer game dynamics towards desirable outcomes, the effectiveness of such interventions critically relies on accurately predicting agents' responses to these incentives -- a task made particularly challenging when the underlying dynamics are unknown and observations are limited. To address this challenge, this work introduces the Side Information Assisted Regression with Model Predictive Control (SIAR-MPC) framework. We extend the recently introduced SIAR method to incorporate the effect of control, enabling it to utilize side-information constraints inherent to game-theoretic applications to model agents' responses to incentives from scarce data. MPC then leverages this model to implement dynamic incentive adjustments. Our experiments demonstrate the effectiveness of SIAR-MPC in guiding systems towards socially optimal equilibria, stabilizing chaotic and cycling behaviors. Notably, it achieves these results in data-scarce settings of few learning samples, where well-known system identification methods paired with MPC show less effective results.

翻译：博弈动态描述了智能体策略如何基于过往互动随时间演化，可能表现出多种不良行为，包括收敛至次优均衡、周期性循环与混沌现象。尽管中央规划者可通过激励机制来缓解此类行为并引导博弈动态趋向理想结果，但此类干预措施的有效性关键依赖于准确预测智能体对激励的响应——当底层动态未知且观测数据有限时，该任务尤为困难。为应对这一挑战，本研究提出侧信息辅助回归与模型预测控制（SIAR-MPC）框架。我们将近期提出的SIAR方法扩展至包含控制效应，使其能够利用博弈论应用中固有的侧信息约束，从稀缺数据中建模智能体对激励的响应。随后，模型预测控制（MPC）利用该模型实施动态激励调整。实验证明SIAR-MPC在引导系统趋向社会最优均衡、稳定混沌与循环行为方面具有显著效果。值得注意的是，该方法在仅需少量学习样本的数据稀缺场景中仍能达成目标，而传统系统辨识方法与MPC结合在此类场景中表现欠佳。