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.

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