Learning and Steering Game Dynamics Towards Desirable Outcomes

ICLR 2025 Conference Submission10092 Authors

Keywords: game dynamics, system identification, model predictive control, sum of squares optimization, steering

Abstract: 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 agent responses to incentives from scarce data. MPC then leverages this model to implement adaptive incentive adjustments. Our experiments demonstrate the efficiency of SIAR-MPC in guiding systems towards socially optimal equilibria, stabilizing chaotic and cycling behaviors. Comparative analyses in data-scarce settings show SIAR-MPC's superior performance compared to pairing MPC with state-of-the-art alternatives like Sparse Identification of Nonlinear Dynamics (SINDy) and Physics Informed Neural Networks (PINNs).

Primary Area: learning on time series and dynamical systems

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Submission Number: 10092