Data-Scarce Identification of Game Dynamics via Sum-of-Squares Optimization

Understanding how players adjust their strategies in games, based on their experience, is a crucial tool for policymakers. It enables them to forecast the system's eventual behavior, exert control over the system, and evaluate counterfactual scenarios. The task becomes increasingly difficult when only a limited number of observations are available or difficult to acquire. In this work, we introduce the Side-Information Assisted Regression (SIAR) framework, designed to identify game dynamics in multiplayer normal-form games only using data from a short run of a single system trajectory. To enhance system recovery in the face of scarce data, we integrate side-information constraints into SIAR, which restrict the set of feasible solutions to those satisfying game-theoretic properties and common assumptions about strategic interactions. SIAR is solved using sum-of-squares (SOS) optimization, resulting in a hierarchy of approximations that provably converge to the true dynamics of the system. We showcase that the SIAR framework accurately predicts player behavior across a spectrum of normal-form games, widely-known families of game dynamics, and strong benchmarks, even if the unknown system is chaotic.