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

Iosif Sakos; Antonios Varvitsiotis; Georgios Piliouras

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arXiv · 2307.06640

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

Iosif Sakos·Antonios Varvitsiotis·Georgios Piliouras

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Abstract

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.

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BibTeX RIS

Iosif Sakos, Antonios Varvitsiotis, Georgios Piliouras. 2023-07-13. Data-Scarce Identification of Game Dynamics via Sum-of-Squares Optimization. https://arxiv.org/abs/2307.06640

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