Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We formalize and study the problem of learning the structure and parameters of graphical games from strictly behavioral data. We cast the problem as a maximum likelihood estimation based on a generative model defined by the pure-strategy Nash equilibria of the game. The formulation brings out the interplay between goodness-of-fit and model complexity: good models capture the equilibrium behavior represented in the data while controlling the true number of equilibria, including those potentially unobserved. We provide a generalization bound for maximum likelihood estimation. We discuss several optimization algorithms including convex loss minimization, sigmoidal approximations and exhaustive search. We formally prove that games in our hypothesis space have a small true number of equilibria, with high probability; thus, convex loss minimization is sound. We illustrate our approach, show and discuss promising results on synthetic data and the U.S. congressional voting records.