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.

考虑从严格的行为数据中学习线性影响博弈 (LIGs) 的结构和参数，通过纯策略 Nash 平衡的最大似然估计 (MLE) 将学习问题转化为生成模型的估计，在控制平衡数量的同时捕捉数据中的均衡行为。该方法可以应用于识别大型 (社交) 网络中最有影响力的个体，并支持决策分析和其他普适性的图形游戏。

从行为数据中学习大规模群体图形化游戏的结构和参数