We consider learning, from strictly behavioral data, the structure andparameters of linear influence games (LIGs), a class of parametric graphicalgames introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategicinference (CSI): Making inferences from causal interventions on stable behaviorin strategic settings. Applications include the identification of the mostinfluential individuals in large (social) networks. Such tasks can also supportpolicy-making analysis. Motivated by the computational work on LIGs, we castthe learning problem as maximum-likelihood estimation (MLE) of a generativemodel defined by pure-strategy Nash equilibria (PSNE). Our simple formulationuncovers the fundamental interplay between goodness-of-fit and modelcomplexity: good models capture equilibrium behavior within the data whilecontrolling the true number of equilibria, including those unobserved. Weprovide a generalization bound establishing the sample complexity for MLE inour framework. We propose several algorithms including convex loss minimization(CLM) and sigmoidal approximations. We prove that the number of exact PSNE inLIGs is small, with high probability; thus, CLM is sound. We illustrate ourapproach on synthetic data and real-world U.S. congressional voting records. Webriefly discuss our learning framework's generality and potential applicabilityto general graphical games.
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