Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions

Abstract

In this paper we obtain sufficient and necessary conditions on the number of samples required for exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions. We consider sparse linear influence games --- a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We show that one can efficiently recover the PSNE set of a linear influence game with $O(k^2\log n)$ samples, under very general observation models. On the other hand, we show that $\Omega (k\log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.

Accepted to AISTATS 2017, Florida. arXiv admin note: substantial text overlap with arXiv:1607.02959

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