AISTATS 2017poster17 citations

Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions

Asish Ghoshal, Jean Honorio

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 $Ω(k \log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.

BibTeX
@InProceedings{pmlr-v54-ghoshal17b,
  title = 	 {{Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions}},
  author = 	 {Ghoshal, Asish and Honorio, Jean},
  booktitle = 	 {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1532--1540},
  year = 	 {2017},
  editor = 	 {Singh, Aarti and Zhu, Jerry},
  volume = 	 {54},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {20--22 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v54/ghoshal17b/ghoshal17b.pdf},
  url = 	 {https://proceedings.mlr.press/v54/ghoshal17b.html},
  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 $Ω(k \log n)$ samples are necessary for any procedure to recover the PSNE set from observations of joint actions.}
}
Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions · AISTATS 2017