Learning Graphical Games from Behavioral Data: Sufficient and Necessary Conditions
This provides theoretical guarantees for learning game structures from data, which is incremental but important for applications in economics and multi-agent systems.
The paper tackles the problem of recovering the pure-strategy Nash equilibria set of graphical games from noisy behavioral data, showing that O(k^2 log n) samples are sufficient and Ω(k log n) samples are necessary for exact recovery in sparse linear influence games.
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.