Network Learning in Quadratic Games from Fictitious Plays

We study the ability of an adversary learning the underlying interaction network from repeated fictitious plays in linear-quadratic games. The adversary may strategically perturb the decisions for a set of action-compromised players, and observe the sequential decisions from a set of action-leaked players. Then the question lies in whether such an adversary can fully re-construct, or effectively estimate the underlying interaction structure among the players. First of all, by drawing connections between this network learning problem in games and classical system identification theory, we establish a series of results characterizing the learnability of the interaction graph from the adversary's point of view. Next, in view of the inherent stability and sparsity constraints for the network interaction structure, we propose a stable and sparse system identification framework for learning the interaction graph from full player action observations. We also propose a stable and sparse subspace identification framework for learning the interaction graph from partially observed player actions. Finally, the effectiveness of the proposed learning frameworks is demonstrated in numerical examples.