Non-equilibrium dynamic games and cyber–physical security: A cognitive hierarchy approach

Abstract

This paper considers the problem of identifying the cognitive capabilities of agents having bounded rationality in a cyber–physical system operating in an uncertain and/or adversarial environment. To categorize the adversaries, we introduce an iterative method of optimal responses that determine the policy of an agent with a level-k intelligence. We then, formulate a model-free learning algorithm to train the different intelligence levels without any knowledge about the physics of the system while quantifying the optimality. By sequential interaction with the adversaries, we learn the true distribution of their levels. Rigorous mathematical proofs show stability of the equilibrium point of the closed-loop system and convergence to the Nash equilibrium as the level of intelligence tends to infinity. Finally, simulation results show the efficacy of our proposed approach.