Security Investment in Cyber-Physical Systems: Stochastic Games With Asymmetric Information and Resource-Constrained Players

This article considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors. Each plant is modeled by a discrete-time stochastic linear system with measurements of each sensor transmitted to the corresponding remote estimator over a shared communication network when their securities are interdependent due to network-induced risks. A dynamic nonzero-sum game with asymmetric information is formulated in which each sensor subject to a resource budget constraint needs to decide whether to invest in security for sending data packets, taking the behaviors of other sensors into account. To overcome the difficulty in characterizing or computing the Nash equilibria (NE), the game with asymmetric information is transformed into another game with symmetric information such that the equilibrium of the original game can be obtained by solving the equilibrium of the new game. Under certain conditions, we devise a backward induction algorithm to obtain a subclass of NE of the original game, known as common information-based Markov perfect equilibria (CIBMPE). Finally, a numerical example is provided to illustrate the results obtained.