Security investment of interdependent and identical CPSs: Stochastic games with asymmetric information

Abstract

This paper considers remote state estimation in cyber‐physical systems (CPSs) with multiple sensors, where measurements of each sensor are transmitted to the corresponding remote estimator over a shared communication network with interdependent security. A stochastic non‐cooperative game framework with asymmetric information is provided, in which each sensor is in pursuit of minimizing the security investment cost on the first stage associated with the expected error covariance as small as possible at the corresponding remote estimator on the second stage. The asymmetry of information among sensors poses a challenge to characterize or compute the Nash equilibria (NE). To overcome the challenge, based on the common information among sensors, the game with asymmetric information is transformed into another game with symmetric information such that a subclass of NE refer to common information based Markov perfect equilibria of the original game can be achieved by using a backward induction algorithm. Finally, a numerical example is presented to verify the obtained results.