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Cyber–Physical Correlation Effects in Defense Games for Large Discrete Infrastructures

Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Hang Seng Management College, Hong Kong, China
The Department of Mechanical and Industrial Engineering, Texas A&M University, Kingsville, TX 78363, USA
Department of Computer Science, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
Department of Industrial and Systems Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
Author to whom correspondence should be addressed.
Games 2018, 9(3), 52;
Received: 1 June 2018 / Revised: 12 July 2018 / Accepted: 20 July 2018 / Published: 23 July 2018
(This article belongs to the Special Issue Game Models for Cyber-Physical Infrastructures)
PDF [670 KB, uploaded 23 July 2018]


In certain critical infrastructures, correlations between cyber and physical components can be exploited to launch strategic attacks, so that disruptions to one component may affect others and possibly the entire infrastructure. Such correlations must be explicitly taken into account in ensuring the survival of the infrastructure. For large discrete infrastructures characterized by the number of cyber and physical components, we characterize the cyber–physical interactions at two levels: (i) the cyber–physical failure correlation function specifies the conditional survival probability of the cyber sub-infrastructure given that of the physical sub-infrastructure (both specified by their marginal probabilities), and (ii) individual survival probabilities of both sub-infrastructures are characterized by first-order differential conditions expressed in terms of their multiplier functions. We formulate an abstract problem of ensuring the survival probability of a cyber–physical infrastructure with discrete components as a game between the provider and attacker, whose utility functions are composed of infrastructure survival probability terms and cost terms, both expressed in terms of the number of components attacked and reinforced. We derive Nash equilibrium conditions and sensitivity functions that highlight the dependence of infrastructure survival probability on cost terms, correlation functions, multiplier functions, and sub-infrastructure survival probabilities. We apply these analytical results to characterize the defense postures of simplified models of metro systems, cloud computing infrastructures, and smart power grids. View Full-Text
Keywords: networked systems; cyber–physical infrastructures; aggregated correlations functions; sum-form, product-form, and composite utility functions networked systems; cyber–physical infrastructures; aggregated correlations functions; sum-form, product-form, and composite utility functions

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Rao, N.S.V.; Ma, C.Y.T.; He, F.; Yau, D.K.Y.; Zhuang, J. Cyber–Physical Correlation Effects in Defense Games for Large Discrete Infrastructures. Games 2018, 9, 52.

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