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A Game Theoretic Study of Attack and Defense in Cyber-Physical Systems Chris Y. T. Ma, Nageswara S. V. Rao, David K. Y. Yau Agenda Motivation System model Boolean attack and defense System with robustness Conclusion Motivation Cyber-physical systems Model a number of engineering infrastructure systems Physical – hardware components Cyber – computations, communications Susceptible to attacks Motivation Our objectives Use of game theoretic formulations to capture the attack and defense of cyber-physical systems Study the survival of the cyber-physical systems using different utility functions Motivation Our observations Pure strategy Nash Equilibrium (NE) may not exist Cost boundaries (budgets) may determine the NE outcome The presence of NE does not mean the system survives System Model System Model Boolean Attack and Defense Special case of attacks where the cyber and physical parts can be attacked or defended as whole units Successful attack on either cyber or physical part will disrupt the whole system Boolean Attack and Defense Boolean Attack and Defense System with Robustness General case when resources are not represented as one whole unit Consider different benefit functions System with Robustness System with Robustness The players’ best response functions General Benefit and Cost Functions General Benefit and Cost Functions One-space cases General Benefit and Cost Functions One-space cases Observation Pure strategy Nash Equilibrium is rare, most likely to exist when the attacker has tight budget General Benefit and Cost Functions Two-space cases General Benefit and Cost Functions Two-space cases Observations Resource allocation is non-trivial even without an attacker, and greedy approach may be sub-optimal, e.g., the S-shaped benefit function The NE results are sensitive to the parameters of the payoff functions in the two spaces General Benefit and Cost Functions Two-space cases Observations System A Cyber space: Ba Physical space: Ba NE: X System B Cyber space: Bb Physical space: Bb NE: X System C Cyber space: Ba Physical space: Bb NE: ? Conclusions Presented a game theoretic formulation of the interplay between a rational attacker and a rational defender in cyber-physical system security Studied the presence (or absence) of pure strategy Nash Equilibrium using different payoff functions