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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
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Motivation
System model
Boolean attack and defense
System with robustness
Conclusion
Motivation
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Cyber-physical systems
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Model a number of engineering infrastructure systems
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Physical – hardware components
Cyber – computations, communications
Susceptible to attacks
Motivation
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Our objectives
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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
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Our observations
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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
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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
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General case when resources are not
represented as one whole unit
Consider different benefit functions
System with Robustness
System with Robustness
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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
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Observation
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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
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Observations
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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
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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
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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