1. A Game Theoretic Study of Attack and Defense in Cyber-Physical Systems
Chris Y. T. Ma, Nageswara S. V. Rao, David K. Y. Yau

2. Agenda Motivation System model Boolean attack and defense
System with robustness
Conclusion

3. Motivation Cyber-physical systems
Model a number of engineering infrastructure systems
Physical – hardware components
Cyber – computations, communications
Susceptible to attacks

4. 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

5. 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

6. System Model

7. System Model

8. 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

9. Boolean Attack and Defense

10. Boolean Attack and Defense

11. System with Robustness
General case when resources are not represented as one whole unit
Consider different benefit functions

12. System with Robustness

13. System with Robustness
The players’ best response functions

14. General Benefit and Cost Functions

15. General Benefit and Cost Functions One-space cases

16. 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

17. General Benefit and Cost Functions Two-space cases

18. 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

19. General Benefit and Cost Functions Two-space cases
Observations
System A
Cyber space: Ba
Physical space: Ba
NE: X
System C
Cyber space: Ba
Physical space: Bb
NE: ?
System B
Cyber space: Bb
Physical space: Bb
NE: X

20. 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