Defending Complex System Against External Impacts Gregory Levitin (IEC, UESTC)

1. Defending Complex System Against External ImpactsGregory Levitin (IEC, UESTC)

2. Game Theory vs. Reliability • Risk arises from technology, nature, humans. • Conventional reliability and risk analysis assume play against static, fixed and immutable factors which are exogenously given. • Intentionality plays increasing role (9/11, terrorists’ attacks). • Game theory assumes play against adaptable, strategic, optimizing, dynamic agents. Need for combining reliability & risk analysis with game theory

3. Game Information Player 1 action xX Player 2 action yY System Payoff: P(x,y)

4. Five Elements of a Game:The players-how many players are there? -does nature/chance play a role? *A complete description of what the players can do – the set of all possible actions (strategies). *The information that players have available when choosing their actions *A description of the payoff consequences for each player for every possible combination of actions chosen by all players playing the game. *A description of all players’ preferences over payoffs

5. System Defender Attacker Expected Damage Strategies Strategies Payoff Payoff

6. Pr{w>W*} S(W*) w W* Survivable system - system that is able to “complete its mission in a timely manner, even if significant portions are incapacitated by attack or accident”. Multi-state system with different performance rates Reliability + vulnerability analysis

7. Multi-state System Combination of Elements G System performance

8. Two types of functional damage assessment Damage proportional to the loss of demand probability Damage proportional to the unsupplied demand D D No damage No damage Demand Demand Damage Damage P P Bridge, Voltage protection Production line, Power generator

9. Performance redundancy System without performance redundancy System with performance redundancy x x Demand No damage Demand Damage System performance System performance Damage Pr(Gx) Pr(Gx)

10. System Defender Attacker Expected Damage Strategies Strategies Payoff Payoff

11. System survivability enhancement by element separation

12. S R=Pr( w>W*) Optimal element separation problem wq ... v q

13. 11 12 13 14 15 16 PARAMETERS OF SYSTEM ELEMENTS 1 8 6 2 9 3 7 4 10 5

14. OPTIMAL SEPARATION SOLUTION FOR v=0.05 11 15 2 8 6 3 13 9 14 1 7 4 10 12 5 16

15. System survivability enhancement by element protection

16. S R=Pr( w>W*) Survivability optimization problem wqc vc ... v q

17. Functional scheme of system List of available elements with given performance distributions List of chosen elements Separation and protection of elements Survivability and cost of possible protections Desired system performance and survivability W, S* Optimal system structure

18. System survivability enhancement by deploying false targets Limited resource No information

19. Defense strategy Separation Damage g Destruction probability Protection v False targets Impact probability p Disinformation

20. System Defender Attacker Expected Damage Strategies Strategies Payoff Payoff

21. Attacker vs. Disaster Impact resources Limited Unlimited Impact direction Strategic (optimal) Random

22. Single attack strategy p=1/N p p Perfect knowledge about the system and ability of impact direction p=1 No knowledge about the system or inability of impact direction Imperfect knowledge about the system p Spi=1

23. Multiple attack strategy with different attack options

24. Vulnerability (destruction probability) as function of actions’ combination Set of attacker’s actions Set of defender’s actions

25. Game with unconstrained resources (non-zero sum game) Attacker’s utility Defender’s losses Losses: d+r min Expected damage: D Defense cost: r Attack cost: R Expected damage: d R r Utility: D-R max

26. Human lives vs. defense budget dilemma Defender’s losses Political decisions Expected damage r Losses Defense cost Constrained Problem r

27. Game with constrained resources (zero sum game) max D min Expected damage: D( attacker’s resource allocation, R defender’s resource allocation) r The resources are almost always constrained (defense budgets etc.)

28. Two period game Defender X:D(X,Y(X))min Attacker Y(X): D(X,Y) max Defender moves first (builds the system over time) MINMAX:

29. R2 R3 R4 R6 R1 R5 R7 Simple analytical models Insight, General recommendations Specific solutions Complex models

30. Importance of protections 1 1 4 8 6 6 11 10 9 15 2 2 12 7 5 16 3 13 10 8 4 9 11 7 17 14 5 3 Single attack with no knowledge Single attack with perfect knowledge Unlimited multiple attacks

31. Example of optimal defense strategies 1 1 4 8 6 6 11 10 9 15 2 2 12 7 5 16 3 13 10 4 8 9 11 3 7 17 14 5 Expected damage Multiple attacks Single attack with perfect knowledge Single attack with no knowledge Defense budget

32. = = Protection vs. separation D=gpv v g

33. = Protection vs. Redundancy (separated elements) Vsyst=vN v N =

34. = = Redundancy with partial protection D=dpv v v

35. Attack on a subset of targets D=gpv p v p v

36. Protection vs. deployment of false targets Single element D=gpv v v p v p

37. Other topics studied • Preventive strike vs. defense • Dynamic (stockpiling) resources • Intelligence vs. attack strength • Imperfect false targets • Double attack strategies • Protection against attacks and disasters • Multiple consecutive attacks

38. levitin@iec.co.illevitin_g@yahoo.com • Additional information • Further research • Related papers • Collaboration