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

1
Defending Complex System Against External
ImpactsGregory Levitin (IEC, UESTC)
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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)
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Five Elements of a GameThe
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
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System
Attacker
Defender
Expected Damage
Strategies
Strategies
Payoff
Payoff
6
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
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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
Production line, Power generator
Bridge, Voltage protection
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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)
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System
Attacker
Defender
Expected Damage
Strategies
Strategies
Payoff
Payoff
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System survivability enhancement by element
separation
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Optimal element separation problem
wq
...
v
q
13
PARAMETERS OF SYSTEM ELEMENTS
1
8
6
2
9
3
7
4
10
5
14
OPTIMAL SEPARATION SOLUTION FOR v0.05
11
15
2
8
6
3
13
9
14
1
7
4
10
12
5
16
15
System survivability enhancement by element
protection
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Survivability optimization problem
wqc
vc
...
q
v
17
Optimal system structure
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System survivability enhancement by deploying
false targets
Limited resource No information
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Defense strategy
Damage
g
Destruction probability
Protection
v
False targets
Impact probability
p
Disinformation
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System
Attacker
Defender
Expected Damage
Strategies
Strategies
Payoff
Payoff
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Attacker vs. Disaster
Impact resources Limited
Unlimited
Impact direction Strategic
(optimal)
Random
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Single attack strategy
Perfect knowledge about the system and ability of
impact direction
p1
No knowledge about the system or inability of
impact direction
Imperfect knowledge about the system
p
Spi1
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Multiple attack strategy with different attack
options
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Vulnerability (destruction probability) as
function of actions combination
Set of attackers actions
Set of defenders actions
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Game with unconstrained resources (non-zero sum
game)
Attackers utility
Defenders losses
Losses dr min
Expected damage D
Defense cost r
Attack cost R
Expected damage d
R
r
Utility D-R max
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Human lives vs. defense budget dilemma
Defenders losses
Political decisions
Expected damage
r
Losses
Defense cost
Constrained Problem
r
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Game with constrained resources (zero sum game)
max
D
min
Expected damage D( attackers
resource allocation, R
defenders resource allocation) r
The resources are almost always constrained
(defense budgets etc.)
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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
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Simple analytical models
Insight,
General recommendations
Specific solutions
Complex models
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Importance of protections
1
1
4
8
6
6
11
10
9
15
2
2
12
7
5
16
3
13
10
4
8
9
11
7
17
14
5
3
Single attack with perfect knowledge
Single attack with no knowledge
Unlimited multiple attacks
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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
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Protection vs. separation
Dgpv
v
g
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Protection vs. Redundancy (separated elements)
VsystvN
v
N

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Redundancy with partial protection
Ddpv
v
v
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Attack on a subset of targets
Dgpv
p
v
p
v
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Protection vs. deployment of false targets Single
element
Dgpv
v
v
p
p
v
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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

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levitin_at_iec.co.illevitin_g_at_yahoo.com

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