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CRISIS STABILITY

A GAME

A GAME--THEORETIC APPROACH

THEORETIC APPROACH

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SCHEDULE

• Structure of the game • Synthetic indexes

• Computation of the value of the game • Computation of the value of the game • Simulations

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SCHEDULE

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STRUCTURE OF THE GAME

• Two players: two nuclear powers

• Under crisis: game of opposed interests: zero-sum game

zero-sum game

• Framework: sequential decisions

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STRUCTURE OF THE GAME

Strategic form (BLUE’s decision tree)

V_BB

Launch attack

Launch

V

(B preempts)

A B

R Wait

Wait 0

Launch

attack VRR

δ_R (B is preempted)

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• δ

_B

= probability that B launches a first

strike to R (from R’s viewpoint)

• δ

= probability that R launches a first

STRUCTURE OF THE GAME Probabilities

• δ

_R

= probability that R launches a first

strike to B (from B’s viewpoint)

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• V_BB=(damage to RED inflicted in BLUE first strike)-(damage to BLUE inflicted in RED retaliation) = -V_RB

STRUCTURE OF THE GAME Values

RED retaliation) = -V_RB

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SCHEDULE

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STRUCTURE OF THE GAME Crisis: δ₌₁

V_BB

Launch attack

Launch

V

(B preempts)

A B

R Wait

Launch

attack VRR

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• Stress-testing of deterrence equilibrium

RB RR

BR BB

CS

V

I

=

−

=

−

SYNTHETIC INDEXES

Crisis stability (Chrzanowski)

• Stress-testing of deterrence equilibrium

• Valid under unusual or special

conditions of conflict

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BB RB SS BR BB CS V V I V V I − = = − = SYNTHETIC INDEXES Differing metrics (Canavan)

• I_cs: what will happened if preempted ?

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V_BB

Launch attack

(B preempts) STRUCTURE OF THE GAME

No crisis: δ₌₀

A B

R Wait

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)

V

,

V

(

max

I

_FB

=

_BB _RR

SYNTHETIC INDEXES Force balance (Chrzanowski)

• Long-run equilibrium

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SCHEDULE

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Optimization

First strike

R

OptimizationOptimization

V

Second strike

COMPUTATION OF THE VALUE Behavior: maximin optimization

A B

R Wait

strike

Second

Optimization

First

strike B

V_BB

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SLBM _SLBM

COMPUTATION OF THE VALUE Behavior: optimization of first strike

MAX for BLUE

ALBM

ICBM

ALBM

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Note: assets

• ICBM: InterContinental Ballistic Missiles (MIRVed)

• BLBM: Bomber Launched Ballistic • BLBM: Bomber Launched Ballistic

Missiles

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SLBM _SLBM

COMPUTATION OF THE VALUE Behavior: optimization of second strike

MIN for RED

ALBM

ICBM

ALBM

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{

p

h

,

k

1 ..

m

}

P

(i)

=

(_hi_,)_k

=

COMPUTATION OF THE VALUE Technology: kill probabilities

• Probability that weapon h owned by agent i will destroy weapon k

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      → 9 . 0 0 0 4 . 0 ICBM ets arg T SLBM ALBM ICBM RED

COMPUTATION OF THE VALUE Technology: kill probabilities

            = 0 0 0 0 ets arg T 8 . 0 0 0 3 . 0 SLBM 7 . 0 0 2 . 0 2 . 0 ALBM 9 . 0 0 0 4 . 0 ICBM

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[

(i)

]

s ) j ( s , k s ) j ( k ) i ( k , h ) i ( k ,

h

p

w

max

p

w

F

=

COMPUTATION OF THE VALUE Behavior: objective function (first strike)

• Impact of weapon h owned by i on weapon k, owned by j

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) j ( k ) i ( k , h ) i ( k ,

h

p

w

F

=

COMPUTATION OF THE VALUE

Behavior: objective function (second strike)

• Impact of weapon h owned by i on weapon k, owned by j

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SCHEDULE

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SLBM _SLBM

COMPUTATION OF THE VALUE Behavior: optimization of first strike

BLBM

ICBM

BLBM

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SLBM _SLBM

COMPUTATION OF THE VALUE Behavior: optimization of second strike

BLBM

ICBM

Interceptors

BLBM

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REFERENCES

Canavan, G.H. (1993) "Impact of differing metrics on crisis stability analysis", Los Alamos National Laboratory, Report LA-UR-93:3043. Canavan, G.H. (1992) "Evolution in strategic forces and doctrine", Los

Alamos National Laboratory, Report LA-12295-MS.

Canavan, G.H. and Teller, E. (1990) "Survivability and effectiveness of near-term strategic defense", Los Alamos National Laboratory,

Report LA-11345-MS.

Chrzanowski, P.L. (1985) "Strategic defense and crisis stability", Lawrence Livermore National Laboratory, Report UCID-20699. Chrzanowski, P.L. (1985) "Crisis stability during a transition to a Chrzanowski, P.L. (1985) "Crisis stability during a transition to a

deterrence posture reliant on defenses", Lawrence Livermore National Laboratory, Report UCID-20590.

Chrzanowski, P.L. (1988) "The transition to a deterrence posture more reliant on strategic defenses", Lawrence Livermore National

Laboratory, Report UCRL-99744.

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REFERENCES

Brams, S.J. and Kilgour, D.M. (1988) Game Theory and National Security, Basil Blackwell, New York, U.S.A.

Kent, G.A. and DeValk, R.J.(1986)"Strategic defenses and the transition to assured survival",RAND R-3369-AF.

Wilkening, D. and Watman, K. (1986)"Strategic defenses and first-strike Wilkening, D. and Watman, K. (1986)"Strategic defenses and first-strike