Iran’s Nuclear
Programme
A U.S. “promise” strategy to
discourage a preemptive Israeli
strike
Fundamentals of the game

Players:
• Policymakers in the Netanyahu administration
(”Israel”)
• Policymakers in the Obama administration
(”the US”)

Game:
• Whether and when to conduct a military strike
against Iran to disrupt its possible nuclear
weapons program
• The US wants Israel to wait for sanctions to be
given a chance to work on Iran, and will
employ a strategic move to achieve this goal
Assumptions


Israel, not the US, will lead in a
strike on Iran
Both the US and Israel prefer a
peaceful outcome
Incomplete information

Israel uncertain about Iran’s ’type’
• ”sanctions-work type” (probability p)
• ”sanctions-fail type” (probability 1-p)

Depending on Israel’s beliefs about
value of p, Israel will decide to attack
Iran now, or wait for sanctions to
work (”Attack now”; ”Wait”)
Moves




Nature selects Iran’s type: ”sanctions-work”
or ”sanctions-fail”
Israel decides whether to attack now, or wait
for sanctions to work
If Israel decides to attack now, US decides
whether or not to join in the attack
If Israel decides to wait, and Iran is of type
”sanctions-fail,” Israel has to decide whether
to attack after a delay or to capitulate to Iran
• If attack, the US must decide whether to join
The Game Tree
Nature
Sanctions Work (p)
Sanctions Don’t Work (1-p)
Israel
Attack
Wait
USA
Wait (Iran moving to
get the bomb)
Attack
USA
Israel
USA
Attack
Join
Don’t
Join
Wait
Join
Don’t
Join
Capitulate
USA
Join
Don’t
Join
Israel: Preferences






Value of a peaceful outcome in which sanctions
work: 10
Base cost of attacking Iran: -5
Benefit if the US joins the attack: 4
Cost of giving Iran time to prepare, if the US
does not join the attack: -3
Cost of giving Iran time to prepare, if the US
joins the attack: -1
Cost of capitulation and a nuclear Iran: -10
Israel: Possible payoffs

Israel does not attack and sanctions work: 10

Israel attacks now and the US does not join: -5

Israel attacks now and the US joins: -1

Sanctions fail, Israel attacks after a wait, and the
US does not join: -8
• Israel forgoes US participation bonus and pays the
higher wait penalty

Sanctions fail, Israel attacks after a wait, and the
US joins: -2
• Israel enjoys US participation bonus and pays the lower
wait penalty

Sanctions fail and Israel capitulates: -10
US: Preferences







Value of a peaceful outcome in which sanctions
work: 10
Base cost of Israeli attack on Iran: 0
Cost of joining the attack: -3
Cost to US interests of giving Iran time to prepare
for an Israeli strike, if the US does not join the
attack: -2
Cost to US interests of giving Iran time to prepare
for an Israeli strike, if the US joins the attack: -1
Cost of capitulation and a nuclear Iran: -10
Note: It is appropriate to think of the US payoffs as ”Israeli beliefs
about US payoffs.”
US: Possible payoffs

Israel does not attack and sanctions work: 10

Israel attacks now and the US does not join: 0

Israel attacks now and the US joins: -3

Sanctions fail, Israel attacks after a wait, and the
US does not join: -2
• US pays the higher wait penalty

Sanctions fail, Israel attacks after a wait, and the
US joins: -4
• Israel pays the lower wait penalty and the cost of joining

Sanctions fail and Israel capitulates: -10
Game Tree before US strategic move
Nature
Sanctions Work (p)
Sanctions Don’t Work (1-p)
Israel
Attack
Wait
USA
Wait (Iran moving to
get the bomb)
Attack
USA
Israel
USA
Attack
Join
Don’t
Join
Don’t
Join
Join
Wait
Capitulate
USA
Join
Don’t
Join
Israel:
-1
-5
10
-1
-5
-2
-8
-10
USA:
-3
0
10
-3
0
-4
-2
-10
Israel expected values
Expected value of attack: -5
 Expected value of wait:
(p)(10) + (1-p)(-8) = 18p - 8

Given these payoffs, Israel will attack now if
it believes p is such that -5 > 18p – 8.
Israel will attack now if p < 3/18 = 16.7%.
The US commitment strategy




The US wants sanctions to be given a chance to
work: it wants to reduce the p value that incites
Israel to attack now
Obama: ”Over the last three years, as President
of the United States, I have kept my
commitments to the state of Israel. There should
not be a shred of doubt by now: when the chips
are down, I have Israel’s back.” March 4. 2012
Publicly announcing US’s committment to join
Israel in an attack adds a cost to the US (Obama)
of staying out of an Israeli attack on Iran.
Cost to the US of breaking promise: -4
Game Tree after US Commitment
Nature
Sanctions Work (p)
Sanctions Don’t Work (1-p)
Israel
Attack
Wait
USA
Wait (Iran moving to
get the bomb)
Attack
USA
Israel
USA
Attack
Join
Don’t
Join
Join
Wait
Don’t
Join
Capitulate
USA
Join
Don’t
Join
Israel:
-1
-4
10
-1
-4
-2
-8
-10
USA:
-3
-4
10
-3
-4
-4
-6
-10
Israel expected values after US
commitment
Expected value of attack: -1
 Expected value of wait:
(p)(10) + (1-p)(-2) = 12p -2

Israel will attack now if it believes p is
such that -1 > 12p – 2.
Israel will attack if p < 1/12 = 8.3%.
Effects of the commitment strategy


Given the payoffs modeled here,
Israel will now give sanctions a
chance for p > 8.3%, not p > 16.7%
That is, a ”more skeptical Israel” will
now give sanctions a chance
Back Up Slides
The Math




Players: “Israel” (Israeli policymakers—Netanyahu
administration), “US” (US policymakers—Obama
administration)
Regardless of Iran’s type, if Israel attacks now and the US
doesn’t join, the two countries will get payoffs:
Israel: AI; US: AUS
If Israel attacks now and the US joins, Israel will enjoy the
benefits of US support (TI), and US policymakers will suffer
being dragged into a war reminiscent of Iraq (TUS).
For Israel: TI > AI;
For US: TUS < AUS.
The best outcome for both countries is if Israel gives
sanctions time to work, and they do indeed work (Iran
abandons its nuclear program):
Israel: BI = MAXI;
US: BUS = MAXUS
The Math


The worst outcome for both countries is if Israel gives
sanctions time to work, then neglects to attack after
sanctions fail, allowing Iran to develop nuclear weapons:
Israel: XI = MINI; US: XUS = MINUS
If Israel gives sanctions time to work, sanctions fail, and
Israel attacks Iran, both Israel and the US will pay some
penalty for having waited (W1, W2).
Israel: TI + W1I OR AI + W2I;
US: TUS + W1US OR AUS + W2US; W1I, W2I, W1US, W2US < 0


Israel’s penalty will be greater if it is forced to attack alone
than if the US joins.
W1I > W2I; |W2I| > |W1I|
The US will still prefer to stay out of an Israeli attack:
TUS + W1US < AUS + W2US
The Math


The commitment mechanism: Obama’s public
commitment to support Israel in a strike on Iran, that
“We’ve got Israel’s back.” Contradicting this statement by
failing to support Israel should it attack Iran would carry a
cost C for the Obama administration, whether Israel attacks
now or later:
US: AUS + CUS OR AUS + W2US + CUS; CUS < 0
This makes staying out of an Israeli attack more costly than
joining:
US: TUS > AUS + CUS;
TUS + W1US > AUS + W2US + CUS
The Math



Israel’s expected payoffs without the US promise:
E[Wait] = p(B) + (1-p)(AI + W2I);
E[Attack] = AI
Israel’s expected payoff if it attacks, with the US promise:
E[Wait] = p(B) + (1-p)(TI + W1I);
E[Attack] = TI
Extent to which US promise improves Israel’s expected
payoffs:
E[Wait] = (1-p)((TI - AI) + (W1I - W2I));
E[Attack] = TI - AI
Game Tree before US Commitment
Nature
Sanctions Work (p)
Sanctions Don’t Work (1-p)
Israel
Israel
Attack
Wait
USA
Wait (Iran moving to
get the bomb)
Attack
USA
Israel
USA
Attack
Join
Don’t
Join
Join
Wait
Don’t
Join
Capitulate
USA
Join
Don’t
Join
Israel: TIsrael
AIsrael
BIsrael
TIsrael
AIsrael
TIsrael + W1Israel AIsrael + W2Israel XIsrael
USA:
AUS
BUS
TUS
AUS
TUS + W1US
TUS
AUS + W2US
XUS
Game Tree with US Commitment
Nature
Sanctions Work (p)
Sanctions Don’t Work (1-p)
Israel
Israel
Attack
Wait
USA
Wait (Iran moving to
get the bomb)
Attack
USA
Israel
USA
Attack
Join
Don’t
Join
Join
Wait
Don’t
Join
Capitulate
USA
Join
Don’t
Join
Israel: TIsrael
AIsrael
BIsrael
TIsrael
AIsrael
TIsrael + W1Israel AIsrael + W2Israel XIsrael
USA:
AUS + CUS
BUS
TUS
AUS + CUS
TUS + W1US
TUS
AUS + W2US +CUS XUS
Effects of the commitment strategy



General effects (not specific to payoffs
modeled here):
1. Attacking now is more attractive for Israel
2. Failure of sanctions is less unattractive:
US involvement cuts wait penalty
Whether commitment strategy succeeds or
fails depends on three Israeli variables: size
of wait-penalty difference (W), US
participation bonus (B), and p
US commitment reduces Israel’s propensity
to attack if: (1-p)(W) > (p)(B)