Iran’s Nuclear ProgrammeIran’s Nuclear Programme

A U A U.S..S. ““promise” strategy to promise” strategy to discourage a preemptive Israeli discourage a preemptive Israeli

strike strike

Fundamentals of the gameFundamentals of the game Players:Players:

• Policymakers in the Netanyahu Policymakers in the Netanyahu administration (”Israel”)administration (”Israel”)

• Policymakers in the Obama administration Policymakers in the Obama administration (”the US”)(”the US”)

Game:Game:• Whether and when to conduct a military Whether and when to conduct a military strike against Iran to disrupt its strike against Iran to disrupt its possible nuclear weapons programpossible nuclear weapons program

• The US wants Israel to wait for sanctions The US wants Israel to wait for sanctions to be given a chance to work on Iran, and to be given a chance to work on Iran, and will employ a strategic move to achieve will employ a strategic move to achieve this goalthis goal

AssumptionsAssumptions

Israel, not the US, will lead Israel, not the US, will lead in a strike on Iranin a strike on Iran

Both the US and Israel prefer a Both the US and Israel prefer a peaceful outcomepeaceful outcome

Incomplete informationIncomplete information

Israel uncertain about Iran’s ’type’Israel uncertain about Iran’s ’type’• ””sanctions-work type” (probability p)sanctions-work type” (probability p)• ””sanctions-fail type” (probability 1-p)sanctions-fail type” (probability 1-p)

Depending on Israel’s beliefs about Depending on Israel’s beliefs about value of value of pp, Israel will decide to , Israel will decide to attack Iran now, or wait for attack Iran now, or wait for sanctions to work (”Attack now”; sanctions to work (”Attack now”; ”Wait”)”Wait”)

MovesMoves Nature selects Iran’s type: Nature selects Iran’s type: ”sanctions-work” or ”sanctions-fail””sanctions-work” or ”sanctions-fail”

Israel decides whether to attack now, Israel decides whether to attack now, or wait for sanctions to workor wait for sanctions to work

If Israel decides to attack now, US If Israel decides to attack now, US decides whether or not to join in the decides whether or not to join in the attackattack

If Israel decides to wait, and Iran is If Israel decides to wait, and Iran is of type ”sanctions-fail,” Israel has of type ”sanctions-fail,” Israel has to decide whether to attack after a to decide whether to attack after a delay or to capitulate to Irandelay or to capitulate to Iran• If attack, the US must decide whether If attack, the US must decide whether to jointo join

Nature

Israel

Sanctions Work (p) Sanctions Don’t Work (1-p)

Attack AttackWait Wait (Iran moving to get the bomb)

Join JoinDon’tJoin

Don’tJoin

JoinDon’tJoin

CapitulateWait

USA USA USA

USA

Attack

Israel

The Game Tree

Israel: PreferencesIsrael: Preferences Value of a peaceful outcome in which Value of a peaceful outcome in which sanctions work: sanctions work: 1010

Base cost of attacking Iran: Base cost of attacking Iran: -5-5 Benefit if the US joins the attack: Benefit if the US joins the attack: 44 Cost of giving Iran time to prepare, Cost of giving Iran time to prepare, if if the US does not join the attackthe US does not join the attack: : -3-3

Cost of giving Iran time to prepare, Cost of giving Iran time to prepare, if if the US joins the attackthe US joins the attack: : -1-1

Cost of capitulation and a nuclear Iran: Cost of capitulation and a nuclear Iran: --1010

Israel: Possible payoffsIsrael: Possible payoffs Israel does not attack and sanctions work: Israel does not attack and sanctions work: 1010

Israel attacks now and the US does not Israel attacks now and the US does not join: join: -5 -5

Israel attacks now and the US joins: Israel attacks now and the US joins: -1-1 Sanctions fail, Israel attacks after a Sanctions fail, Israel attacks after a wait, and the US does not join: wait, and the US does not join: -8-8• Israel forgoes US participation bonus Israel forgoes US participation bonus andand pays pays the higher wait penaltythe higher wait penalty

Sanctions fail, Israel attacks after a Sanctions fail, Israel attacks after a wait, and the US joins: wait, and the US joins: -2-2• Israel enjoys US participation bonus Israel enjoys US participation bonus andand pays pays the lower wait penaltythe lower wait penalty

Sanctions fail and Israel capitulates: Sanctions fail and Israel capitulates: -10-10

US: PreferencesUS: Preferences Value of a peaceful outcome in which sanctions Value of a peaceful outcome in which sanctions work: work: 1010

Base cost of Israeli attack on Iran: Base cost of Israeli attack on Iran: 00 Cost of joining the attack: Cost of joining the attack: -3-3 Cost to US interests of giving Iran time to Cost to US interests of giving Iran time to prepare for an Israeli strike, prepare for an Israeli strike, if the US does not if the US does not join the attackjoin the attack: : -2-2

Cost to US interests of giving Iran time to Cost to US interests of giving Iran time to prepare for an Israeli strike, prepare for an Israeli strike, if the US joins the if the US joins the attackattack: : -1-1

Cost of capitulation and a nuclear Iran: Cost of capitulation and a nuclear Iran: -10-10

Note: It is appropriate to think of the US payoffs as ”Israeli Note: It is appropriate to think of the US payoffs as ”Israeli beliefs about US payoffs.”beliefs about US payoffs.”

US: Possible payoffsUS: Possible payoffs Israel does not attack and sanctions work: Israel does not attack and sanctions work: 1010 Israel attacks now and the US does not join: Israel attacks now and the US does not join: 0 0

Israel attacks now and the US joins: Israel attacks now and the US joins: -3-3 Sanctions fail, Israel attacks after a wait, Sanctions fail, Israel attacks after a wait, and the US does not join: and the US does not join: -2-2• US pays the higher wait penaltyUS pays the higher wait penalty

Sanctions fail, Israel attacks after a wait, Sanctions fail, Israel attacks after a wait, and the US joins: and the US joins: -4-4• Israel pays the lower wait penalty and the cost of Israel pays the lower wait penalty and the cost of joiningjoining

Sanctions fail and Israel capitulates: Sanctions fail and Israel capitulates: -10-10

Nature

Israel

Sanctions Work (p) Sanctions Don’t Work (1-p)

Attack AttackWait Wait (Iran moving to get the bomb)

Join JoinDon’tJoin

Don’tJoin

JoinDon’tJoin

CapitulateWait

USA USA USA

USA

Attack

Israel:

USA:

-1

-3

-5

0

10

10

-1

-3

-5

0

-2

-4

-8

-2

-10

-10

Israel

Game Tree before US strategic move

Israel expected valuesIsrael expected values

Expected value of attack: Expected value of attack: -5-5 Expected value of wait:Expected value of wait:

(p)(10) + (1-p)(-8) = (p)(10) + (1-p)(-8) = 18p - 818p - 8

Given these payoffs, Israel will Given these payoffs, Israel will attack now if it believes p is such attack now if it believes p is such that -5 > 18p – 8.that -5 > 18p – 8.

Israel will attack now if p < 3/18 = Israel will attack now if p < 3/18 = 16.7%16.7%..

The US commitment strategyThe US commitment strategy The US wants sanctions to be given a chance to The US wants sanctions to be given a chance to work: it wants to work: it wants to reducereduce the p value that the p value that incites Israel to attack nowincites Israel to attack now

Obama: Obama: ”Over the last three years, as President ”Over the last three years, as President of the United States, I have kept my commitments of the United States, I have kept my commitments to the state of Israel. There should not be a to the state of Israel. There should not be a shred of doubt by now: shred of doubt by now: when the chips are down, when the chips are down, I have Israel’s back.”I have Israel’s back.” March 4. 2012 March 4. 2012

Publicly announcing US’s committment to join Publicly announcing US’s committment to join Israel in an attack Israel in an attack adds a cost to the US adds a cost to the US (Obama)(Obama) of staying out of an Israeli attack on of staying out of an Israeli attack on Iran.Iran.

Cost to the US of breaking promise: Cost to the US of breaking promise: -4-4

Nature

Israel

Sanctions Work (p) Sanctions Don’t Work (1-p)

Attack AttackWait Wait (Iran moving to get the bomb)

Join JoinDon’tJoin

Don’tJoin

JoinDon’tJoin

CapitulateWait

USA USA USA

USA

Attack

Israel:

USA:

-1

-3

-4

-4

10

10

-4

-4

-2

-4

-8

-6

-10

-10

Israel

Game Tree after US Commitment

-1

-3

Israel expected values after US Israel expected values after US commitmentcommitment

Expected value of attack: Expected value of attack: -1-1 Expected value of wait:Expected value of wait:

(p)(10) + (1-p)(-2) = (p)(10) + (1-p)(-2) = 12p -212p -2

Israel will attack now if it Israel will attack now if it believes p is such that -1 > 12p – believes p is such that -1 > 12p – 2.2.

Israel will attack if p < 1/12 = Israel will attack if p < 1/12 = 8.3%8.3%..

Effects of the commitment strategyEffects of the commitment strategy

Given the payoffs modeled here, Given the payoffs modeled here, Israel will now give sanctions Israel will now give sanctions a chance for a chance for p > 8.3%p > 8.3%, not , not p > p > 16.7%16.7%

That is, a ”more skeptical That is, a ”more skeptical Israel” will now give sanctions Israel” will now give sanctions a chancea chance

Back Up SlidesBack Up Slides

The MathThe Math Players:Players: “Israel” (Israeli policymakers—Netanyahu “Israel” (Israeli policymakers—Netanyahu

administration), “US” (US policymakers—Obama administration)administration), “US” (US policymakers—Obama administration)

Regardless of Iran’s type, if Israel attacks now and the US Regardless of Iran’s type, if Israel attacks now and the US doesn’t join, the two countries will get payoffs: doesn’t join, the two countries will get payoffs: Israel: AIsrael: AII; US: A; US: AUSUS

If Israel attacks now and the US joins, Israel will enjoy the If Israel attacks now and the US joins, Israel will enjoy the benefits of US support (Tbenefits of US support (TII), and US policymakers will suffer ), and US policymakers will suffer being dragged into a war reminiscent of Iraq (Tbeing dragged into a war reminiscent of Iraq (TUSUS). ). For Israel: TFor Israel: TII > A > AII; ; For US: TFor US: TUSUS < A < AUSUS..

The best outcome for both countries is if Israel gives The best outcome for both countries is if Israel gives sanctions time to work, and they do indeed work (Iran sanctions time to work, and they do indeed work (Iran abandons its nuclear program): abandons its nuclear program): Israel: BIsrael: BII = MAX = MAXII; ; US: BUS: BUSUS = MAX = MAXUSUS

The MathThe Math The worst outcome for both countries is if Israel gives The worst outcome for both countries is if Israel gives sanctions time to work, then neglects to attack after sanctions sanctions time to work, then neglects to attack after sanctions fail, allowing Iran to develop nuclear weapons: fail, allowing Iran to develop nuclear weapons: Israel: XIsrael: XII = MIN = MINII; US: X; US: XUSUS = MIN = MINUSUS

If Israel gives sanctions time to work, sanctions fail, and If Israel gives sanctions time to work, sanctions fail, and Israel attacks Iran, both Israel and the US will pay some Israel attacks Iran, both Israel and the US will pay some penalty for having waited (Wpenalty for having waited (W11, W, W22). ).

Israel: TIsrael: TII + W + W1I1I OR A OR AII + W + W2I2I; ; US: TUS: TUSUS + W + W1US1US OR A OR AUSUS + W + W2US2US; W; W1I1I, W, W2I2I, W, W1US1US, W, W2US2US < 0 < 0

Israel’s penalty will be greater if it is forced to attack Israel’s penalty will be greater if it is forced to attack alone than if the US joins.alone than if the US joins.WW1I1I > W > W2I2I; ; |W|W2I2I| > |W| > |W1I1I||

The US will still prefer to stay out of an Israeli attack: The US will still prefer to stay out of an Israeli attack: TTUSUS + W + W1US1US < A < AUSUS + W + W2US2US

The MathThe Math The commitment mechanism: The commitment mechanism: Obama’s public Obama’s public

commitment to support Israel in a strike on Iran, commitment to support Israel in a strike on Iran, that “We’ve got Israel’s back.” Contradicting this that “We’ve got Israel’s back.” Contradicting this statement by failing to support Israel should it statement by failing to support Israel should it attack Iran would carry a cost C for the Obama attack Iran would carry a cost C for the Obama administration, whether Israel attacks now or administration, whether Israel attacks now or later: later: US: AUS: AUSUS + C + CUSUS OR A OR AUSUS + W + W2US2US + C + CUSUS; C; CUSUS < 0 < 0

This makes staying out of an Israeli attack more This makes staying out of an Israeli attack more costly than joining:costly than joining:US: TUS: TUSUS > A > AUSUS + C + CUSUS; ; TTUSUS + W + W1US1US > A > AUSUS + W + W2US2US + C + CUSUS

The MathThe Math Israel’s expected payoffs Israel’s expected payoffs withoutwithout the US promise: the US promise:E[Wait] = p(B) + (1-p)(AE[Wait] = p(B) + (1-p)(AII + W + W2I2I););E[Attack] = AE[Attack] = AII

Israel’s expected payoff if it attacks, Israel’s expected payoff if it attacks, withwith the the US promise:US promise:E[Wait] = p(B) + (1-p)(TE[Wait] = p(B) + (1-p)(TII + W + W1I1I); ); E[Attack] = TE[Attack] = TII

Extent to which US promise improves Israel’s Extent to which US promise improves Israel’s expected payoffs:expected payoffs:E[Wait] = (1-p)((TE[Wait] = (1-p)((TII - A - AII) + (W) + (W1I1I - W - W2I2I)); )); E[Attack] = TE[Attack] = TII - A - AII

Nature

Israel Israel

Sanctions Work (p) Sanctions Don’t Work (1-p)

Attack AttackWait Wait (Iran moving to get the bomb)

Join JoinDon’tJoin

Don’tJoin

Join Don’tJoin

CapitulateWait

USA USA USA

USA

Attack

Israel:

USA:

TIsrael

TUS

AIsrael

AUS

BIsrael

BUS

TIsrael

TUS

AIsrael

AUS

TIsrael + W1Israel

TUS + W1US

AIsrael + W2Israel

AUS + W2US

XIsrael

XUS

Israel

Game Tree before US Commitment

Nature

Israel Israel

Sanctions Work (p) Sanctions Don’t Work (1-p)

Attack AttackWait Wait (Iran moving to get the bomb)

Join JoinDon’tJoin

Don’tJoin

Join Don’tJoin

CapitulateWait

USA USA USA

USA

Attack

Israel:

USA:

TIsrael

TUS

AIsrael

AUS + CUS

BIsrael

BUS

TIsrael

TUS

AIsrael

AUS + CUS

TIsrael + W1Israel

TUS + W1US

AIsrael + W2Israel

AUS + W2US +CUS

XIsrael

XUS

Israel

Game Tree with US Commitment

Effects of the commitment strategyEffects of the commitment strategy

General effects (not specific to payoffs General effects (not specific to payoffs modeled here):modeled here):1.1. Attacking now is more attractive for Attacking now is more attractive for

IsraelIsrael2.2. Failure of sanctions is Failure of sanctions is less less

unattractiveunattractive: US involvement cuts wait : US involvement cuts wait penaltypenalty

Whether commitment strategy succeeds or Whether commitment strategy succeeds or fails depends on three Israeli variables: fails depends on three Israeli variables: size of wait-penalty difference size of wait-penalty difference (W),(W), US US participation bonus participation bonus (B),(B), and and pp

US commitment reduces Israel’s propensity to US commitment reduces Israel’s propensity to attack if: attack if: (1-p)(W) > (p)(B)(1-p)(W) > (p)(B)