Dispensa+- 5- Deterrence -New Developments

Question 1

Actions and Types

Answer 1

• Two countries: A and B
• Country B constituted by Leader (L) and Elite (E)
  They both may be hawks or doves.

Question 2

Timing

4steps

Answer 2

1. L provokes a crisis (m=1) or not (m=0)
2. E decides whether to support L (s = 1) or challenge L (s = 0)
3. Country A decides whether to retaliate (r = 1) or not (r = 0)
4. Ruler of country B decided whether to escalate (x = 1) or not (x = 0)

Question 3

Political Instability

Answer 3

Leader needs support of elite to stay in power

• if Elite chooses support, Leader remains in power
• if Elite seizes power, it becomes Ruler

If Elite decides to seize power, domestic payoffs lose fraction (1−δ): internal conflict is inefficient

Question 4

Stakes of the Conflict

Answer 4

For hawks in country B:
-	π1 from provocation 
-	π2 from escalation 
For doves in country B:
-	provocation and escalation give payoff of 0 
For country A:
-	−λ1 from provocation 
-	−λ2 from escalation

Question 5

Retaliation

Answer 5

• Costly for country to execute: c > 0
• Costly for members of country B to endure (deterrence by punishment; impose costs): k > 0
• retaliatory actions reduce the disutility associated with an escalated conflict by q ∈ (0, 1), where q represents the effectiveness of sanctions and military operations
  • −λ2 becomes −(1−q)λ2

Question 6

Domestic Payoffs

Answer 6

Leader and Elite disagree about domestic politics:
They care about the ideological type of ruler, θR.

Member i of B receives a domestic political payoff given by
u(θi;θR)=θi ·θR +(1−θi)(1−θR),
if θi = θR (ideological agreement), payoff equal to 1
if θi ̸= θR (ideological disagreement), payoff equal to 0

If Elite seizes power from Leader, domestic payoff becomes δ

Question 7

Perfect Bayesian Equilibrium:

Answer 7

1. L: provocation strategy, given Θ (ideological composition of B)
2. E: support strategy, given Θ and L’s decision
3. A: retaliation strategy, given decisions of L and E, and system of beliefs considering the ideological composition of B
4. Ruler: escalation strategy for the ruler, considering the previous choices.

Question 8

Model of conventional deterrence scenario

Answer 8

Elite is removed (= fixing exogenously decision to support, s*=1)
L is a hawk (ΘL=1)
q is the effectiveness of sanctions (extent that retaliation reduces the influence of escalation on the status quo)

Question 9

credibility constraint

When should country A retaliate?

Answer 9

Ua Not retaliate <= Ua retaliate
−λ1 −λ2 ≤ −λ1 −(1−q)λ2 −c
so when c ≤ qλ2 ≡ c∗

Question 10

capability constraint

when does a threat deters provocation?

Answer 10

UL no prov ≥ UL prov
1 ≥ π1 + 1 + (1 − q)π2 − k
so when k ≥ π1 + (1 − q)π2 ≡ k∗

Question 11

Key features of the adapted general model:

Answer 11

1- Incomplete information
2- Political instability
3- Ideological disagreement

Question 12

Successful deterrence means

Answer 12

no provocation
Credibility Constraint: c ≤ c ∗
Capability Constraint: k ≥ k ∗
Necessary and jointly sufficient for deterrence success

Question 13

Model with 1

incomplete information

Answer 13

• Probability that L is hawk is μ
• Standard costly signalling game: L is sender and A is receiver
• a dove wouldn’t provoke a crisis, so if L provoked a crisis, L is a hawkIf credibility constraint is satisfied → retaliation after provocation
  If capability constraint is satisfied → successful deterrence

Question 14

Model with 2

Political instability

Answer 14

• Political Instability: country B has L and E, they are both hawks
• No incomplete info - common knowledge that L and E are hawks
• E is a hawk, so if L provokes a crisis, even if E takes power, country A might retaliate
  Since conflict is inefficient, E supports L → everything just like when E is absentIf credibility constraint is satisfied → retaliation after provocation
  If capability constraint is satisfied → successful deterrence

Question 15

Model with 2 and 3
Political instability and Ideological disagreement
salience constraint

Answer 15

L is a dove and E is a hawk
‘‘the threat of retaliation by country A can alter the relative salience of ideological disagreements within country B’’
- Country A retaliates if and only if L provoked a crisis and a hawkish ruler controls country B

If E’s decision does not affect whether A retaliates, the ideological disagreement between L and E is the only relevant dimension determining E’s choice

If E’s support prevents retaliation, then E will support a
dovish L if and only if
supporting> seizing power
π1 ≥π1 +δ+(1−q)π2 −k

which, after rearranging, holds as long as
k ≥δ+(1−q)π2(1)≡k∗∗
Salience constraint

Question 16

Conventional Logic of Deterrence with 2 and 3
Political instability and Ideological disagreement
insights on salience constraint

Answer 16

salience constraint: When avoiding retaliation is more important than ideological disagreement

Salience constraint ̸= capability constraint

• salience constraint emerges from E’s decision calculus
• capability constraint emerges from L’s incentives when anticipating retaliationWith political insecurity, salience constraint generates the key strategic force in the modelIf the credibility constraint and the salience constraint are satisfied, then

(i) when country B is ideologically cohesive, E seizes power if and only if doing so prevents retaliation
(ii) when country B is ideologically divided, E supports L if and only if support prevents retaliation

Question 17

Conventional Logic of Deterrence with 2 and 3
Political instability and Ideological disagreement
instability curse

Answer 17

L is hawkish and E is a dove
Credibility and capability constraints hold

Then
- Country A: retaliates if and only if L provoked a crisis and kept power
- Elite in Country B: seizes power from L regardless of
provocation choice
- Leader in Country B: provokes a crisis

Hawkish L cannot be prevented from provoking a crisis

The Instability Curse : Doves interrupt the direct connection between provocation and retaliation

Question 18

The Instability Curse

further insights

Answer 18

(1) Alignment of interests between A and E
E will not escalate the conflict
⇒ not sequentially rational for A to strike when E gains power
(2) Breaks connection between L and terminal nodes where k is received

Question 19

Conventional Logic of Deterrence with 2 and 3
Political instability and Ideological disagreement
The Deterrence Curse

Answer 19

L is dovish and E is a hawk
Credibility and salience constraints hold
Then
- Country A: retaliates if and only if L provoked a crisis and E takes power
- Elite in Country B: supports L if and only if L provokes a crisis
- Leader in Country B: provokes a crisis

E supports L only if doing so avoids a retaliation (only possible if L provokes a crisis)

The Deterrence Curse : Dove’s tactical provocation of an international crisis to prevent an internal challenge

Question 20

The Deterrence Curse

further insights

Answer 20

(1) Ability to deter E from seizing power makes deterrence of provocation fail:
  Credibility constraint (c ≤ c ∗ )
  Salience constraint (k ≥ k ∗∗ ) 

(2) Commitment problem:
country A would be better off if she could commit to protect the interests of a dovish L
Without provocation, A has no incentive to retaliate
Provocation forces A to have an interest in who controls B

Question 21

Political instability and Ideological disagreement and incomplete information
The Instability Curse
Proposition—Part I

Answer 21

Suppose the credibility and salience constraints hold. Then, if π1 > 1 the strategy profile is
Country A: retaliates following provocation and support
Elite in Country B: supports only if cohesive and L does not provoke
Leader in Country B: provoke a crisis

it is an equilibrium if and only if c ≥ cˆ ≡ (μC / μC +μH)(1 − q)π2

Question 22

The Deterrence Curse

Answer 22

Dove’s tactical provocation of an international crisis to prevent an internal challenge

Question 23

A is better off in

Answer 23

the Instability Curse equilibrium than in the Deterrence Curse equilibrium

Question 24

The Instability Curse

Answer 24

Doves interrupt the direct connection between provocation and retaliation

Question 25

Political instability and Ideological disagreement and incomplete information
The Instability Curse
Proposition—Part I
implications

Answer 25

• Provocation reveals L is hawkish → A will strike if L keeps power
• Dovish E takes power from L to avoid retaliation
• When c ≥ cbarre, country A reluctant to retaliate
• Hawkish E mimiks dovish E
• After seeing provocation and a change in leadership in country B, country A does not know if it is facing a hawk or dove
• Reluctancy to retaliate means that this uncertainty is enough to discourage A from retaliating
  But if π1 > 1 → hawkish leader in cohesive group is better off not provoking

Question 26

Political instability and Ideological disagreement and incomplete information
The Deterrence Curse
Proposition—Part II

Answer 26

Suppose the credibility and capability constraints are satisfied, then the strategy profile
- Country A: strikes following provocation and nonsupport
- Elite in Country B: supports if L provokes a crisis and
challenges if L does not provoke a crisis, unless Θ = ΘC
- Leader in Country B: provoke a crisis

is an equilibrium

Question 27

Political instability and ideological disagreement affect

deterrence

Answer 27

Under incomplete information, such failures mean some conflicts will escalate

Question 28

Inaction Strategy: Never Strike

Answer 28

Instability Curse: A is at least as well off using a policy of inaction
Deterrence Curse: strictly better off using a policy of inaction
Inaction breaks the curses - country A ignores informational content of L’s and E’s actions
However, A must face some escalated threats