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QR 38 Signaling II (Applications), 4/19/07 I. The logic of alliances and other commitments PowerPoint Presentation
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QR 38 Signaling II (Applications), 4/19/07 I. The logic of alliances and other commitments II. Modeling alliances. Logic of signaling important in modern study of international relations. Illustrate by considering a specific application, to the study of military alliances.

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slide1
QR 38

Signaling II (Applications), 4/19/07

I. The logic of alliances and other commitments

II. Modeling alliances

i logic of alliances and other commitments
Logic of signaling important in modern study of international relations.
  • Illustrate by considering a specific application, to the study of military alliances.
  • Could apply this same logic to other types of international agreements.
I. Logic of alliances and other commitments
alliances
Types of alliances:
  • Non-aggression (friendship, neutrality)
  • Mutual defense (will focus on these)
  • One-sided defense
  • Commitments to consult (ententes)
  • Collective security agreements
Alliances
alliances and credibility
Credibility problems in alliances because of lack of external enforcement.
  • As many as 73% of alliance members may fail to live up to their commitments in the face of attack.
  • So, are alliances worthless?
  • No – need to consider the possibility that alliances are deterring attacks; a selection effect.
Alliances and credibility
alliances and deterrence
Consider alliances from a potential attacker’s perspective:
  • Some uncertainty about whether alliance will hold
  • Assume that if it does, the attacker will lose; otherwise could win easily
  • So, alliances that are credible will not be attacked
Alliances and deterrence
alliances and deterrence1
So looking only at cases where there has been an attack gives us a biased sample; these are the alliances most likely to fail.
  • Could be many alliances that are reliable and so effective in deterring attacks.
Alliances and deterrence
alliances and deterrence2
Why does signing a formal commitment to an alliance make a difference?
  • If states have common interests, they will come to one another’s defense
  • If they don’t have common interests, signing a formal alliance won’t help
  • So alliances are either unnecessary or ineffective
Alliances and deterrence
alliances and deterrence3
Alternative, strategic argument:
  • Costly signaling
  • What is necessary for an alliance to create a separating equilibrium, distinguishing reliable from unreliable types?
    • Differential costs for reliable and unreliable types.
    • These might be costs of changing military structure, stationing troops
    • Why would they be higher for unreliable types?
Alliances and deterrence
alliances and deterrence4
Reputational effects are also possible:
  • If a country doesn’t live up to the terms of an alliance, may find it difficult to attract allies in the future
  • Example of U.S. aiding France in Vietnam.
Alliances and deterrence
joining alliances
Why join an alliance? Different states might have different reasons (BdM).
  • Autonomy-security tradeoff
  • More likely to join alliances with those who share common interests
Joining alliances
ii modeling alliances
How would we capture the logic of alliances in a model with uncertainty?
  • Assume two types of alliance partners (C), reliable and unreliable
  • C is reliable with probability p.
  • Begin with simple model of uncertainty; then add opportunity for signaling.
  • Calculate the critical value of p at which an attack is rational.
II. Modeling alliances
modeling alliances
a>b>c>dModeling alliances

d, b, c

Help

C

Fight

No

B

b, d, d

Attack

No

A wins

a, c, b

A

d, b, d

Reliable

(p)

Help

No

SQ

c, a, a

C

Nature

Fight

b, d, c

No

B

Unreliable

(1-p)

Attack

No

A wins

a, c, b

A

No

SQ c, a, a

modeling alliances1
Solve each half of the game as if there is no uncertainty
  • Equilibrium outcome if C is reliable is for the status quo to prevail, because if A attacks B will fight and C will help
  • Equilibrium outcome if C is unreliable is for A to attack and B to back down (A wins), because C won’t help.
Modeling alliances
modeling alliances2
Can calculate the critical value of p for which A decides to attack:
  • EU(attack)=pd+(1-p)a
  • = pd+a– pa
  • = p(d-a)+a
  • EU(no attack)=c
  • Attack if p(d-a)+a>c
  • p(d-a)>c-a
  • p<(c-a)/(d-a) (d-a is negative)
Modeling alliances
interpreting results
As the value of the status quo (c) increases, the critical value of p increases; so there is a larger range of p that gives rise to no attack.
  • As the payoff for fighting both B and C (d) goes down, the critical value of p increases, so an attack is less likely.
Interpreting results
adding signaling
How would we add signaling to this model?
  • Add a step after Nature’s move, allowing B and C to join an alliance.
  • This involves a cost, x, subtracted from C’s payoffs.
  • But x is higher from an unreliable than a reliable type.
Adding signaling
adding signaling1
If the differential in x is high, a separating equilibrium: only reliable C’s will sign.
  • If the differential in x is low and p is high, pooling equilibrium:
    • Both reliable and unreliable C’s will sign
    • Because p is high, A believes that C will help and so will not attack
Adding signaling
adding signaling2
If the differential in x is low and p is low, get a semi-separating equilibrium: can’t sustain pooling because A doesn’t believe C is reliable, but can’t separate because unreliable A’s have incentive to bluff
  • What does a mixed strategy mean here?
    • Unreliable C signs alliance probabilistically
    • If C signs alliance, A attacks with some probability between 0 and 1.
Adding signaling