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Understanding the Logic of Alliances in International Relations

Explore the importance of signaling in the study of alliances and commitments in international relations, focusing on military alliances and credibility issues. Analyze different types of alliances and the impact of formal commitments on deterrence. Learn how to model alliances and signaling in uncertain scenarios.

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Understanding the Logic of Alliances in International Relations

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  1. QR 38 Signaling II (Applications), 4/19/07 I. The logic of alliances and other commitments II. Modeling alliances

  2. 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

  3. Types of alliances: • Non-aggression (friendship, neutrality) • Mutual defense (will focus on these) • One-sided defense • Commitments to consult (ententes) • Collective security agreements Alliances

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. a>b>c>d Modeling 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. Equilibria of signaling game

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