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

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