Game theory is not my forte, but when simple, informed by knowledge of cases and actually tested it can add significant value to policy debates. In the most recent issue of International Organization (also available here), Muhammet Bas (Harvard) and Andrew Coe (USC) outline a “Dynamic Theory of Nuclear Proliferation and Preventive War.” Their target is a class of models that are static—capabilities are acquired instantly or in the very next period—and in which one state randomizes over acquiring nuclear weapons while the other randomizes over whether to attack or not. The authors are also going after the preferred means of testing such theories in massive country-year or dyad-year panels, with the unrealistic assumption that each observation is temporally independent or that unit-specific dependence decays rapidly. They opt, rather, for some simple coding of known country cases, treating each as unfolding over its own variable time. This method makes a lot of sense to me.
Their approach is to focus on two stochastic features of proliferation games: the uncertainty that any investment (by B for convention) will in fact lead to acquisition or improvements in capabilities; and the uncertainty with respect to whether these improvements will be effectively observed (by A for convention). The model has the appealing feature of effectively generating a typology of equilibrium pathways:
- Surprise success. “A” tolerates “B’s” investment since it appears unlikely to succeed, but then “B” masters the process and acquires nuclear weapons (or improves its capacity) unexpectedly. The outcome: “the process is calm and ends quickly in proliferation.” This appears to conform with the North Korean case.
- Hard intelligence of progress. As in the first scenario, “A” tolerates “B’s” investment but then gets hard intelligence that the program has advanced and attacks to stop it. A key empirical question is whether this is closer to where we are now if we expand “success” and “intelligence” to include development of particularly undesirable capabilities.
- “A” lacks firm intelligence, but is increasingly apprehensive. A crisis arises and war occurs.
- Crises could defuse if A initially believes that B is progressing but then learns that in fact capabilities were exaggerated.
To me, outlining these different pathways is itself a contribution, although with the caveat that it may be hard to actually know which one we are on; I return to that problem. But the modeling yields some testable implications. Most notably, as long as the effect of proliferation on the balance of power is high enough relative to the costs of preventive attack, such attack should occur if and only if the program in question is estimated to be nearing success. Put differently, the likelihood of attack hinges not only on standard cost-benefit calculus but on intelligence estimates.
The empirical work is devoted primarily to showing whether 27 cases, coded with respect to capabilities (of B) and intelligence (of A), conform with the various pathways. North Korea enters twice: from 1982-1994 as a case in which hard intelligence did generate a “serious consideration of attack,” at the height of the first nuclear crisis; and from 1995-2006, which is coded as a “no serious consideration of attack” because of the surprise element noted in the development of North Korean capabilities shown in the 2006 test.
The model seems to extend into the current era, where information is hardening that North Korean capabilities are increasing rapidly. The problem—as always—is in assessing the key parameters: whether “the effect of proliferation on the balance of power is high enough relative to the costs of preventive attack.” It has long been a staple of the North Korea policy world that the costs of preventive attack would be high because of geography: the vulnerability of Seoul.
But those assessments could shift—opening up dangerous gaps between the US and South Korea—as North Korea develops a first strike or even a second strike capability with respect to the US homeland; this is the risky new policy space we are now in.
In addition, some ideas about “attack” might be less costly than a pre-emptive strike on the North Korean homeland. For example, shooting down a missile test is less costly than taking out Yongbyon or the launch sites.
The model also has few counterintuitive things to say about defense, pre-emptive capabilities and even sanctions. It is typically assumed that BMD works in part by discouraging proliferation. I never found this convincing for a regime such as North Korea’s which has some strong domestic reasons to pursue its program. And it is certainly not the case in a world where missile capabilities are evolving rapidly. As Bas and Coe note, defense may also render proliferation less bad and thus delay the need for attack.
Such a debate is also in train, whether defense can adequately substitute for pre-emption. Similar observations pertain to bunker-busting conventional or low-yield nuclear capabilities. They should—in theory—deter proliferation. But again, Bas and Coe note that they have the perverse effect of widening consideration of pre-emption.
Finally, they note that sanctions may also have the perverse effects of accelerating proliferation. If A believes that they are adequate to have material effect, then they are a substitute for attacking. This has certainly been the case with respect to North Korea policy, where ratcheting up sanctions is seen as more appealing that facing unsavory military options.
As with all game theoretic models, the challenge is in testing. For example, is such a model relevant to a world where a state has broken out but is advancing along some known technological frontier? Is further modification necessary? But Bas and Coe appear to have gotten much closer to realism than some of the other formal and quantitative work we have reviewed on this issue, and there is ample room for more case work along the lines they have opened up.