At the Columbia political economy seminar this week, Tomas Sjostrom presented a paper he co-authored with Sandeep Baliga on "Strategic Ambiguity and Arms Proliferation" (link). A central puzzle that the paper attempts to address is why a leader would want to propagate ambiguity about his country's strategic capabilities. The study is motivated by the use of strategic ambiguity by the leaders of Iraq, Iran, and Israel, for example. It is the last case, Israel, that is particularly puzzling. Here is a country that is generally believed to have strategic weapons but nonetheless has chosen to sustain a level of ambiguity. This would seem to contradict rational deterrence logic, which proposes that the strong should prefer to make it known that they are strong in order to deter attack. The other two cases may be slightly less puzzling, given that incentives to "bluff" are readily admitted by the rational deterrence logic.
In a manner that departs from much conventional wisdom in the popular press, Baliga and Sjostrom do not consider such ambiguity as being the product of attempts to balance against a multitude of possible threats, both internal and external, or attempts to construct a reputation. Rather, they limit their analysis to the stark case of a single interaction between only two actors. The situation is an asymmetric one, where player B decides whether to arm or not and whether or not to allow inspections to reveal its armament status. Player A merely decides whether to attack B or not, perhaps out of an interest in preventing an armed B from passing nuclear weapons to a terrorist organization or threatening allies of A (although the latter are not part of the model).
An important feature of their model is that the players are not certain about each other's "type". Player A can be of a type that would always prefer to attack, to attack only when the opportunity is ripe, to attack reluctantly and only when it seems really necessary, or to never want to attack. Player B can be of the type that inflicts more or less harm to A if B is able to maintain a strategic arsenal (e.g. more or less prone to pass weapons to terrorists, challenge allies of A, etc.).
Given such uncertainty, Baliga and Sjostrom derive a number of conditions under which B would prefer not to allow inspections and thus maintain ambiguity about its weapons status. Some of the results are along the lines of "bluffing" to deter attack from those "opportunists" who would only attack when the situation is ripe. They also show conditions under which something like the curious "Israel scenario" might emerge: Suppose B believes that A is apt to suspect that B is of the type that will cause significant harm to A if B is able to maintain an arsenal. Suppose as well that B places great weight on the possibility that A is of the type that will only attack reluctantly and if it deems it is really necessary to do so. Then B's interests might be best served by arming itself, and thus being able to better fend any attack that might come its way, but to also deny inspections to prevent the "reluctant" A-types from finding sufficient reason to attack B.
I frankly cannot see how this corresponds to the real-world Israel scenario (who are the "reluctant" attackers in this scenario?). There might be other cases that are a better fit. But it is an interesting little result. Another interesting feature of the paper is that they always consider how communication between A and B might affect equilibrium behavior. I feel like this type of analysis of communication is not done often enough.