Suppose that two nations A and B each possess a nuclear arsenal and are rational utility-maximizers. Suppose further that B has some interest in provoking A, possibly by attacking her with nuclear weapons. In the hope of preventing this from happening, A informs B of à conditional intention on her part to retaliate against B with nuclear weapons should B in fact attack A. By doing so A attempts to lower the probability of B's attacking A by increasing B's estimate (...) of the conditional probability of A's retaliating once provoked. Problematic deterrent situations are those in which B prefers to attack A without retaliation, A prefers most of all that she not be attacked, and A prefers an attack-with-no-retaliation scenario to an attack-with-retaliation scenario. Feature is à result of the fact that A prefers to minimize nuclear devastation, i.e., A would herself be worse off retaliating than not retaliating to an attack. Now, if B knows all of this to be the case then A's expression of a conditional intention to retaliate will not in fact deter B from attacking, since A is rational and will not act contrary to her own best interests. B has no reason to fear A's retaliation and therefore B has no reason not to attack. Deterrence, it seems, is an irrational policy among fully rational actors. This is one version of the so-called paradox of deter-rence. If expressing a conditional retaliatory intention is the best way for A to ward off an attack, then the paradox can be strengthened as follows: It is rational for A to intend to act irrationally. (shrink)