The purpose of this project is to analyze the strategic aspects of nuclear deterrence and limited retaliation within a game-theoretic framework. Special emphasis will be given to examining the effects of incomplete information. Most existing formal work on deterrence theory focuses on some form of nuclear brinkmanship. In a nuclear brinkmanship crisis, a state attempts to protect its interests by manipulating the risk that the crisis will end in an unlimited, all-out, nuclear exchange. The crisis is a competition in taking risks in which each state tries to convince its adversary that the risk is too high and that it should back down. There is, however, another approach to deterrence that is not based on brinkmanship and manipulating the risk of an unlimited nuclear attack. In this approach, a state attempts to protect its interests by inflicting a limited amount of punishment in order to make the threat to inflict more damage in the future credible. During a crisis, then, a state tries to make the threat of future punishment sufficiently credible that its adversary backs down. This second approach, based on limited retaliation, has received little attention in the formal literature. The primary goal of this project is to extend the formal analysis of deterrence theory to the study of the strategy of limited retaliation. This research is important because it will shed some light on the issue of the relation between limited nuclear options and the likelihood that a crisis will escalate into a war. Does increasing the number of limited options make a nuclear war more "thinkable" and, thus, reduce crisis stability by making war more likely? Or, does increasing the number of options enhance the credibility of a state's retaliatory threats, strengthen deterrence and, therefore, increase crisis stability?
