Many game-theoretic analyses of deterrence confirm the commonsense view that what determines whether a defender can effectively deter a challenger from an unwanted action is (1) the challenger’s perception of the level of punishment that the defender will be able to impose on the challenger should it take the action, and (2) the challenger’s level of belief about the likelihood of the defender actually carrying out this punishment. Reduction of the defender’s forces may affect both the defender’s ability to retaliate and its perceived willingness to do so. Game-theoretic methods are used to assess how the limits on both of these parameters are related, subject to the condition that deterrence remains effective. The results indicate that the defending side can often make do with smaller forces, provided its (apparent) resolve is high. But force structure is important—the models suggest that implementation of an “all-or-nothing” deployment (as called for by a doctrine of massive retaliation, for example) may reduce not only costs, but also deterrence effectiveness.
Kilgour, D. Marc and Zagare, Frank C., "The Impact of Conventional Force Reductions on Strategic Deterrence: A Game-Theoretic Analysis" (2001). Mathematics Faculty Publications. 1.