Optimization of stability index versus first strike cost

This note studies the impact of maximizing the stability index rather than minimizing the first strike cost in choosing offensive missile allocations. It does so in the context of a model in which exchanges between vulnerable missile forces are modeled probabilistically, converted into first and second strike costs through approximations to the value target sets at risk, and the stability index is taken to be their ratio. The value of the allocation that minimizes the first strike cost for both attack preferences are derived analytically. The former recovers results derived earlier. The latter leads to an optimum at unity allocation for which the stability index is determined analytically. For values of the attack preference greater than about unity, maximizing the stability index increases the cost of striking first 10--15%. For smaller values of the attack preference, maximizing the index increases the second strike cost a similar amount. Both are stabilizing, so if both sides could be trusted to target on missiles in order to minimize damage to value and maximize stability, the stability index for vulnerable missiles could be increased by about 15%. However, that would increase the cost to the first striker by about 15%. It is unclear why--having decided to strike--he would do so in a way that would increase damage to himself