Limits on linearity of missile allocation optimization

Optimizations of missile allocation based on linearized exchange equations produce accurate allocations, but the limits of validity of the linearization are not known. These limits are explored in the context of the upload of weapons by one side to initially small, equal forces of vulnerable and survivable weapons. The analysis compares analytic and numerical optimizations and stability induces based on aggregated interactions of the two missile forces, the first and second strikes they could deliver, and they resulting costs. This note discusses the costs and stability indices induced by unilateral uploading of weapons to an initially symmetrical low force configuration. These limits are quantified for forces with a few hundred missiles by comparing analytic and numerical optimizations of first strike costs. For forces of 100 vulnerable and 100 survivable missiles on each side, the analytic optimization agrees closely with the numerical solution. For 200 vulnerable and 200 survivable missiles on each side, the analytic optimization agrees with the induces to within about 10%, but disagrees with the allocation of the side with more weapons by about 50%. The disagreement comes from the interaction of the possession of more weapons with the shift of allocation from missiles to value that they induce