Determining the Class of Payoffs That Yield Force-Level-Independent Optimal Fire-Support Strategies

By considering a specific problem, this paper examines the dependence of the structure of optimal time-sequential combat strategies on the quantification of military objectives. The paper determines the class of terminal payoffs that yield force-level-independent (i.e., state-variable-independent) optimal strategies to the fire-support differential game of Kawara. The functional form of payoffs that yield state-variable-independent optimal strategies to this Lanchester-type differential game is shown to be determined by a linear first-order partial differential equation. Kawara's main result was that the time at which an optimal strategy tells one to switch from concentrating all supporting fires on enemy artillery to all on enemy infantry does not depend on the force levels (provided that neither side's supporting units can be all destroyed before a certain time). This paper shows that Kawara chose essentially the only type of payoff that yields his main result. Furthermore, the structure of the optimal time-sequential fire-support strategies is shown to depend on the quantification of infantry force superiority in the model, with seemingly equivalent measures of force superiority yielding different structures for the optimal strategies.