On the optimal trade-off between fire power and intelligence in a Lanchester model

Combat between governmental forces and insurgents is modelled in an asymmetric Lanchester-type setting. Since the authorities often have little and unreliable information about the insurgents, ‘shots in the dark’ have undesirable side-effects, and the governmental forces have to identify the location and the strength of the insurgents. In a simplified version in which the effort to gather intelligence is the only control variable and its interaction with the insurgents based on information is modelled in a non-linear way, it can be shown that persistent oscillations (stable limit cycles) may be an optimal solution. We also present a more general model in which, additionally, the recruitment of governmental troops as well as the attrition rate of the insurgents caused by the regime’s forces, i.e. the ‘fist’, are considered as control variables.