Confronting entrenched insurgents

During counterinsurgency operations, government forces with superior firepower confront weaker low-signature insurgents. Under what conditions should government (Blue) forces attack insurgent (Red) strongholds? How should the government allocate its force across different strongholds when the insurgents' threat to the Blue civilian population must be taken into account? How should the government respond to ‘smart’ insurgents who anticipate the government's optimal plan of attack and prepare accordingly? How do the results change when the government takes Red civilian casualties resulting from attacks on insurgent strongholds into account? This article addresses these questions. Using Lanchester models modified to account for imperfect intelligence, we formulate an optimal force allocation problem for the government and develop a knapsack approximation that has tight error bounds. We also model a sequential force allocation game between the insurgents and the government and solve for its equilibrium. When the government has perfect intelligence, in equilibrium the insurgents concentrate their force in a single stronghold that the government either attacks or not depending upon the resulting casualty count. Otherwise, under reasonable assumptions regarding the government's behavior and intelligence capabilities, it is optimal for the insurgents to ‘spread out’ in a way that maximizes the number of soldiers required to win all battles. If the government worries about Red civilian casualties, the insurgents have a strong incentive to blend in with the Red civilian population, because this can prevent government attacks while allowing the insurgents to inflict casualties on Blue civilians. Such strategic behavior makes it harder for the government to protect its citizens from insurgent attacks.