Confronting Entrenched Insurgents

Abstract

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.

On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness

“…Operations research originated from the efforts of military applications during World War II but has been widely resumed with respect to homeland security after September 11, 2001(Brown, Carlyle, Salmeron, & Wood, 2006Hu, Homem-de Mello, & Mehrotra, 2011;Kaplan, Kress, & Szechtman, 2010;McLay, Jacobson, & Nikolaev, 2009;Wright, Liberatore, & Nydick, 2006). Among different techniques of operations research, game theory is a popular tool to capture the strategic interactions between the terrorists and the government on resource allocation problems among multiple targets (Cox, 2009;Hall, 2009;Hausken, 2002;Insua, Rios, & Banks, 2009).…”

On the value of terrorist’s private information in a government’s defensive resource allocation problem

“…Jenelius et al (2010) analyze the impact of the degree of attacker information asymmetry on the likelihood of an attack and show that a less-informed attacker may cause more damage to a defender. Kaplan et al (2010) also consider the uninformed attacker setting and characterize a simple rule for the attacker's optimal strategy.…”

Analytic Modeling of Insurgencies

“…Similarly to [3], Kaplan et al [31] use modified Lanchester models to study the force allocation problem of both the government and the insurgents and, using a sequential force allocation game between the two sides, obtain an equilibrium. It is shown that the insurgents' optimal strategy depends on the government level of situational awareness; when the government has perfect intelligence, in equilibrium the insurgents concentrate their force in a single stronghold that the government either attacks or leave unengaged, depending upon the resulting casualty count.…”