Michael A. Allen and Julie VanDusky – both founders of the blog Quantitative Peace –  have published  Employing Force: The Decision to Use Private Actors in Inter-State Wars

. An excerpt:

The contemporary rise to infamy of Blackwater Worldwide and the private corporation’s misdeeds in the Iraq War has historical precedents. That is, it is not unheard of for a state to employ non-state actors to carry out traditional state activities such as the use of force – something the modern

state is supposed to have a monopoly over. In this paper, we build a game theoretic model that determines the prospects for using non-state actors in combat on behalf of the state. From this model, we hypothesize that despite the risk of agency loss by these private combatants, certain

conditions increases the likelihood of their use. Specifically, autocratic polities are predicted to have a positive influence on the employment of non-state combatants while their democratic peers will prefer to abstain from such activities. We test these hypotheses using a censored probit model for all bilateral wars from 1816-2002.