The average length of civil wars has more than doubled in the postcolonial era. Might such a solution be the result of rational action on the part of governments? Acemoglu et al consider an infinite period model with Elites, Citizens (who may work, or join the military), and Rebels. The economy begins in a state of civil war. The government chooses one of three army sizes. In the minimum size, the war ends with probability p, and there is no chance of coup. In the medium size, the war ends immediately, in future periods the military size can be reduced to minimum, but a coup can be staged as long as the military is medium size. In the “oversized” case, the war ends immediately and coups can be attempted, but the military is sufficiently strong that the government cannot reduce its size after the war ends. All three choices are Markov Perfect Equilibria. In particular, if the civil war has little effect on Elite revenue, and if the small military has a decent chance of ending the war, the government will not purchase a military large enough to stop the rebels immediately. If the army is made large enough to end the war, the government may prefer to oversize it as a commitment device; a medium sized army may declare a coup right after the war ends because they know the rational Elites will just shrink the army in the next period, and paying extra (in discounted terms) from now until forever for an oversize army may cost less for the Elites than being removed in a coup.
Interestingly, a more developed state, who can more effectively raise tax revenue, is more likely to let a civil war linger than a weaker state because if the state has effective institutions, it is “more valuable” to potential coup plotters, and therefore the wages necessary to avoid a coup will increase as a function of state effectiveness. Note though that the model assumed coups are possible at all, so essentially we are discussing countries which can raise a lot of revenue but who do not have institutions effective enough to prevent militaries from enacting a coup.
More generally, and as usual in a paper by Acemoglu (my pick for the best “young” economist), this is also a great example of a parsimonious but useful model.