Models of Repression and Inclusion

Abstract

The Collier-Hoeffler model is extended in two ways: first by examining the possibility of altogether avoiding the conflict if mutual concessions are agreed upon, and, second, to include the application of repression and reprisals by the government as deterrence for the guerrillas staging the rebellion. By allowing the fighting effectiveness to differ for the two sides, the effect of other factors such as terrain on the development of guerrilla forces is examined. Combinations of high repression and low inclusion in power sharing seem to be conducive to the onset of a civil war. Moreover, the application in the Greek civil war shows that persecutions tended to inflame the severity of the conflict, rather than suppress it.

Appendix

4.1.1 Proof of Proposition 1

Differentiating (4.3) we get

$$ \frac{\partial {p}_1}{\partial r}=\frac{m_1}{r}\bullet \frac{A_1{A}_2{r}^{m_1}{q}^{m_2}}{{\left[{A}_1{r}^{m_1}+{A}_2{q}^{m_2}\right]}^2}=\frac{m_1}{r}\bullet {p}_1\bullet {p}_2 $$

(4.21a)

Similarly

$$ \frac{\partial {p}_2}{\partial q}=\frac{m_2}{q}\bullet \frac{A_1{A}_2{r}^{m_1}{q}^{m_2}}{{\left[{A}_1{r}^{m_1}+{A}_2{q}^{m_2}\right]}^2}=\frac{m_2}{q}\bullet {p}_1\bullet {p}_2 $$

(4.21b)

Dividing (4.21a, 4.21b) by parts, expression (4.4) is readily obtained.

4.1.2 Proof of Proposition 2

Recalling (4.9a, 4.9b), taking into account (4.3), the concavity of (p _j , j = 1,2) and the fact that (L _j <V _j , j = 1,2) we obtain:

$$ \frac{\partial^2{H}_1}{\partial {r}^2}=\frac{\partial^2{p}_1}{\partial {r}^2}\bullet \left({V}_1-{L}_1\right)<0 $$

(4.22a)

and

$$ \frac{\partial^2{H}_2}{\partial {q}^2}=-\frac{\partial^2{p}_2}{\partial {q}^2}\bullet \left({V}_2-{L}_2\right)>0 $$

(4.22b)

4.1.3 Proof of Proposition 3

The first-order condition for maximizing (Π ₁ ) as in (4.6a) yields that guerrillas should mobilize an army of a size such that it satisfies

$$ {w}_1=\left({V}_1-{L}_1\right)\bullet \frac{\partial {p}_1}{\partial r} $$

(4.23a)

Substituting from (4.21a) it gives that

$$ {w}_1r={m}_1\bullet \left({V}_1-{L}_1\right)\bullet {p}_1\bullet \left(1-{p}_1\right) $$

(4.23b)

The maximum payoff becomes

$$ {\varPi}_{1 max}=\left({V}_1-{L}_1\right)\bullet \left[{m}_1{p}_1^2+\left(1-{m}_1\right){p}_1-\frac{D-{L}_1}{V_1-{L}_1}\right] $$

(4.24)

For a repression strong enough so that D>L ₁, the second-order expression within the square brackets has only one positive root, say π ₁ >0. In terms of model parameters it becomes:

$$ {\pi}_1=-\frac{1-{m}_1}{2{m}_1}+\frac{1}{2{m}_1}\bullet {\left\{{\left(1-{m}_1\right)}^2+4\frac{D-{L}_1}{V_1-{L}_1}\right\}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$

(4.25)

For the maximum payoff to be positive, and thus entering the conflict to be meaningful, it requires that p ₁ >π ₁. Given that probability p ₁ is increasing in (r), this condition is translated into an army threshold of r>r _MIN . The threshold in (4.15) is calculated in terms of model parameters from the inverse conflict success function:

$$ {r}_{MIN}=inv\;{p}_1\left[{\pi}_1\right] $$

(4.26)

Similarly the government’s maximum payoff is obtained as

$$ {\varPi}_{2 max}=\left({V}_2-{L}_2\right)\bullet \left[{m}_2{p}_2^2+\left(1-{m}_2\right){p}_2+\frac{L_2}{V_2-{L}_2}\right] $$

(4.27)

This remains always positive; therefore, no threshold for the state army applies.