A Dynamic Model of Conflict and Cooperation

Figure 3: Transitions between the corner and interior solutions.

the second term overpowers it. Indeed, differentiation of the left-hand side of (C.7), which is
denoted by Φ (Z), with respect to Z yields

dΦ (Z)    1 ₇^ρ

-=Γ~ = —Z^δ

dZ    ρn

which implies that for smaller values of Z the left-hand side of (C.7) takes a positive slope,
while for larger values of Z that takes a negative slope. Noting that Φ (0) = 0, these results
together imply that the function Φ (Z) displays a U-shaped curve, as illustrated in Fig.3. This
diagram shows that for larger values of c₃, as happens with c⁰₃ in Fig.3, (C.7) is satisfied at
any value of Z and thus a (Z)=1is a global solution to the HJB equation (C.5), whereas for
smaller values of c3 as happens with c⁰₃⁰ in Fig.3, it is satisfied for smaller Z, is then violated,
and finally is satisfied for larger values of Z again. ■

References

Acemoglu, D., S. Johnson and J.A. Robinson, 2001, The colonial origins of comparative
development: An empirical investigation, American Economic Review 91, 1369- 1401.

Auty, R.M., 2001, Resource abundance and economic development, Oxford: Oxford University
Press.

Collier, P. and A. Hoeffler, 2004, Greed and Grievance in Civil War, Oxford Economic Papers,

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