A Dynamic Model of Conflict and Cooperation

set (such as land territories and natural resources) or (tangible and intangible) the stock of
durables. We want our model to capture the role of productive and aggressive activities with
the understanding that aggressive investment causes an inward shift of the aggregate produc-
tion possibility frontier. Accordingly, we use a setup where appropriation and production are
two substitutable investment choices. Specifically, let an individual decide at each point in
time how much resources to devote for appropriation ai ≥ 0 and production li ≥ 0. The
individual resource (e.g. time) constraint is:

a_i + l_i = e_i,                                               (1)

where e_i is the endowment of a fill-in activity that is not subject to appropriation.⁴ We will
set e_i =1 for ease of exposition. The time arguments have been suppressed in this and all
subsequent equations.

The common-pool stock is subject to appropriation. The stock is generated by accumula-
tion of output. Output is produced with a linear production technology:

n

Y(l1,...,ln)=     lj,                                         (2)

j=1

which captures the idea that higher productive efforts by agents cause an outward shift of
the production possibility frontier for the economy as a whole. The output of production can
be stored to augment the common-pool stock. However, storage entails costs such that the
stock Z evolves according to

Z = Y(lι,...,ln) - δZ,                                (3)

where δ ∈ (0,1) is the rate at which output will depreciate if stored for future consumption, Zi
denotes the change of Z over time and Z (0) ≥ 0 is the initial stock.

A main ingredient of the model is the conflict technology which, for any given values
of a1 ,...,an, determines each agent’s probability of winning sole possession in obtaining the

⁴ The standard assumption that each agent has some essential property rights is implicit in this formulation.
Individual’s labor supply is such an example. Maxwell and Reuveny (2005) further assume that labor supply
is growing over time as a result of the growth of population. However, in order to keep the model simple, we
assume that the population of agents remains constant over time.

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