A Dynamic Model of Conflict and Cooperation



to describe true dynamic situations which are not ‘stationary’. More recently, Maxwell and
Reuveny (2005) construct a conflict model with two competing groups in which each group’s
population and a stock of common (natural)-resources both change over time. Since three non-
linear differential equations characterizing the dynamic paths of these stock variables do not
allow an analytical solution, they resort to numerical simulations. These exercises reveal that
mild conflict activity depresses the use of natural resources for production, thus possibly cre-
ating a Pareto improvement compared to cooperative situations where there is no appropriate
activity, and, moreover, tends to reduce the volatility of those stocks through the transition.
Although their model generates interesting insights, they still assume that agents are myopic.
The authors in the literature have called for a full dynamic and multi-period model of the
Skaperdas-Hirshleifer-Grossman and Kim-based literature which incorporates the behavior of
non-myopic agents who taking into account the consequences of their future actions, which is
also left as an open question in Maxwell and Reuveny (2005).1 The goal of this paper is to
accomplish this task.

We develop a forward-looking agent-based infinite horizon general-equilibrium model to
study the dynamic evolution of self-enforcing property rights. There are various ways of
extending one-shot, static models of Skaperdas, Hirshleifer, and Grossman and Kim to a
dynamic setting. Following their models, we first assume that the initial resource endowment
is fixed over time. This assumption would be defended either by interpreting the initial
resource endowment as a time or labor supply, or by assuming the fixed population in order to
keep the model tractable. The relevant state variable in our dynamic model is a durable stock
which accumulates through time according to the production process using collective efforts
of all parties involved. This durable stock is exhaustible or rival in the sense that one agent’s
1 More recently, there is another class of dynamic conflicting models that include, e.g., Gradstein (2003)
and Gonsalez (2007). There are several important differences between the models in these papers and the one
in ours. First, in their models a flow of the output produced each period is sub ject to predation, while in
our model a stock variable is subject to predation. Secondary and more importantly, those papers investigate
the relationship between conflict and economic growth in the standard growth model based explicitly on
the investment and saving decisions of a large number of economic agents. Hence, their models are mostly
concerned with the macroeconomic consequences, such as growth effects of insecure property rights. Since
our model is a straightforward dynamic extension of Grossman, Hershleifer and Skaperdas which allows for
static interaction among a small number of economic agents, it enables one to directly compare our results
with those in static conflicting models and thus to highlight the strategic role of appropriation among those
few agents in the intertemporal context.



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