1 Introduction
Most of the conflict theory papers have used a one-shot game set-up1. We believe this does not
correspond to reality and is certainly incapable of modeling real conflict situations. The dynamic
aspects of the conflict come at least from two sources: first, the preferences on the good in dispute
are not static; second, agents in conflict can influence the future of the conflict by making investment
in conflict’s technology, and by adapting to different environments. To illustrate the first aspect,
let’s think about sports. We consider that the first time Roger Federer won a Grand Siam he felt
happier that when he won his n-th championship. If we assume that each title is a different kind of
good, this fact cannot be explained by decreasing marginal utility. However, it seems appealing to
assume that Federer’s valuation for his titles have changed with past success. The second source of
dynamic concern in conflict is the obvious one. Agents try to do the best they can when fighting
for the control of a valuable resource. They will try to improve their technology and to adapt to
the conflict environment, making explicit choices to achieve their goals. These aspects cannot be
accounted for in a static conflict model.
This paper works on a dynamic conflict model that incorporate both aspects at some extent. The
aim is to give one more step in the study of dynamic conflicts. Many authors have explored dynamic
aspects in conflict modeling. Hirshleifer (1995)2, Grossman and Kim (1995) and Skaperdas (1992),
among other authors, have called attention to the importance of modeling the events developed in
a dynamic conflict. However, perhaps the only ones interested in giving formal answers have been
Maxwell and Reuveny (2001, 2005) and Eggert, ichi Itaya and Mino (2008). They induce dynamics
in a one-period-conflict model introducing differential equations to account for the exogenous evo-
lution of some state variables. Our paper generalizes their work in some dimensions. We explicitly
model the endogenous state variables that generate the inter-temporal links needed for a proper
dynamic conflict. This is done through investment in the conflict technology, resembling standard
macroeconomics models.
Furthermore, although Maxwell and Reuveny (2001, 2005) have constructed a dynamic model for
two players, they have recognized that their model’s agents are myopic. We try to improve this
limitation proposing a model with N forward-looking agents. We assume the existence of a private
set of information for each agent and a public information set, and this allow the agents of our model
1For example Hirshleifer (1995), Skaperdas (1992), Grossman and Kim (1995), Neary (1997) and Anderton, Anderton
and Carter (1999).
2This author was the first to propose an extended methodology in the analysis of conflict, allowing for a dynamic
set-up. Nevertheless, like is mentioned in Maxwell and Reuveny (2001), Hirshleifer’s model does not use equations
describing the paths of variables over time.