Conflict and Uncertainty: A Dynamic Approach

to plan the future with some knowledge about the underlying distributions associated with random
states of nature. This implies that our agents maximize the discounted sum of expected future
utility, not only the current revenue. This differentiates a dynamic conflict from a repeated-game
conflict.

Finally we include dynamics in the valuations of agents. It is usual to find conflict theory models
that assume that the preferences on the good in dispute are static. To incorporate this dynamic
aspect, we use a simple deterministic rule that defines the evolution of the subjective valuation for
the good in dispute according to the results obtained by the agents in the recent past.

Although through the paper we will give examples about military conflicts, this is not the only
application of our model. Using the same set up, the model could be easily extended to analyze
political party disputes, RλT) competitions, business races, lobbyists in legislatures or any similar
dispute. Besides that, we believe that dynamic models of conflict can have applications to dynamic
auction processes. Auctions are non-violent conflicts with a specific allocation rule, that could fit
the dynamic set-up proposed in this paper.

The paper is organized as follows: the next section introduces the model. The third section goes
through some details of the model that are useful for a better understanding of the conflict context.
Then we characterize the solution of our game under a specific allocation rule, followed by a simple
example with the aim of understanding how the model works. We conclude with a summary of our
main findings.

2 The Model

This section presents the set up model concentrating on the main assumptions that we use. We also
explain with some detail the timing of the whole game.

2.1 Axiomatization

Suppose there exists a divisible resource R_t and th ere are I ∈ N* agents (individuals or groups] that
are competing to obtain a share of valued divisible resource (like the government of some country,
the control over a key population, the monopoly on a natural resource, a victory in a military conflict
etc.).

Furthermore as mentioned by Hirshleifer (1989) R_t lacks of future well-defined property rights.
That is, R_t or any fraction of it, at the beginning of the period t could be property of someone, but

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