Conflict and Uncertainty: A Dynamic Approach

The graphics show impulse response to exogenous shocks, in linear differences from the steady
state.

An exogenous increase in the total amount of the resource in dispute increases the possibilities of
the agents. Because of their higher endowment, they are able to devote more resources to the conflict.
Both agents increase the effort, and the dissipation increases. This happens because the reaction
function of both agents is increasing in the total amount of the valuable resource. The consumption
and the investment of both agents increases. The share obtained by each agent depends on the
relative strength and the cost of effort.

The shock to investment increases the effectiveness of conflict technology of the agent that receives
the positive shock. Then this agent increases her investment because each unit of investment is more
effective than the last. In order to keep up, the other agent also invests more in technology. This
decreases the consumption and effort of both agents. The increase in both technology coefficients
has ambiguous effects on the share obtained by each agent. This depends on the relative strength
and the cost of effort.

The shock to the valuation of the agent two increases the utility of present consumption with
respect to future consumption, because the shock is transitory. This generates a decrease in the
investment made by agent two, and an increase in consumption. To increase present consumption,
agent two must exert more effort and dissipation increases at the moment of the shock. However,
due to less investment, effort costs are higher and this reduces effort for the next periods. Dissipation
is lower after the shock.

5.3.2 Impulse response with adaptation to harder environment

Now we analyze the dynamic response of the stable model with adaptation to harder environments.
We capture the fact that the weak agent adapts to the environment and increases the effectiveness
of her conflict technology according to the variation of the success rate. In this case

■ S S ∖ S S ∖²
δⁱ (st) = δi + αⁱ ( ɪ - 1 ) + bⁱ S - 1 )
∖^st-ι     /        ∖^st-ι     /

The economic interpretation of the impulse response does not change. However the adaptive
behaviour of the agents has important effects in the dynamic response to exogenous shocks.

Note that the endogenous response of the depreciation rate to the success index induces oscillating
behaviour in the dissipation. Then we cannot rule out this mechanism as generator of rich dynamics
and possibly as a chaos source in the model.

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