Conflict and Uncertainty: A Dynamic Approach

If vi > 0 is the long-run value scale para meter, the value scale parameter vⁱ must satisfy the
following relation:

vⁱ = vⁱ (vⁱ,sⁱ)

where sⁱ is the success rate in steady state.

5 Example: The symmetric information case.

In this paper we will carry on with an applied example of the model presented before. First we will
explain the symmetric information equilibrium. We assume the following functional forms, which
are quite standard in the literature:

(ct)^1-σi

1 ^{- σ}i

(et)^1+ηi

1 + ηi

^αtet

Pj∈I ^{αj ej}

(1 - δⁱ (st)) αt + zt⅛t

(ςi ∖ S si

-g--1 I + bⁱ ( -g--1

ii

^st-1     /        ∖^st-1

where (∀i ∈ I) ^cr_i, η_i, δi ≥ θj.

Assume that there is no asymétrie information in the conflict environment. Then all the shocks are
unknown to all the agents, so everybody has the same information set each period. Then the optimal
conditions simplify, because now E£ = E_t, the expected value is taken with the same information
set for all the agents.

All functions are differentiable, so the solution for the problem of agent i ∈ I is characterized by:

^αt (∑j∈I∖{i} ^αjet )
(Pj∈I αjet )²

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