Conflict and Uncertainty: A Dynamic Approach

η_i = η, αⁱ₀ = α₀, v0 = v₀, vⁱ = v and z^t_t = z_t we can explicitly solve for effort levels and dissipation:

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( ⅛ R*)¹⁺ⁿ

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I ( I-¹ Rt)^1+,

The dissipation, the total cost of conflict, is increasing in R_t, the amount of the valuable resource
in dispute, and is increasing in I, the total number of agents in conflict.

In this particular case the dissipation does not depend on the dynamics of the model. This is
because everybody make the same choices and the conflict technology does not change with time
(even if α^l_t changes, it changes in the same amount for all the agents, so the relative strength of
the conflict groups does not change). The dynamic change is observed in the investment in conflict
technology and in consumption, but not in effort nor dissipation.

Therefore it is uninteresting for the conflict theory the game where all the agents are the same,
because the dynamic choices are not reflected in dissipation.

5.1 Two-group’s case

For a conflict with two groups which differ (we can extend this to any number of agents), the first
order conditions are

V¹ I    ^o1⁶1    R ^{(б1) +}

^vt ( 0161+0262^Rt      1+η1

„.2 I    ⁰2⁶2    R     (⁶2) ⁺'

^vt I 0_t¹6_t¹+02 62 ^Rt      1+η2

_λ1 _λ.2   2

1    1        6 +10 +16 +1                  1            1              1

^β1 E^tγt+1^zt+1 ( 1   1     2   2 )2 ^Rt+1 = ^γt   ^β1E^tγt+1 (1 ^δ (^st+1))

(0 +16 +1+0 +16 +1)

2 _λ.1 _λ1

2 2 22  ~2       ⁶t+1⁰t+1⁶t+1     D _ 2,2    q 2 ∕∙v2   Λι X 22 λλ

^β2E^tγt+1^zt+1 ₍ 1   1    2   2 )2 R^t+¹ = ^γt ^{- β2}E^tγt+1 (1 ^{- δ} (^st+1))

(0t+16t+1+0t+16t+1)

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