Theory of civil war under asymmetric information

Munich Personal RePEc Archive

Theory of civil war under asymmetric information

Jellal, Mohamed

Al Makrîzi Institut D’économie, Rabat , Morocco

26 July 2014

Online at https://mpra.ub.uni-muenchen.de/57600/

MPRA Paper No. 57600, posted 27 Jul 2014 20:36 UTC

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

 

   ₀, ₁

 

F  f 

 

  d

d

F

 f





1 0



 

 



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   

M  r  s,  ,    .

sT

  

 T - s  + sw -   s (2)

= U

(1)

sy +

s - T

=



 r

r

V



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

  y + w

 

s 

  r

   

M  r s,  ,    .



   ^{= 0 }  ^{  and r}    ⁼  ^{, }  ^{  .}

s

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𝑀(𝜃) 𝑉(𝜃,𝜃) 𝜃 𝜃

𝑉(𝜃,𝜃)

∀𝜃,𝜃 ∈ Ω)

𝑉(𝜃,𝜃) = 𝑇 − 𝑠 𝜃 𝜃 − 𝑟 𝜃 +𝑠 𝜃 𝑦

𝑉 𝜃 = 𝑉(𝜃,𝜃)

∀𝜃,𝜃 ∈ Ω (𝜃,𝜃) ≥ 𝑉(𝜃,𝜃)

∀𝜃 ∈ Ω 𝑉(𝜃,𝜃) ≥0

Max_𝑠(.)𝑈 = 𝑇 − 𝑠 𝜃 𝑟 𝜃 _𝜃^𝜃 +𝑠 𝜃 𝑤 − Ψ 𝑠 𝜃 𝑑𝐹 𝜃

∀𝜃,𝜃 ∈ Ω 𝑉(𝜃,𝜃) ≥ 𝑉(𝜃,𝜃)

∀𝜃 ∈ Ω 𝑉(𝜃,𝜃) ≥0

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𝑀(𝜃)

𝑀(𝜃) 𝑉 𝜃 = 𝑇 − 𝑠 𝑥 𝑑𝑥_𝜃^𝜃 𝑠′ 𝜃 ≤0 ∀𝜃 ∈ Ω

𝑉 𝜃 𝑉 𝜃 = Max

𝜃) 𝑉(𝜃,𝜃) = 𝑇 − 𝑠 𝜃 𝜃 − 𝑟 𝜃 +𝑠 𝜃 𝑦 𝑉 𝜃

∀𝜃 ∈ Ω 𝑉′ 𝜃 = 𝑇 − 𝑠 𝜃 ≥0 𝑉′′ 𝜃 =−𝑠′ 𝜃 ≥ 0 𝑠′ 𝜃 ≤ 0 ∀𝜃 ∈ Ω

𝑉′ 𝜃 = 𝑇 − 𝑠 𝜃 𝑉 𝜃 = 0 𝑉 𝜃 = 𝑇 − 𝑠 𝑥 𝑑𝑥_𝜃^𝜃

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𝑉 𝜃 = 𝑇 − 𝑠 𝑥 𝑑𝑥_𝜃^𝜃

𝑉 𝜃 𝜃

𝜃

𝜃 𝑠′ 𝜃 ≤0

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𝑉(𝜃) = 𝑇 − 𝑠 𝜃 𝜃 − 𝑟 𝜃 +𝑠 𝜃 𝑦

𝑇 − 𝑠 𝜃 𝑟 𝜃 = 𝑇 − 𝑠 𝜃 𝜃+ 𝑠 𝜃 𝑦+𝑉(𝜃)

U = 𝑇 − 𝑠 𝜃 𝜃_𝜃^𝜃 +𝑠 𝜃 𝑦+𝑤 − Ψ 𝑠 𝜃 − 𝑉(𝜃) 𝑑𝐹 𝜃

𝑉 𝜃

𝑉 𝜃 = 𝑇 − 𝑠 𝑥 𝑑𝑥

𝜃 𝜃

U = 𝑇 − 𝑠 𝜃 𝜃_𝜃^𝜃 +𝑠 𝜃 𝑦+𝑤 − Ψ 𝑠 𝜃 −^1−𝐹_𝑓(𝜃^(𝜃₎⁾ 𝑇 − 𝑠 𝜃 𝑑𝐹 𝜃

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Max_𝑠(.)𝑈 = 𝑇 − 𝑠 𝜃 𝜃_𝜃^𝜃 +𝑠 𝜃 𝑦+𝑤 − Ψ 𝑠 𝜃 −^1−𝐹_𝑓(𝜃^(𝜃₎⁾ 𝑇 − 𝑠 𝜃 𝑑𝐹 𝜃

Ψ′ 𝑠 𝜃 = 𝑦+𝑤 − 𝜃+1− 𝐹(𝜃) 𝑓(𝜃)

𝑑𝑈

𝑑𝑠 𝜃 =−𝜃+𝑦+𝑤 − Ψ′ 𝑠 𝜃 +1− 𝐹 𝜃 𝑓 𝜃 = 0

Ψ′ 𝑠 𝜃 𝑦 +𝑤

−𝜃+^{1−𝐹(𝜃)}

𝑓(𝜃)

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𝑑𝑠 𝜃

𝑑 𝑦+𝑤 = 1

Ψ" 𝑠 𝜃 ≥ 0

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