From 6e636c80340be03bf6e53cf3ac384064f76ba864 Mon Sep 17 00:00:00 2001
From: Will King <kin12017@byui.edu>
Date: Fri, 14 May 2021 13:16:01 -0700
Subject: [PATCH] Recording code stuff

---
 Code/2Firm_vfi.jl | 63 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 Code/2Firm_vfi.jl

diff --git a/Code/2Firm_vfi.jl b/Code/2Firm_vfi.jl
new file mode 100644
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+++ b/Code/2Firm_vfi.jl
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+#=
+The purpose of this is to set up a 2-firm, finite, dynamic orbit use model.
+
+# TODO LIST
+ - [ ] Set up loss functions
+ - [ ] Set up utility functions
+ - [ ] Set up State×Choice → Utility matrix
+ - [ ] Set up VFI
+ - [ ] Run it
+ - [ ] ?
+ - [ ] Profit!!!!
+=#
+
+#=
+Model Description
+
+V({sʲₜ}, Dₜ) = max{xⁱ} U(sⁱₜ) - F(xⁱ) + β V({sʲₜ₊₁}, Dₜ₊₁)
+
+Utility Function: Similar to Rao Rondina
+U(s) = ηs - ρ
+
+Laws of motion
+sʲₜ₊₁ = (1-l({sʲₜ},Dₜ))sʲₜ + xʲₜ
+Dₜ₊₁ = (1-δ)Dₜ + g(Dₜ) + γ⋅ ∑ⱼ sʲₜ⋅l({sʲₜ},Dₜ) + Γ⋅∑ xʲₜ
+
+Loss Function: Similar to Rao Rondina
+lⁱ({sʲₜ},Dₜ) = 1-exp(  -α₁⋅∑{i≠j}sʲₜ - α₂⋅sʲₜ - α₃⋅Dₜ  )
+
+Autofragmentation Function: See Rao Rondina for a description (pg48)
+g(Dₜ) = ζ⋅Dₜ⋅(1-exp(-α₄⋅Dₜ))
+
+Launch Costs
+F(xⁱ) = F⋅xⁱ
+
+=#
+
+#Setup Model Constants
+const α1 = 1e-2
+const α2 = 1e-2
+const α3 = 1e-2
+const α4 = 1e-2
+const ζ = 3
+const δ = 2e-2
+const F = 5
+const γ = 10
+const Γ = 2
+
+#=
+Potential Structs
+
+Maybe a view onto the state space?
+With methods which show own and other sizes as vectors?
+=#
+
+#Loss Function
+function loss(constellation_sizes::Vector{<:Int},debris::Float64,owner::Int)
+    1-exp(-α1*sum(constellation_sizes) + (α1-α2)*constellation_sizes[owner] - α3*debris)
+end
+
+#=
+I think that I might need to consider the launch quantities  of the other operators
+as a state variable and use a nash equilibrium style idea of equilibrium.
+=#