diff --git a/2021-04-02_WrittenWork.pdf b/2021-04-02_WrittenWork.pdf new file mode 100644 index 0000000..9a71dad Binary files /dev/null and b/2021-04-02_WrittenWork.pdf differ diff --git a/Code/2Firm_vfi.jl b/Code/2Firm_vfi.jl new file mode 100644 index 0000000..3b33854 --- /dev/null +++ b/Code/2Firm_vfi.jl @@ -0,0 +1,58 @@ +#= +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 diff --git a/CurrentWriting/Main.pdf b/CurrentWriting/2021-03-06_Notes_on_main.pdf similarity index 95% rename from CurrentWriting/Main.pdf rename to CurrentWriting/2021-03-06_Notes_on_main.pdf index 6ffa058..f674e20 100644 Binary files a/CurrentWriting/Main.pdf and b/CurrentWriting/2021-03-06_Notes_on_main.pdf differ diff --git a/CurrentWriting/sections/03_SurvivalAnalysis.tex b/CurrentWriting/sections/03_SurvivalAnalysis.tex index c98b806..10d8307 100644 --- a/CurrentWriting/sections/03_SurvivalAnalysis.tex +++ b/CurrentWriting/sections/03_SurvivalAnalysis.tex @@ -31,8 +31,8 @@ The marginal survival rates when a given constellation $i$ changes size are: =& \sum_{i=1}^N \left[ \frac{R_i}{S_t} \right] - \frac{R}{S_t} +\sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{} \label{EQ:i} \end{align} -Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival rate- -across constellation operators. +Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival +rate across constellation operators. The derivation of \cref{EQ:i} is in Appendix \ref{APX:Derivations:SurvivalRates}. Direct comparison between the marginal survival rates of an individual operator and the social planner's fleet cannot proceed further without specifying the functional loss forms $l^i(\cdot)$