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@wehlutyk
Created December 10, 2020 03:38
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m environment at `~/Code/Research/Tom's self-organization of stateless complex societies in the Andes/Project.toml`\n"
]
}
],
"source": [
"]activate ."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"using Random\n",
"using LightGraphs\n",
"using LinearAlgebra: Symmetric\n",
"using ProgressMeter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model definition"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"utility (generic function with 4 methods)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"utility(Uij::Bool, Bi::T, Bj::T) where T =\n",
" # Compute utility based on whether i and j cooperate or not\n",
" Bi == Bj ? Uij : ~Uij\n",
"\n",
"utility(U::AbstractArray{Bool,2},\n",
" B::AbstractArray{T,1},\n",
" G::SimpleGraph{Int},\n",
" Bi::T, i::Int) where T =\n",
" sum(utility(U[i, j], Bi, B[j]) for j in neighbors(G, i))\n",
"\n",
"utility(U, B, G, i) = utility(U, B, G, B[i], i)\n",
"utility(U, B, G) = sum(utility(U, B, G, i) for i in 1:length(B))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"preference (generic function with 4 methods)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"preference(Pij, Bi::T, Bj::T) where T =\n",
" # Compute preference based on whether i and j cooperate or not\n",
" Bi == Bj ? Pij : -Pij\n",
"\n",
"preference(P::AbstractArray{Float64,2},\n",
" B::AbstractArray{T,1},\n",
" G::SimpleGraph{Int},\n",
" Bi::T, i::Int) where T =\n",
" sum(preference(P[i, j], Bi, B[j]) for j in neighbors(G, i))\n",
"\n",
"preference(P, B, G, i) = preference(P, B, G, B[i], i)\n",
"preference(P, B, G) = sum(preference(P, B, G, i) for i in 1:length(B))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"prefutility (generic function with 3 methods)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"prefutility(U::AbstractArray{Bool,2},\n",
" P::AbstractArray{Float64,2},\n",
" B::AbstractArray{T,1},\n",
" G::SimpleGraph{Int},\n",
" Bi::T, i::Int) where T =\n",
" utility(U, B, G, Bi, i) + preference(P, B, G, Bi, i)\n",
"\n",
"prefutility(U, P, B, G, i) = prefutility(U, P, B, G, B[i], i)\n",
"prefutility(U, P, B, G) = sum(prefutility(U, P, B, G, i) for i in 1:length(B))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"newpreference (generic function with 2 methods)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"newpreference(Pij::Float64, Bi::T, Bj::T, rate::Float64) where T =\n",
" # Only update half the time, and update the preference depending on whether i and j cooperate or not\n",
" Pij + rand(Bool) * (Bi == Bj ? rate : -rate)\n",
"\n",
"newpreference(P::AbstractArray{Float64,2},\n",
" B::AbstractArray{T,1},\n",
" G::SimpleGraph{Int},\n",
" rate,\n",
" i::Int) where T =\n",
" [has_edge(G, i, j) ? newpreference(P[i, j], B[i], B[j], rate) : P[i, j] for j in 1:length(B)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Run the model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Make simulations reproducible\n",
"Random.seed!(1)\n",
"\n",
"# Graph parameters\n",
"N = 100 # 500\n",
"#G_k = 50\n",
"#G_β = 0.005\n",
"G = complete_graph(N) # watts_strogatz(N, G_k, G_β)\n",
"\n",
"# Simulation parameters\n",
"timesteps = 1000\n",
"#resets = 1000\n",
"\n",
"# Possible behaviours\n",
"@enum Behaviour A=1 B=2\n",
"# Let us use the regular `rand()` function for sampling with `rand(Behaviour, n)`\n",
"Random.rand(rng::AbstractRNG, ::Random.SamplerType{Behaviour}) =\n",
" Behaviour(rand(rng, 1:length(instances(Behaviour))))\n",
"\n",
"# Habituation parameters\n",
"#habituation = true\n",
"habit_prob = 0.05#0.0001\n",
"habit_rate = 0.005;"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# Initial utilities and preferences\n",
"utilities = Symmetric(rand(Bool, (N, N)))\n",
"preferences = zeros(N, N);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"simulate (generic function with 1 method)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function simulate(resets::Int, habituation::Bool)\n",
" utility_history = zeros(resets, timesteps)\n",
" @showprogress \"Simulating...\" for reset in 1:resets\n",
" # Randomize initial behaviours\n",
" behaviours = rand(Behaviour, N)\n",
"\n",
" # FIXME: random order or random selection? \n",
" for (step, i) in enumerate(rand(1:N, timesteps))\n",
" # Compute new behaviour\n",
" prefutilityA = prefutility(utilities, preferences, behaviours, G, A::Behaviour, i)\n",
" prefutilityB = prefutility(utilities, preferences, behaviours, G, B::Behaviour, i)\n",
" newbehaviour = prefutilityA > prefutilityB ? A : B\n",
" #println()\n",
" #println(\"i = $i\")\n",
" #println(\"prefutilityA = $(prefutilityA), prefutilityB = $(prefutilityB), newbehaviour = $(newbehaviour)\")\n",
"\n",
" # Update preferences\n",
" if habituation && (rand() < habit_prob)\n",
" #println(\"old preferences = $(preferences[i, :])\")\n",
" preferences[i, :] = newpreference(preferences, behaviours, G, habit_rate, i)\n",
" #println(\"new preferences = $(preferences[i, :])\")\n",
" end\n",
"\n",
" # Update behaviour (after the preference update as it should be based on the previous behaviour)\n",
" behaviours[i] = newbehaviour\n",
"\n",
" # Track history\n",
" utility_history[reset, step] = utility(utilities, behaviours, G)\n",
" end\n",
" end\n",
" utility_history\n",
"end "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32mSimulating...100%|██████████████████████████████████████| Time: 0:00:38\u001b[39m\n",
"\u001b[32mSimulating...100%|██████████████████████████████████████| Time: 0:00:42\u001b[39m\n",
"\u001b[32mSimulating...100%|██████████████████████████████████████| Time: 0:00:41\u001b[39m\n"
]
},
{
"data": {
"text/plain": [
"3000×1000 Array{Float64,2}:\n",
" 4820.0 4850.0 4892.0 4892.0 4892.0 … 5606.0 5606.0 5606.0 5606.0\n",
" 5028.0 5028.0 5028.0 5028.0 5028.0 5572.0 5572.0 5572.0 5572.0\n",
" 5052.0 5052.0 5052.0 5052.0 5052.0 5580.0 5580.0 5580.0 5580.0\n",
" 4838.0 4838.0 4838.0 4884.0 4898.0 5618.0 5618.0 5618.0 5618.0\n",
" 4922.0 4932.0 4946.0 4946.0 4946.0 5570.0 5570.0 5570.0 5570.0\n",
" 5034.0 5034.0 5068.0 5068.0 5068.0 … 5628.0 5628.0 5628.0 5628.0\n",
" 5036.0 5036.0 5036.0 5062.0 5062.0 5594.0 5594.0 5594.0 5594.0\n",
" 5016.0 5016.0 5016.0 5016.0 5016.0 5560.0 5560.0 5560.0 5560.0\n",
" 4850.0 4868.0 4882.0 4888.0 4888.0 5550.0 5550.0 5550.0 5550.0\n",
" 5044.0 5062.0 5064.0 5086.0 5108.0 5620.0 5620.0 5620.0 5620.0\n",
" 4952.0 4952.0 4952.0 4966.0 5016.0 … 5600.0 5600.0 5600.0 5600.0\n",
" 4942.0 4968.0 4968.0 4970.0 4972.0 5584.0 5584.0 5584.0 5584.0\n",
" 4952.0 4952.0 4952.0 4952.0 4962.0 5618.0 5620.0 5620.0 5620.0\n",
" ⋮ ⋱ \n",
" 4972.0 4972.0 4958.0 4972.0 4972.0 5652.0 5652.0 5652.0 5652.0\n",
" 5014.0 5014.0 4992.0 5026.0 5032.0 5652.0 5652.0 5652.0 5652.0\n",
" 5002.0 5036.0 5036.0 5050.0 5048.0 … 5652.0 5652.0 5652.0 5652.0\n",
" 5030.0 5030.0 5030.0 5030.0 5030.0 5652.0 5652.0 5652.0 5652.0\n",
" 4958.0 4958.0 4944.0 4946.0 4948.0 5652.0 5652.0 5652.0 5652.0\n",
" 5098.0 5098.0 5098.0 5098.0 5112.0 5652.0 5652.0 5652.0 5652.0\n",
" 4946.0 4946.0 4960.0 4960.0 4960.0 5652.0 5652.0 5652.0 5652.0\n",
" 4902.0 4902.0 4928.0 4928.0 4928.0 … 5652.0 5652.0 5652.0 5652.0\n",
" 4880.0 4898.0 4898.0 4904.0 4918.0 5652.0 5652.0 5652.0 5652.0\n",
" 4894.0 4924.0 4924.0 4914.0 4908.0 5652.0 5652.0 5652.0 5652.0\n",
" 4878.0 4878.0 4878.0 4878.0 4878.0 5652.0 5652.0 5652.0 5652.0\n",
" 4884.0 4884.0 4884.0 4884.0 4884.0 5652.0 5652.0 5652.0 5652.0"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"utility_history = [\n",
" simulate(1000, false);\n",
" simulate(1000, true);\n",
" simulate(1000, false)\n",
"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot results"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"using AbstractPlotting, CairoMakie, StatsBase"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"┌ Info: Makie/AbstractPlotting is caching fonts, this may take a while. Needed only on first run!\n",
"└ @ AbstractPlotting /home/sl/.julia/packages/AbstractPlotting/JCbJs/src/utilities/texture_atlas.jl:115\n"
]
},
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"text/plain": [
"Scene (960px, 540px):\n",
" 46 Plots:\n",
" ├ Combined{AbstractPlotting.axis2d,Tuple{Tuple{Tuple{Float32,Float32},Tuple{Float32,Float32}}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" ├ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" └ Combined{AbstractPlotting.lines,Tuple{Array{Point{2,Float32},1}}}\n",
" 1 Child Scene:\n",
" └ Scene (960px, 540px)\n",
"\n",
"To show the scene in a window, try setting `AbstractPlotting.inline!(false)`."
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"scene = Scene()\n",
"for reset in 1:15\n",
" lines!(scene, 1:timesteps, utility_history[reset, :], color = :red)\n",
" lines!(scene, 1:timesteps, utility_history[1000 + reset, :], color = :lightgreen)\n",
" lines!(scene, 1:timesteps, utility_history[2000 + reset, :], color = :darkblue)\n",
"end\n",
"scene"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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