Symmetric - asymmetric CSE test case

This example is using the asymmetric afrprogs code with two players with the same distribution (i.e. symmetric). The purpose is to test that the asymmetric code base can reproduce the symmetric result and we can also test this further by comparing the result to the BNE.

Install dependencies

Enter the Julia REPL (julia) and run:

using Pkg
Pkg.add("ConstrainedStrategicEquilibrium")

Load required modules

using ConstrainedStrategicEquilibrium
using Plots
using Distributions
using NonlinearSolve

Define some parameters

Here we set the initial and final values of n.

inin = 2
maxn = 6

6

Solve for 2 players

Start from n=2 like the original sym.f code with the following initial guess:

xguess = [1.58285, 1.02813, -1.66483]

3-element Vector{Float64}:
  1.58285
  1.02813
 -1.66483

Create the problem:

cse_prob2 = AsymmetricAfrprogsCSEProblem(
    inin=inin,
    maxn=maxn,
    np=2,
    mc=10000,
    solver_kwargs=(show_trace=Val(false), maxiters=2000, abstol=1e-6, reltol=1e-6),
    solver_initial_guess=xguess,
    distributions=[Beta(3, 3), Beta(3, 3)],
    knot_refinement_strategy=:even_spacing,
)

AsymmetricAfrprogsCSEProblem(np=2, mc=10000, n=2..6)

Compute the solution to the CSE problem for 2 players:

solutions2 = compute_cse(cse_prob2)

5-element Vector{ConstrainedStrategicEquilibrium.AsymmetricCSESolution}:
 AsymmetricCSESolution(n=02, C_1=(NaN, NaN), C_2=2.40e-08)
 AsymmetricCSESolution(n=03, C_1=(9.30e-04, 9.30e-04), C_2=4.67e-07)
 AsymmetricCSESolution(n=04, C_1=(4.70e-04, 4.70e-04), C_2=4.98e-07)
 AsymmetricCSESolution(n=05, C_1=(2.63e-04, 2.63e-04), C_2=4.62e-07)
 AsymmetricCSESolution(n=06, C_1=(1.91e-04, 1.91e-04), C_2=4.93e-07)

We also compute the BNE for 2 players for the same problem:

bne2x = Vector{Float64}(undef, 101)
bne2y = Vector{Float64}(undef, 101)
for m = 1:101
    ti = (m - 1.0) / 100.0
    if ti == 0
        true_bne = 0.0
    else
        true_bne = compute_bne(ti, cse_prob2.distributions[1], cse_prob2.np)
    end
    bne2x[m] = ti
    bne2y[m] = true_bne
end

Solve for 4 players

Define the initial guess and create the problem:

xguess = [-log(0.25), -log(0.25), log(0.25)]
cse_prob4 = AsymmetricAfrprogsCSEProblem(
    inin=inin,
    maxn=maxn,
    np=4,
    mc=10000,
    solver_kwargs=(show_trace=Val(false), maxiters=2000, abstol=1e-6, reltol=1e-6),
    solver_initial_guess=xguess,
    distributions=[Beta(3, 3), Beta(3, 3)],
    knot_refinement_strategy=:even_spacing,
)

AsymmetricAfrprogsCSEProblem(np=4, mc=10000, n=2..6)

Compute the solution to the CSE problem for 4 players:

solutions4 = compute_cse(cse_prob4)

5-element Vector{ConstrainedStrategicEquilibrium.AsymmetricCSESolution}:
 AsymmetricCSESolution(n=02, C_1=(NaN, NaN), C_2=4.45e-10)
 AsymmetricCSESolution(n=03, C_1=(1.07e-03, 1.07e-03), C_2=4.59e-07)
 AsymmetricCSESolution(n=04, C_1=(5.14e-04, 5.14e-04), C_2=2.30e-08)
 AsymmetricCSESolution(n=05, C_1=(2.99e-04, 2.99e-04), C_2=1.38e-07)
 AsymmetricCSESolution(n=06, C_1=(2.05e-04, 2.05e-04), C_2=2.01e-07)

We also compute the BNE for 4 players for the same problem:

bne4x = Vector{Float64}(undef, 101)
bne4y = Vector{Float64}(undef, 101)
for m = 1:101
    ti = (m - 1.0) / 100.0
    if ti == 0
        true_bne = 0.0
    else
        true_bne = compute_bne(ti, cse_prob4.distributions[1], cse_prob4.np)
    end
    bne4x[m] = ti
    bne4y[m] = true_bne
end

Results

First some sanity checking that both problems were solved successfully.

if length(solutions2) != length(solutions2)
    throw("solutions are not the same length")
end
if (!solutions2[end].success) || (!solutions4[end].success)
    throw("final solution not successful")
end

Plot the two CSE solutions and BNE solutions on the same graph:

cseplot(
    solutions2[end],
    cse_label=Dict(:bidder1 => "CSE 1 (np=2)", :bidder2 => "CSE 2 (np=2)"),
    cse_colour=Dict(:bidder1 => :1, :bidder2 => :2),
    knot_label=Dict(:bidder1 => "", :bidder2 => ""),
    dpi=300,
)
cseplot!(
    solutions4[end],
    cse_label=Dict(:bidder1 => "CSE 1 (np=4)", :bidder2 => "CSE 2 (np=4)"),
    cse_colour=Dict(:bidder1 => :3, :bidder2 => :4),
    knot_label=Dict(:bidder1 => "", :bidder2 => ""),
    title="Comparing CSE against BNE for num players 2 and 4\nasym code but all bidders are Beta(3,3)",
    dpi=300,
)
plot!(bne2x, bne2y, label="BNE (np=2)", dpi=300, seriescolor=:5)
plot!(bne4x, bne4y, label="BNE (np=4)", dpi=300, seriescolor=:6)

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