Okay, here is an example that worked with the callback and domain restriction but doesn’t work now. No worries if you’re too busy to look - I really, really appreciate the help!
using JuMP
using Ipopt
using DataFrames, CSV
using DifferentialEquations
using Distributions
using NLsolve
type Bidder
bidder_id::String
b::Vector{Float64}
score::Float64
end
type Auction
contract_no::Int64
num_bidders::Int64
T::Int64
bidders::Array{Bidder}
q_a::Vector{Float64}
q_a_model::Vector{Float64}
q_o::Vector{Float64}
c::Vector{Float64}
sigma_t_sq::Vector{Float64}
gamma::Float64
item_ids::Vector{Int64}
optb_denom::Array{Float64}
optb_num_coeff::Array{Float64}
optb_num_main::Array{Float64}
extra_work_payment::Float64
winning_alpha::Float64
highest_alpha::Float64
lowest_alpha::Float64
alpha_lgmean::Float64
sigma_lgalpha::Float64
dollar_scale::Int64
end
type AuctionEquilibrium
auction_seqid::Int64
contract_no::Int64
alpha_types::Vector{Float64}
score_maps::Vector{Float64}
expost_cost::Vector{Float64}
end
type AugmentedAuctionEquilibrium
auction_seqid::Int64
contract_no::Int64
alpha_types::Vector{Float64}
score_maps::Vector{Float64}
expost_cost::Vector{Float64}
winning_eq_score::Float64
winning_eq_cost::Float64
end
auc = Auction(30163,
6,
80,
Bidder[
Bidder("69", [3.0, 50.0, 7.5, 7.5, 1.8, 1.3, 0.25, 0.6, 1.8, 1.4, 5.0, 0.6, 5.0, 5.0, 2.55, 2.55, 6.15, 0.9, 1.6, 0.85, 1.2, 0.3, 0.36, 0.38, 0.65, 0.335, 6.0, 3.5, 3.75, 0.07, 0.8, 2.25, 4.5, 5.0, 0.04, 5.5, 0.95, 0.013, 0.3, 0.3, 0.66, 0.8, 0.18, 0.185, 0.17, 0.07, 0.66, 0.8, 0.49, 0.045, 0.17, 1.25, 1.25, 0.07, 3.1, 1.2, 3.0, 0.11, 0.9, 18.0, 4.5, 0.6, 0.55, 0.9, 0.3, 0.075, 1.45, 0.125, 7.5, 3.0, 0.5, 0.35, 0.14, 0.145, 0.15, 14.5, 3.5, 55.0, 145.0, 336.0], 951.971),
Bidder("108", [5.3, 70.0, 15.0, 7.0, 1.2, 1.075, 0.15, 0.95, 1.7, 3.0, 4.0, 1.0, 1.0, 2.0, 0.0001, 0.0001, 0.0001, 0.55, 1.1, 0.85, 0.95, 0.6, 0.35, 0.375, 0.75, 0.4, 0.7, 2.8, 3.5, 0.1, 0.825, 1.85, 4.8, 3.81, 0.06, 3.81, 0.381, 0.0045, 0.07, 0.35, 0.55, 0.71, 0.1, 0.21, 0.175, 0.085, 0.656, 0.786, 0.488, 0.044, 0.166, 1.233, 1.233, 0.07, 3.2, 1.0, 1.875, 0.07, 0.7, 19.0, 2.6, 0.55, 0.47, 0.6, 0.25, 0.1, 1.52, 0.15, 2.65, 4.0, 1.0, 0.35, 0.2, 0.2, 0.25, 17.0, 3.1, 90.0, 200.0, 330.0], 992.433),
Bidder("15", [6.0, 100.0, 30.0, 12.0, 6.5, 2.0, 0.2, 0.655, 1.6, 2.0, 1.5, 0.0001, 0.001, 0.001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 1.0, 1.0, 0.575, 0.3, 0.3, 0.985, 0.3, 3.5, 6.25, 3.3, 0.15, 0.5, 3.5, 4.0, 6.0, 0.1, 6.0, 0.6, 0.025, 0.1, 0.25, 0.51, 0.69, 0.26, 0.22, 0.16, 0.12, 0.67, 0.8, 0.5, 0.05, 0.17, 1.25, 1.25, 0.08, 3.2, 0.8, 2.9, 0.082, 0.82, 15.0, 2.1, 1.3, 0.5, 0.85, 0.45, 0.062, 1.3, 0.125, 4.5, 2.0, 1.25, 0.45, 0.2, 0.2, 0.125, 17.0, 3.5, 80.0, 160.0, 291.6], 1010.56),
Bidder("113", [5.0, 100.0, 5.0, 5.0, 2.5, 2.5, 0.25, 1.0, 2.5, 2.0, 5.0, 0.75, 4.5, 4.0, 2.3, 2.75, 7.5, 1.0, 1.5, 1.2, 1.2, 2.0, 0.4, 0.4, 1.0, 0.6, 7.5, 3.0, 3.5, 0.05, 0.3, 2.5, 3.0, 6.5, 0.04, 6.5, 0.65, 0.1, 0.1, 0.5, 0.85, 0.85, 0.5, 0.5, 0.5, 0.1, 0.8, 0.8, 0.7, 0.1, 0.15, 1.5, 1.5, 0.1, 2.5, 1.0, 3.5, 0.2, 0.75, 15.0, 3.5, 2.0, 0.9, 0.9, 0.5, 0.175, 1.75, 0.15, 6.0, 2.2, 1.0, 0.4, 0.2, 0.25, 0.3, 27.5, 4.0, 60.0, 150.0, 250.0], 1020.65),
Bidder("27", [10.0, 90.0, 20.0, 10.0, 1.0, 1.0, 0.2, 1.0, 1.5, 1.5, 5.0, 0.8, 2.0, 3.0, 2.5, 2.8, 6.0, 1.0, 2.0, 1.0, 1.2, 0.7, 0.25, 0.3, 1.0, 0.15, 5.0, 3.0, 3.5, 0.1, 0.5, 2.5, 4.0, 5.0, 0.1, 5.0, 1.2, 0.05, 0.2, 0.4, 0.82, 1.0, 0.2, 0.25, 0.2, 0.08, 0.6, 1.0, 0.6, 0.05, 0.2, 1.3, 1.3, 0.08, 4.0, 1.5, 3.0, 0.2, 1.1, 15.0, 3.0, 1.0, 1.0, 0.5, 0.3, 0.1, 1.3, 0.1, 6.5, 3.0, 1.5, 0.5, 0.3, 0.3, 0.1, 18.0, 2.5, 60.0, 165.0, 350.0], 1052.92),
Bidder("30", [3.5, 63.25, 15.0, 12.25, 1.2, 1.5, 0.24, 0.8, 2.5, 0.6, 1.5, 0.55, 1.0, 1.95, 0.5515, 1.65, 2.3, 2.3, 2.3, 1.2, 1.2, 0.5, 0.35, 0.25, 1.0, 0.45, 3.1385, 1.87, 3.1, 0.05, 3.0, 2.25, 3.45, 5.4, 0.076, 4.8, 0.48, 0.025, 0.03, 0.65, 0.85, 1.0, 0.5, 0.25, 0.23, 0.1, 0.6562, 0.7875, 0.488, 0.044, 0.166, 1.233, 1.233, 0.0657, 3.1, 0.65, 2.4, 0.135, 0.88, 12.0, 2.625, 2.0, 0.41, 0.65, 0.5, 0.15, 0.66, 0.13, 7.7, 2.0, 1.5, 0.45, 0.16, 0.16, 0.644, 20.91, 3.325, 201.3, 186.0, 358.5], 1169.53)
],
[1.0, 1.0, 1.0, 1.0, 4.305, 5.64, 0.66, 6.3, 4.876, 1.313, 1.0, 1.7, 0.0, 1.936, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 3.5, 0.0, 3.0, 2.0, 2.56, 2.0, 2.026, 7.758, 2.0, 0.0, 2.0, 2.359, 0.8361, 1.919, 7.0, 2.794, 1.6, 7.57, 2.7, 0.5, 5.52, 5.14, 1.0, 2.0, 3.0, 7.3, 0.76, 1.14, 2.0, 2.0, 4.0, 2.0, 2.0, 4.3, 0.493, 1.0, 1.191, 0.0, 1.1, 1.45, 1.144, 0.954, 0.0, 1.33, 2.0, 2.0, 1.37, 6.0, 1.342, 2.0, 1.0968, 1.4, 2.78, 2.83, 0.0, 4.2301, 2.464, 1.0, 1.0, 1.0],
[0.966373, 1.03436, 1.03854, 1.03706, 0.899599, 10.2544, 2.6365, 0.791545, 7.95488, 1.5645, 1.05316, 1.98792, 0.97056, 1.51926, 7.57679, 7.51483, 1.00723, 0.132271, 1.00289, 2.05508, 1.17663, 0.896151, 2.10946, 2.15079, 1.92008, 0.329052, 2.08897, 5.54745, 0.325804, 2.04633, 2.04073, 2.0651, 1.27009, 1.57682, 0.723703, 1.96701, 1.73725, 2.73545, 1.96947, 1.29554, 5.99257, 4.8658, 1.05778, 2.09554, 2.09466, 6.9172, 1.03985, 0.372803, 2.29, 2.16601, 8.72816, 2.18974, 2.17816, 5.25118, 1.12995, 0.754065, 1.13315, 2.08308, 2.28083, 1.54813, 0.12893, 0.126055, 0.133338, 0.579984, 1.00542, 1.01635, 1.31789, 6.07841, 1.25241, 1.87727, 0.588432, 2.41505, 2.52315, 3.44419, 1.02171, 5.31657, 2.50114, 1.02333, 1.03668, 0.99921],
[1.0, 1.0, 1.0, 1.0, 5.5, 9.95, 2.5, 4.6, 7.7, 1.5, 1.0, 2.0, 1.0, 1.5, 7.5, 7.5, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0, 2.3, 2.0, 2.0, 5.5, 2.0, 2.0, 2.0, 2.0, 1.15, 1.45, 8.5, 1.83, 1.6, 3.0, 2.0, 1.3, 6.0, 5.0, 1.0, 2.0, 2.0, 7.0, 1.0, 0.4, 2.0, 2.0, 8.0, 2.0, 2.0, 5.5, 1.2, 0.9, 1.1, 2.0, 2.2, 1.2, 0.8, 1.0, 1.0, 1.1, 1.0, 1.0, 1.4, 6.0, 1.35, 2.0, 0.575, 2.4, 2.4, 3.3, 1.0, 5.25, 2.43, 1.0, 1.0, 1.0], [5.0, 67.481, 40.0, 37.45, 1.4, 2.2, 0.2, 0.55, 1.2, 1.25, 5.411, 0.25, 2.0, 3.5, 0.5, 0.75, 0.65, 0.65, 0.65, 0.9, 0.9, 0.45, 0.25, 0.3, 0.75, 0.35, 15.0, 2.0, 5.0, 0.05, 0.75, 3.0, 2.7, 3.5, 0.044, 3.2, 0.66, 0.004, 0.09, 0.35, 0.7, 0.85, 0.025, 0.22, 0.15, 0.1, 0.4, 0.5, 0.525, 0.06, 0.1, 1.0, 1.0, 0.05, 3.5, 2.0, 2.5, 0.07, 0.5, 12.0, 1.8, 1.5, 0.36, 0.6, 0.35, 0.09, 1.0, 0.25, 7.0, 7.0, 0.6, 0.6, 0.125, 0.125, 0.075, 16.4, 3.3, 25.0, 95.15, 220.335],
# [6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5, 6.10217e-5],
[0.266744, 0.0273225, 0.0421256, 0.0369319, 14.6476, 22.9854, 1.60495, 11.302, 15.6259, 0.615968, 0.0455594, 0.886161, 0.184613, 0.474107, 12.6213, 11.5017, 0.21842, 0.399528, 0.195885, 0.947867, 1.32736, 0.278993, 0.974505, 0.972442, 1.60564, 1.62458, 0.819462, 6.38442, 1.75707, 0.96529, 0.883053, 0.878317, 0.291857, 0.580641, 27.6958, 1.03356, 0.698904, 3.12308, 1.43728, 0.539892, 11.1259, 7.61012, 0.233439, 1.05164, 1.05777, 13.2366, 0.225638, 0.0384456, 0.574783, 0.655254, 11.0342, 0.462189, 0.446732, 7.68193, 0.450646, 0.312049, 0.307968, 1.05974, 1.27164, 0.367653, 0.34818, 0.433924, 0.482024, 0.375989, 0.201127, 0.325242, 0.667156, 9.42226, 0.654951, 0.85768, 0.104165, 1.50268, 1.75021, 3.37543, 0.227249, 5.03697, 1.43975, 0.0304967, 0.0331136, 0.161771],
0.6826130247891279,
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80],
[-1.5131, 3.89486, -1.24173, -9.59145, 0.747652, 1.44794, -2.50622, -0.157109, 0.343891, -2.98074, -32.7223, -3.67103, -7.41064, -1.99665, -0.532382, -0.38287, -7.30409, -3.69846, -8.21912, -2.76577, -1.71772, -5.77714, -3.31557, -3.27313, -1.73864, -1.78881, 10.7598, 0.503338, 3.02247, -3.54961, -3.18483, -0.956048, -4.14559, -0.838532, -0.489197, 0.123921, -3.31727, -1.66486, -2.32753, -3.8333, -0.236908, -0.291461, -7.41735, -3.08405, -3.13491, -0.818766, -7.29965, -17.5757, -5.52017, -5.24277, -1.15959, -6.51784, -6.77796, -1.19387, -1.12625, -3.01074, -3.70539, -3.20879, -2.50567, 6.32945, -2.1918, -2.50377, -3.24424, -4.48277, -8.28796, -5.25166, -2.64572, -0.856315, 3.41898, 2.94877, -8.9902, -2.17478, -2.25734, -1.57351, -7.57005, 14.5892, 0.367736, -31.9679, 42.6842, 209.596],
[0.00804566, 0.0785483, 0.0509461, 0.0581106, 0.00080585, 0.000929025, 0.003343, 0.000873496, 0.00105756, 0.00522625, 0.0471063, 0.00484367, 0.011625, 0.00679004, 0.00127531, 0.00139944, 0.00982573, 0.00537167, 0.0109561, 0.00452834, 0.00323368, 0.00769242, 0.00440456, 0.00441391, 0.00307423, 0.00264208, 0.00523791, 0.00184883, 0.00244285, 0.00444661, 0.00486072, 0.00488693, 0.00845639, 0.00535941, 0.000658661, 0.0037999, 0.00491315, 0.00206156, 0.00298639, 0.00516765, 0.00115737, 0.00141005, 0.00919358, 0.00408151, 0.00405786, 0.00113496, 0.00951142, 0.022329, 0.00746763, 0.00655054, 0.00155598, 0.00928683, 0.00960816, 0.00153656, 0.00571483, 0.00618979, 0.00766555, 0.00405031, 0.00371292, 0.00700486, 0.0049311, 0.00494588, 0.00445234, 0.00627877, 0.0106705, 0.00659858, 0.00450358, 0.00136664, 0.00442366, 0.00500451, 0.0118468, 0.00342769, 0.00294291, 0.00209817, 0.00944397, 0.0022369, 0.00362224, 0.0703728, 0.0648113, 0.0132665],
[-0.0705317, 1.79982, 1.26654, 1.40457, -0.30851, 0.0196543, 0.108125, -0.330944, 0.0236111, 0.140789, 1.49203, 0.0197956, -0.0792282, 0.0875003, 0.0148866, 0.0109489, 0.100937, -2.13481, 0.090367, 0.0893706, -0.597983, -0.31913, 0.142725, 0.185531, -0.215395, -1.01031, 0.144729, 0.0201933, -0.93597, 0.0786908, 0.0796696, 0.107854, 0.469833, 0.2554, -0.276229, 0.158789, 0.230287, -0.0704781, -0.000628079, 0.0274074, 0.00732072, -0.00790154, 0.310958, 0.119024, 0.117503, 0.0015787, 0.242251, -0.553278, 0.556083, 0.298562, 0.0767308, 0.474636, 0.465135, -0.0217838, -0.116005, -0.424942, 0.160538, 0.106354, 0.0891904, 0.995242, -1.89333, -1.97991, -1.76723, -1.33972, 0.100579, 0.0958125, -0.0919954, 0.0177554, -0.118465, -0.108551, 0.21072, 0.033676, 0.0906773, 0.0571992, 0.160741, 0.0286561, 0.0744131, 1.25088, 1.55519, 0.0866853],
32.887551,
1.513837763112417,
1.5896136462082893,
1.1563027292545096,
0.18945827107692492,
0.25238806156330307,
1000)
function getBoundarySMax(alpha_max, auc, q_b, q_e, sigma_sq)
function ce_fun(svec)
s_max_var = svec[1]
return getCE_riskaverse_scale(alpha_max, s_max_var, auc, q_b, q_e,sigma_sq)
end
risky_cost_term = alpha_max*(auc.c' * (q_b - (auc.gamma * sigma_sq * 0.5)))
s_max_sol = nlsolve(ce_fun, [risky_cost_term]; inplace = false)
return s_max_sol.zero[1]
end
function getCE_riskaverse_scale(alpha, s, auc, q_b, q_e , sigma_sq)
b_opt = getBidVector( s, alpha, auc, q_b, q_e, sigma_sq)
b_min_c = b_opt - (alpha*auc.c);
profit_ce = (q_b' * b_min_c) - ((auc.gamma) * 0.5 * ((sigma_sq .* b_min_c)' * b_min_c));
return profit_ce
end
function getBidVector( s, alpha, auc, q_b, q_e, sigma_sq)
# Compute the optimal unit bid vector for each score by solving the quadratic optimization problem
m = Model(solver=IpoptSolver(print_level=0))
# m = Model(solver=GurobiSolver(OutputFlag=0))
@variables m begin
b[i=1:auc.T] >= 0
end
@NLobjective( m,
Min,
(sum( ( (auc.gamma^2) * 0.5 * sigma_sq[i] * (b[i]^2) - auc.gamma * (q_b[i] + auc.gamma * sigma_sq[i] * alpha * auc.c[i]) * b[i] ) for i=1:auc.T))
)
@constraint(m, sum( b[i] * q_e[i] for i=1:auc.T ) == s)
status = JuMP.solve(m)
b_min = getvalue(b)
return b_min
end
function getDbDsVec(b, alpha, auc, q_b, q_e, sigma_sq)
# %Computes anayltical derivative of the optimal bid function of item t
# % w.r.t. score s given alpha
pos_b = [ifelse(b[t] > 0, 1, 0) for t=1:auc.T]
if (sum(sigma_sq) > 0)
denom = 1.0/(sum((q_e[t]^2 * pos_b[t]) / sigma_sq[t] for t in 1:auc.T))
db_ds = [((q_e[t] * pos_b[t] / sigma_sq[t]) * denom) for t in 1:auc.T]
else
db_ds = [ifelse(b[t] > 0, (q_b[t]/q_e[t]), 0) for t=1:auc.T]
end
return(db_ds)
end
function ode_multi_item_w_risk_aversion( auc, alpha, s, qb, qo, sigma_sq)
alpha_dist = LogNormal(auc.alpha_lgmean, auc.sigma_lgalpha)
f(a) = pdf(alpha_dist, a);
F(a) = cdf(alpha_dist, a);
b_opt = getBidVector( s, alpha, auc, qb, qo, sigma_sq)
db_ds = getDbDsVec(b_opt, alpha, auc, qb, qo, sigma_sq)
println("u: ", s, "; t: ", alpha)
b_min_c = b_opt - (alpha*auc.c);
profit_ce = (qb' * b_min_c) - ((auc.gamma) * 0.5 * ((sigma_sq .* b_min_c)' * b_min_c));
profit_term = (exp(auc.gamma * (profit_ce)) - 1)
numerator = (f(alpha) ./ (1 - F(alpha) - 0.000000001)) * (auc.num_bidders - 1);
denominator = db_ds' * ((auc.gamma .* qb) - (auc.gamma^2 .* sigma_sq .* b_min_c) );
numerator = numerator * profit_term;
println("numerator: ", numerator)
println("denominator: ", denominator)
ds_dc = numerator / denominator; # Note: this should be a scalar
println("du/dt: ", ds_dc)
println("\n")
return ds_dc
end
function getExPostCost(auc, alpha, s, qb, qo, sigma_sq)
b_opt = getBidVector( s, alpha, auc, qb, qo, sigma_sq)
total_cost = b_opt' * auc.q_a
return(total_cost)
end
function getScalingAuctionEquilibrium(auc_seqid, auc, qb_input, qe_input, sigma_sq_input, alpha_grid)
alpha_min = alpha_grid[1]
alpha_max = alpha_grid[length(alpha_grid)]
alpha_span = (alpha_max,alpha_min);
s_max = getBoundarySMax(alpha_max, auc, qb_input, qe_input, sigma_sq_input)
ode_multi_item_w_risk_aversion_subs(ds, s, p, alpha) = (ds .= ode_multi_item_w_risk_aversion(auc, alpha, s, qb_input, qe_input, sigma_sq_input))
println("init u: ", s_max)
println("t span: ", alpha_span)
eq_prob = ODEProblem(ode_multi_item_w_risk_aversion_subs, s_max, alpha_span)
# eq_sol = DifferentialEquations.solve(eq_prob, isoutofdomain=(u,p,t) -> any(x -> ((x < 0) | (x > s_max)), u), alg_hints=[:stiff])
eq_sol = DifferentialEquations.solve(eq_prob, Rodas5(autodiff=false), isoutofdomain=(u,p,t) -> any(x -> (x < 0)))
eq_sol_save = [eq_sol(a) for a in alpha_grid]
eq_cost_save = [getExPostCost(auc, a, eq_sol(a) , qb_input, qe_input, sigma_sq_input) for a in alpha_grid]
score_at_winning_alpha = eq_sol(auc.winning_alpha)
cost_at_winning_alpha = getExPostCost(auc, auc.winning_alpha, score_at_winning_alpha, qb_input, qe_input, sigma_sq_input)
return(AugmentedAuctionEquilibrium(auc_seqid, auc.contract_no, alpha_grid, eq_sol_save, eq_cost_save, score_at_winning_alpha, cost_at_winning_alpha))
end
function getMinimalAuctionCFcomparison(auc, gridlength=50)
alpha_max = auc.highest_alpha*1.2;
alpha_min = auc.lowest_alpha*0.8;
alpha_grad = (alpha_max-alpha_min)/gridlength;
alpha_grid = alpha_min:alpha_grad:(alpha_max); #Using a fairly coarse grid for this demo though :(
data_eq = getScalingAuctionEquilibrium(1, auc, auc.q_a_model, auc.q_o, auc.sigma_t_sq, alpha_grid)
results = DataFrame(data_alpha = data_eq.alpha_types,
data_score = data_eq.score_maps,
data_cost = data_eq.expost_cost
)
return(results, data_eq)
end
getMinimalAuctionCFcomparison(auc)
but I’ve used similar things with other ODEs that seem to work fine.
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