Optimal Auctions through Deep Learning

Getting Started

Install the following packages:

• Python 2.7
• Tensorflow
• Numpy and Matplotlib packages
• Easydict - pip install easydict

Running Experiments in the paper

Default hyperparameters specified in regretNet/cfgs/.
For training the network, testing the mechanism learnt and computing the baselines, run:

cd regretNet
python run_train.py [setting_name]
python run_test.py [setting_name]
python run_baseline.py [setting_name]

setting_no	setting_name
(I)	additive_1x2_uniform
(II)	unit_1x2_uniform_23
(III)	additive_2x2_uniform
(IV)	CA_sym_uniform_12
(V)	CA_asym_uniform_12_15
(VI)	additive_3x10_uniform
(VII)	additive_5x10_uniform

For additional experiments in the appendix, run:

python run_train_additional.py [setting_name]
python run_test_additional.py [setting_name]
python run_baseline_additional.py [setting_name]

setting_no	setting_name
(a)	additive_1x2_uniform_416_47
(b)	additive_1x2_uniform_triangle
(c)	unit_1x2_uniform
(d)	additive_1x10_uniform
(e)	additive_1x2_uniform_04_03
(f)	unit_2x2_uniform

Running single bidder auctions using RochetNet

Default hyperparameters specified in rochetNet/cfgs/.
For training the network, testing the mechanism learnt and computing the baselines, run:

cd rochetNet
python run_train.py [setting_name]
python run_test.py [setting_name]
python run_baseline.py [setting_name]

setting_no	setting_name
(a)	additive_1x2_uniform
(b)	additive_1x2_uniform_416_47
(c)	additive_1x2_uniform_triangle
(d)	additive_1x2_uniform_04_03
(e)	additive_1x10_uniform
(f)	unit_1x2_uniform
(g)	unit_1x2_uniform_23

Running single item auctions using MyersonNet

Default hyperparameters specified in myersonNet/cfgs/.
For training the network, testing the mechanism learnt and computing the baselines, run:

cd myersonNet
python run_train.py [setting_name]
python run_test.py [setting_name]
python run_baseline.py [setting_name]

setting_no	setting_name
(a)	uniform
(b)	asymmetric_uniform
(c)	exponential
(d)	irregular

Settings

• additive_1x2_uniform: A single bidder with additive valuations over two items, where the items is drawn from U[0, 1].

• unit_1x2_uniform_23: A single bidder with unit-demand valuations over two items, where the item values are drawn from U[2, 3].

• additive_2x2_uniform: Two additive bidders and two items, where bidders draw their value for each item from U[0, 1].

• CA_sym_uniform_12: 2 bidders and 2 items, with v_1,1, v_1,2, v_2,1, v_2,2 ∼ U[1, 2], v_1,{1,2} = v_1,1 + v_1,2 + C₁ and v_2,{1,2} = v_2,1 + v_2,2 + C₂, where C₁, C₂ ∼ U[−1, 1].

• CA_asym_uniform_12_15: 2 bidders and 2 items, with v_1,1, v_1,2 ∼ U[1, 2], v_2,1, v_2,2 ∼ U[1, 5], v_1,{1,2} = v_1,1 + v_1,2 + C₁ and v_2,{1,2} = v_2,1 + v_2,2 + C₂, where C₁, C₂ ∼ U[−1, 1].

• additive_3x10_uniform: 3 additive bidders and 10 items, where bidders draw their value for each item from U[0, 1].

• additive_5x10_uniform: 5 additive bidders and 10 items, where bidders draw their value for each item from U[0, 1].

• additive_1x2_uniform_416_47: Single additive bidder with preferences over two non-identically distributed items, where v₁ ∼ U[4, 16]and v₂ ∼ U[4, 7].

• additive_1x2_uniform_triangle: A single additive bidder with preferences over two items, where (v₁, v₂) are drawn jointly and uniformly from a unit-triangle with vertices (0, 0), (0, 1) and (1, 0).

• unit_1x2_uniform: A single unit-demand bidder with preferences over two items, where the item values from U[0, 1]

• additive_1x10_uniform: A single additive bidder and 10 items, where bidders draw their value for each item from U[0, 1].

• additive_1x2_uniform_04_03: A Single additive bidder with preferences over two items, where the item values v₁ ∼ U[0, 4], v₂ ∼ U[0, 3]

• unit_2x2_uniform: Two unit-demand bidders and two items, where the bidders draw their value for each item from identical U[0, 1].

Visualization

Allocation Probabilty plots for unit_1x2_uniform_23 setting learnt by regretNet:

Allocation Probabilty plots for additive_1x2_uniform_416_47 setting learnt by rochetNet:

For other allocation probability plots, check-out the ipython notebooks in regretNet or rochetNet folder.