This directory contains code for reproducing experiments in the paper
Yushi Bai and Paul Gölz. Envy-free and Pareto-optimal Allocations for Asymmetric Agents. IJCAI 2022. https://arxiv.org/pdf/2109.08971.pdf
General details on the experiments, on our test machine, and on library versions used can be found in Appendix F.1 of the paper.
This directory is subdivided into three subdirectories:
1. ./figure4/
This directory contains the Mathematica code for producing Figure
4 in the paper. The Mathematica notebook is called ./figure4/figure4.nb,
and a separate file ./figure4/figure4.pdf displays the code and
output to make the code accessible without the Mathematica software.
Finally, the directory contains two PDF files generated by running
the notebook, which are the panels of Figure 4.
2. ./main_experiments/
This directory contains the main experiments, which compute multipliers
for the five example distributions, and then simulate many random
instances to see how likely the multiplier algorithm, round robin,
and the MNW algorithm are to satisfy envy-freeness and Pareto-optimality.
This code is found in ./main_experiments/experiments.py. This
file can be run as python3 experiments.py (we use Python 3.7.10).
This command will print some of the results in standard output;
reference output is captured in a file ./main_experiments/reference.txt.
In addition, it produces three PDFs with the plots of Figures 3,
5, and 6, and three CSV files that record the raw data underlying
these plots.
3. ./multiplier_evaluation/
Finally, we check the multipliers generated as part of the
experiments.py script above (and output on standard output) in
Mathematica. Specifically, we calculate the deviation of the agent
probabilities from the target value and, in an attempt to explain
the slow convergence, we calculate a certain gap in conditioned
expected values that is mentioned in the paper. The main notebook
is called ./multiplier_evaluation/multiplier_evaluation.nb, with
a corresponding PDF file that shows the code and reference output.