ZERO is a modular C++ library for Mathematical Programming Games. It provides a comprehensive toolkit of modeling interfaces, helper tools, and algorithms to design games and find their Nash equilibria.

Documentation

The documentation is available here.

Citing

If you use ZERO for your research, please refer to the following papers:

• ZERO: Playing Mathematical Programming Games

  @article{Dragotto_2021_ZEROSoftware,
    title        = {{ZERO: Playing Mathematical Programming Games}},
    author       = {Dragotto, Gabriele and  Sankaranarayanan, Sriram and Carvalho, Margarida and Lodi, Andrea},
    year         = 2021,
    journal     = {arXiv},
    volume       = {abs/2111.07932},
    url          = {https://arxiv.org/abs/2111.07932},
    eprinttype   = {arXiv}
  }
  
  

• The Cut and Play Algorithm: Computing Nash Equilibria via Outer Approximations:

  @article{Dragotto_2021_CNP,
    title        = {{The Cut-and-Play Algorithm: Computing Nash Equilibria via Outer Approximations}},
    author       = {Carvalho, Margarida and Dragotto, Gabriele and Lodi, Andrea and Sankaranarayanan, Sriram},
    year         = 2023,
    journal      = {arXiv},
    volume       = {abs/2111.05726},
    url          = {https://arxiv.org/abs/2111.05726},
    eprinttype   = {arXiv}
  }
  

• The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming:

  @article{Dragotto_2021_ZERORegrets,
    title        = {{The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming}},
    author       = {Dragotto, Gabriele and Scatamacchia, Rosario},
    year         = 2023,
    journal      = {INFORMS Journal on Computing},
    volume       = {To Appear},
    url          = {https://doi.org/10.1287/ijoc.2022.0282}
  }
  

• Mathematical Programming Games, Ph.D. Thesis:

  @phdthesis{Dragotto_2022_Thesis,
    title        = {{Mathematical Programming Games}},
    author       = {Dragotto, Gabriele},
    year         = 2022,
    school       = {Polytechnique Montr{\'e}al},
    url=         = {https://publications.polymtl.ca/10220/}
  }
  

LICENSE

This code is distributed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International.

Maintenance

• @gdragotto - Contact: gdragotto@princeton.edu
• @ssriram1992 - Contact: srirams@iima.ac.in