Introduction

This is the developper’s guide to the GTNash Python/Sagemath toolbox.

The GTNash toolbox proposes a set of tools to represent games in (i) normal form (ii) succinct (polymatrix, graphical, hypergraphical) form (iii) succinct form with incomplete information (bayesian, bayesian hypergraphical).

The GTNash toolbox also proposes procedures to compute pure Nash equilibira through enumeration and mixed Nash equilibria in normal-form games (Porter, Nudelman and Shoam’s algorithm), polymatrix games (Lemke-Howson algorithm) and hypergraphical game (including complete /incomplete information games) by a algorithm extending Wilson’s algorithm.

Please refer to [FJS2022] for a description of the algorithm. Also use [FJS2022] if you wish to cite the software.

In normal use, GTNash is intended to be used as a Python package, called from and used within the Sagemath software system. All sources and a Sagemath/Jupyter Quickstart notebook are available in the gtnash project repository.

[FJS2022]

Fargier, H., Jourdan, P. and R. Sabbadin. A Path-following Polynomial Equations Systems Approach for Computing Nash Equilibria. Proc’ of AAMAS, 2022.