QEGS: A Mathematica Package for the Analysis of Quantum Extended Games

TL;DR

This paper introduces QEGS, a Mathematica package for analyzing quantum extensions of classical 2x2 games, enabling the study of Nash equilibria and strategic properties within quantum game theory.

Contribution

The paper presents a new Mathematica package that automates the analysis of quantum extensions of classical games, including equilibrium computation and strategy elimination.

Findings

The package can generate all quantum game extensions with one or two strategies.

It can determine Nash equilibria and eliminate dominated strategies.

The package is also applicable to classical game analysis.

Abstract

Quantum games have attracted much attention in recent years due to their ability to solve decision-making dilemmas. The aim of this study is to extend previous work on quantum games by introducing a Mathematica package QEGS (Quantum Extension Game Solver) dedicated to the study of quantum extensions of classical $2\times2$ games based on the EWL scheme. The package generates all possible game extensions with one or two unitary strategies, which are invariant with respect to isomorphic transformations of the initial games. The package includes a number of functions to study these extensions, such as determining their Nash equilibria in pure strategies, eliminating dominated strategies, or computing maximin strategies. Independently of quantum extensions, these functions can also be used to analyze classical games. Reporting to a pdf is available. The discussion includes an outline of future research directions, such as the exploration of mixed-strategy Nash equilibria and potential real-world applications in fields like quantum computing and secure communications.