Nash equilibria in four-strategy quantum game extensions of the Prisoner's Dilemma

TL;DR

This paper explores Nash equilibria in four-strategy quantum extensions of the Prisoner's Dilemma, revealing complex strategic behaviors and equilibria closer to Pareto optimality than classical solutions.

Contribution

It introduces a novel quantum game framework with two additional strategies and analyzes all Nash equilibria across five invariant classes.

Findings

Quantum Nash equilibria are more diverse than classical ones.

Quantum extensions yield equilibria closer to Pareto optimal solutions.

The study enhances understanding of strategic behavior in quantum decision-making.

Abstract

This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. The quantization process involves extending the classical game by introducing two additional unitary strategies. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. For each class, we identify and analyse all possible Nash equilibria. Our results reveal the complexity and diversity of strategic behaviour in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In the case of the standard Prisoner's Dilemma, the resulting Nash equilibria of quantum extensions are found to be closer to Pareto optimal solutions than those of the classical equilibrium.