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

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 unde...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Frąckiewicz, Piotr, Gorczyca-Goraj, Anna, Grzanka, Krzysztof, Nowakowska, Katarzyna, Szopa, Marek
Format: Article
Language:English
Subjects:
Game theory
Games
Prisoners
Online Access:Get full text
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Summary: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.
ISSN:2331-8422