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

• URL: http://arxiv.org/abs/2411.01711v1
• Date: Sun, 03 Nov 2024 23:09:36 GMT
• Title: Nash equilibria in four-strategy quantum game extensions of the Prisoner's Dilemma
• Authors: Piotr Frąckiewicz, Anna Gorczyca-Goraj, Krzysztof Grzanka, Katarzyna Nowakowska, Marek Szopa,
• Abstract summary: This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. For each class, we identify and analyse all possible Nash equilibria. Results reveal the complexity and diversity of strategic behaviour in the quantum setting.
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• 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.

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