Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game
The concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner’s Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of...
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| Format: | Article |
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MDPI AG
2025-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/7/755 |
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| author | Piotr Frąckiewicz Anna Gorczyca-Goraj Krzysztof Grzanka Katarzyna Nowakowska Marek Szopa |
| author_facet | Piotr Frąckiewicz Anna Gorczyca-Goraj Krzysztof Grzanka Katarzyna Nowakowska Marek Szopa |
| author_sort | Piotr Frąckiewicz |
| collection | DOAJ |
| description | The concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner’s Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. The resulting Nash equilibria are found to be more closely aligned with Pareto-optimal solutions than those of the conventional Nash equilibrium outcome of the classical game. Our results demonstrate the complexity and diversity of strategic behavior in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In particular, we provide a detailed characterization of strategy profiles and their corresponding Nash equilibria, thereby extending the understanding of quantum strategies’ impact on traditional game-theoretical problems. |
| format | Article |
| id | doaj-art-16e03ce9849e49cda4b73b90c12b22a3 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-16e03ce9849e49cda4b73b90c12b22a32025-08-20T03:07:54ZengMDPI AGEntropy1099-43002025-07-0127775510.3390/e27070755Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma GamePiotr Frąckiewicz0Anna Gorczyca-Goraj1Krzysztof Grzanka2Katarzyna Nowakowska3Marek Szopa4Institute of Exact and Technical Sciences, Pomeranian University in Słupsk, ul. Bohaterów Westerplatte 64, 76-200 Słupsk, PolandDepartment of Operations Research, University of Economics in Katowice, ul. Bogucicka 3, 40-287 Katowice, PolandDepartment of Operations Research, University of Economics in Katowice, ul. Bogucicka 3, 40-287 Katowice, PolandInstitute of Exact and Technical Sciences, Pomeranian University in Słupsk, ul. Bohaterów Westerplatte 64, 76-200 Słupsk, PolandDepartment of Operations Research, University of Economics in Katowice, ul. Bogucicka 3, 40-287 Katowice, PolandThe concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner’s Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. The resulting Nash equilibria are found to be more closely aligned with Pareto-optimal solutions than those of the conventional Nash equilibrium outcome of the classical game. Our results demonstrate the complexity and diversity of strategic behavior in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In particular, we provide a detailed characterization of strategy profiles and their corresponding Nash equilibria, thereby extending the understanding of quantum strategies’ impact on traditional game-theoretical problems.https://www.mdpi.com/1099-4300/27/7/755game isomorphismEisert–Wilkens–Lewenstein schemequantum extended gamesNash equilibriumPrisoner’s Dilemma |
| spellingShingle | Piotr Frąckiewicz Anna Gorczyca-Goraj Krzysztof Grzanka Katarzyna Nowakowska Marek Szopa Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game Entropy game isomorphism Eisert–Wilkens–Lewenstein scheme quantum extended games Nash equilibrium Prisoner’s Dilemma |
| title | Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game |
| title_full | Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game |
| title_fullStr | Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game |
| title_full_unstemmed | Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game |
| title_short | Nash Equilibria in Four-Strategy Quantum Extensions of the Prisoner’s Dilemma Game |
| title_sort | nash equilibria in four strategy quantum extensions of the prisoner s dilemma game |
| topic | game isomorphism Eisert–Wilkens–Lewenstein scheme quantum extended games Nash equilibrium Prisoner’s Dilemma |
| url | https://www.mdpi.com/1099-4300/27/7/755 |
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