The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

Iqbal, Azhar; Chappell, James M.; Abbott, Derek

doi:10.1016/j.physleta.2018.08.011

Cited by 6 publications

(4 citation statements)

References 38 publications

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“…Quantum games can be physically implemented by a quantum computer operating according to the above algorithm. Such an algorithm was carried out experimentally [ 54 , 55 ] in EPR-type experiments based on measurements of the Stern Gerlach effect. The players initially share an entangled pure quantum state

.…”

Section: Ewl Quantization Protocol In Frąckiewicz–pykacz Parameterizationmentioning

confidence: 99%

Efficiency of Classical and Quantum Games Equilibria

Szopa

2021

Entropy

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Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied.

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.…”

Section: Ewl Quantization Protocol In Frąckiewicz–pykacz Parameterizationmentioning

confidence: 99%

Efficiency of Classical and Quantum Games Equilibria

Szopa

2021

Entropy

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“…In the end, we would like to stress on the recent studies connecting Bell nonlocality [47,48], a quantum secure direct communication scheme [49] and security of quantum key distribution schemes [50] with game theory. In view of these works, in principle, all quantum cryptographic schemes (see [51,52] for a review) can be viewed from the perspective of game theory, as a game to perform cryptanalysis and obtain security proofs.…”

Section: Discussionmentioning

confidence: 99%

Noisy three-player dilemma game: robustness of the quantum advantage

Kairon

Thapliyal

Srikanth

et al. 2020

Quantum Inf Process

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Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the persistence of the quantum advantage under corruption of the input states and how this depends on parameters of the payoff table. Specifically, experimental fidelity and error are observed not to be properly anti-correlated; i.e., there are instances where a class of experiments with higher fidelity yields a greater error in the payoff. Further, we find that the classical strategy will always outperform the quantum strategy if corruption is higher than 50%.

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“…Quantum games can be physically implemented by a quantum computer operating according to the above algorithm. Such an algorithm was carried out experimentally [39,40] in EPR-type experiments based on measurements of the Stern Gerlach effect. The players initially share an entangled pure quantum state | 0 ⟩.…”

Section: Quantum Gamesmentioning

confidence: 99%

Pareto Efficiency of Mixed Quantum Strategy Equilibria

Szopa¹

2021

Preprint

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The aim of the paper is to investigate Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto optimality. We study four games: the prisoner's dilemma, battle of the sexes and two versions of the game of chicken. The correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device. We analyze the quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism with the full SU(2) space of players’ strategy parameters. It has been shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also analyzed.

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The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

Cited by 6 publications

References 38 publications

Efficiency of Classical and Quantum Games Equilibria

Efficiency of Classical and Quantum Games Equilibria

Noisy three-player dilemma game: robustness of the quantum advantage

Pareto Efficiency of Mixed Quantum Strategy Equilibria

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