Social optimality in quantum Bayesian games

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

doi:10.1016/j.physa.2015.05.020

Cited by 19 publications

(10 citation statements)

References 76 publications

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“…This brings us to question whether the unitary transformations are really necessary in the setup of a quantum game. A proposed scheme [8][9][10]12] for playing a quantum game in which players' strategic moves are not unitary transformations uses the setting of an Einstein-Podolsky-Rosen (EPR) experiment [4,[14][15][16][17][18]. Two players are located in spacelike-separated regions and share a singlet state.…”

Section: Introductionmentioning

confidence: 99%

A game theoretical perspective on the quantum probabilities associated with a GHZ state

Iqbal

Abbott

2018

Quantum Inf Process

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In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein-Podolsky-Rosen (EPR) experiment that depends on three players' directional choices in the experiment. We define the players' moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.

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Section: Introductionmentioning

confidence: 99%

A game theoretical perspective on the quantum probabilities associated with a GHZ state

Iqbal

Abbott

2018

Quantum Inf Process

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“…In order to obtain an improved comparison between classical and quantum games, it was suggested [24] that the players' strategy sets need to be identical. This has motivated proposals [33][34][35] of quantum games in which players' strategies are classical, as being convex linear combinations (with real coefficients) of the classical strategies, and the quantum game emerges from the non-classical aspects of a shared probabilistic physical system-as expressed by the constraints on relevant probabilities and their marginals [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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

2018

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The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein-Podolsky-Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

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“…After that, comparing with their classical counterpart game models, the quantum game theory has exhibited great superiority and different characters [4][5][6][7] . It was used to investigate the social problem and market features [8,9] .…”

Section: Introductionmentioning

confidence: 99%

A survey of the current status of research on quantum games

Huang

2018

2018 4th International Conference on Information Management (ICIM)

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obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The WestminsterResearch online digital archive at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners.Whilst further distribution of specific materials from within this archive is forbidden, you may freely distribute the URL of WestminsterResearch: ((http://westminsterresearch.wmin.ac.uk/).In case of abuse or copyright appearing without permission e-mail repository@westminster.ac.uk Huang, Dingxuan & Li, Shuliang Abstract -Quantum games have gained considerable interest from researchers. In this paper, on the basis of the Web of Science database, through the use of the social network analysis methods, the literature on quantum games is analyzed from three aspects: the keywords co-occurrence, coauthorship, and co-citation. In the process of analysis, the main quantum game models are reviewed with graphical illustrations. Our paper provides a survey and outline of the current status of research in this field, and identify directions for future work.. A Survey of the Current Status of Research on Quantum Games. In: Proceedings of the 2018 4th International Conference on Information Management (ICIM2018), 25th to 27th May 2018, Oxford, United Kingdom. IEEE. pp.46-52. ISBN: 978-1-5386-6146-8/18. A Survey of the Current Status of Research on Quantum Games

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Social optimality in quantum Bayesian games

Cited by 19 publications

References 76 publications

A game theoretical perspective on the quantum probabilities associated with a GHZ state

A game theoretical perspective on the quantum probabilities associated with a GHZ state

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

A survey of the current status of research on quantum games

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