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Type: Journal article
Title: N-player quantum games in an EPR setting
Author: Chappell, J.
Iqbal, A.
Abbott, D.
Citation: PLoS One, 2012; 7(5):1-9
Publisher: Public Library of Science
Issue Date: 2012
ISSN: 1932-6203
Statement of
James M. Chappell, Azhar Iqbal and Derek Abbott
Abstract: The N-player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player’s strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players’ strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for N-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the players’ payoffs and mixed Nash equilibrium are determined. Players’ N|N payoff matrices are then defined using linear functions so that common two-player games can be easily extended to the N-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners’ Dilemma game for general N§2. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs. By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford’s geometric algebra (GA), it is shown how the N-player case becomes tractable. The new mathematical approach presented here has wide implications in the areas of quantum information and quantum complexity, as it opens up a powerful way to tractably analyze N-partite qubit interactions.
Keywords: Humans; Linear Models; Probability; Mathematical Concepts; Game Theory; Quantum Theory
Rights: Copyright: © 2012 Chappell et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
RMID: 0020118969
DOI: 10.1371/journal.pone.0036404
Appears in Collections:Electrical and Electronic Engineering publications

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