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Analyzing Three-Player Quantum Games in an EPR Type Setup

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  • James M Chappell
  • Azhar Iqbal
  • Derek Abbott

Abstract

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.

Suggested Citation

  • James M Chappell & Azhar Iqbal & Derek Abbott, 2011. "Analyzing Three-Player Quantum Games in an EPR Type Setup," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-11, July.
    • Handle: RePEc:plo:pone00:0021623
    DOI: 10.1371/journal.pone.0021623
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    References listed on IDEAS

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    1. Binmore, Ken, 2007. "Game Theory: A Very Short Introduction," OUP Catalogue, Oxford University Press, number 9780199218462.
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    Cited by:

    1. James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "N-Player Quantum Games in an EPR Setting," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    2. James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-8, January.
    3. Angsheng Li & Xi Yong, 2015. "Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-24, February.
    4. Iqbal, Azhar & Chappell, James M. & Abbott, Derek, 2015. "Social optimality in quantum Bayesian games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 798-805.

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