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Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

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  • James M Chappell
  • Azhar Iqbal
  • Derek Abbott

Abstract

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

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  • 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.
    • Handle: RePEc:plo:pone00:0029015
    DOI: 10.1371/journal.pone.0029015
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    References listed on IDEAS

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    1. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    2. 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.
    3. Binmore, Ken, 2007. "Game Theory: A Very Short Introduction," OUP Catalogue, Oxford University Press, number 9780199218462.
    4. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
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    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. 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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