PLoS ONE (Jan 2011)

Analyzing three-player quantum games in an EPR type setup.

  • James M Chappell,
  • Azhar Iqbal,
  • Derek Abbott

DOI
https://doi.org/10.1371/journal.pone.0021623
Journal volume & issue
Vol. 6, no. 7
p. e21623

Abstract

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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.