Analyzing three-player quantum games in an EPR type setup

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.

21 pages, 3 figures

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• N-player quantum games in an EPR setting
• Analysis of two-player quantum games in an EPR setting using geometric algebra
• Two-player quantum games: When player strategies are via directional choices
• On the equivalence between non-factorizable mixed-strategy classical games and quantum games
• Social optimality in quantum Bayesian games