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

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