  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.
