  This paper extends our probabilistic framework for two-player quantum games
to the mutliplayer case, while giving a unified perspective for both classical
and quantum games. Considering joint probabilities in the standard
Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use
this setting in order to play general three-player non-cooperative symmetric
games. We analyze how the peculiar non-factorizable joint probabilities
provided by the EPR-Bohm setting can change the outcome of a game, while
requiring that the quantum game attains a classical interpretation for
factorizable joint probabilities. In this framework, our analysis of the
three-player generalized Prisoner's Dilemma (PD) shows that the players can
indeed escape from the classical outcome of the game, because of
non-factorizable joint probabilities that the EPR setting can provide. This
surprising result for three-player PD contrasts strikingly with our earlier
result for two-player PD, played in the same framework, in which even
non-factorizable joint probabilities do not result in escaping from the
classical consequence of the game.
