  We use the standard three-party Einstein-Podolsky-Rosen (EPR) setting in
order to play general three-player non-cooperative symmetric games. We analyze
how the peculiar non-factorizable joint probabilities that may emerge in the
EPR setting can change outcome of the game. Our setup requires that the quantum
game attains classical interpretation for factorizable joint probabilities. We
analyze the generalized three-player game of Prisoner's Dilemma (PD) and show
that the players can indeed escape from the classical outcome of the game
because of non-factorizable joint probabilities. This result for three-player
PD contrasts strikingly with our earlier result for two-player PD for which
even non-factorizable joint probabilities are not found to be helpful to escape
from the classical outcome of the game.
