  We construct quantum games from a table of non-factorizable joint
probabilities, coupled with a symmetry constraint, requiring symmetrical
payoffs between the players. We give the general result for a Nash equilibrium
and payoff relations for a game based on non-factorizable joint probabilities,
which embeds the classical game. We study a quantum version of Prisoners'
Dilemma, Stag Hunt, and the Chicken game constructed from a given table of
non-factorizable joint probabilities to find new outcomes in these games. We
show that this approach provides a general framework for both classical and
quantum games without recourse to the formalism of quantum mechanics.
