  A game-theoretic setting provides a mathematical basis for analysis of
strategic interaction among competing agents and provides insights into both
classical and quantum decision theory and questions of strategic choice. An
outstanding mathematical question, is to understand the conditions under which
a classical game-theoretic setting can be transformed to a quantum game, and
under which conditions there is an equivalence. In this paper, we consider
quantum games as those that allow non-factorizable probabilities. We discuss
two approaches for obtaining a non-factorizable game and study the outcome of
such games. We demonstrate how the standard version of a quantum game can be
analyzed as a non-factorizable game and determine the limitations of our
approach.
