A game-theoretic setting provides a mathematical basis for analysis ofstrategic interaction among competing agents and provides insights into bothclassical and quantum decision theory and questions of strategic choice. Anoutstanding mathematical question, is to understand the conditions under whicha classical game-theoretic setting can be transformed to a quantum game, andunder which conditions there is an equivalence. In this paper, we considerquantum games as those that allow non-factorizable probabilities. We discusstwo approaches for obtaining a non-factorizable game and study the outcome ofsuch games. We demonstrate how the standard version of a quantum game can beanalyzed as a non-factorizable game and determine the limitations of ourapproach.
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