  We give a concise and self-contained introduction to the theory of Quantum
Games by reviewing the seminal works of Meyer, Eisert-Wilkens-Lewenstein,
Marinatto-Weber and Landsburg, which initiated the study of this field. By
generalizing this body of work, we formulate a protocol to
$\textit{Quantumize}$ any finite classical $n$-player game, and use a novel
approach of describing such a Quantum Game in terms of commuting Payoff
Operators. We describe what advantages can be gained by players by quantumizing
such a game, particularly, what additional Nash Equilibria the players can
achieve and the Pareto-Optimality of these additional equilibria.
