  A simple and general formulation of the quantum game theory is presented,
accommodating all possible strategies in the Hilbert space for the first time.
The theory is solvable for the two strategy quantum game, which is shown to be
equivalent to a family of classical games supplemented by quantum interference.
Our formulation gives a clear perspective to understand why and how quantum
strategies outmaneuver classical strategies. It also reveals novel aspects of
quantum games such as the stone-scissor-paper phase sub-game and the
fluctuation-induced moderation.
