  Using the representation introduced in \cite{frame}, an artificial game in
quantum strategy space is proposed and studied. Although it has well-known
classical correspondence, which has classical mixture strategy Nash Equilibrium
states, the equilibrium state of this quantum game is an entangled strategy
(operator) state of the two players. By discovering such behavior, it partially
shows the independent meaning of the new representation. The idea of
entanglement of strategies, instead of quantum states, is proposed, and in some
sense, such entangled strategy state can be regarded as a cooperative behavior
between game players.
