An artificial game with equilibrium state of entangled strategy

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.