  We investigate quantum strategy in moving frames by considering Prisoner's
Dilemma and propose four thresholds of $\gamma$ for two players to determine
their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in
relativistic situation that the quantum feature of the game would be enhanced
and diminished for different players whose particle's initial spin direction
are respectively parallel and antiparallel to his/her movement direction, that
is, for the former the quantum feature of the game is enhanced while for the
latter the quantum feature would be diminished. Thus a classical latter could
still maintain his/her strictly dominant strategy (classical strategy) even if
the game itself is highly entangled.
