  Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement
of Nash equilibrium concept. We investigate the consequences when a small group
of mutants using quantum strategies try to invade a classical ESS in a
population engaged in symmetric bimatrix game of Prisoner's Dilemma. Secondly
we show that in an asymmetric quantum game between two players an ESS pair can
be made to appear or disappear by resorting to entangled or unentangled initial
states used to play the game even when the strategy pair remains a Nash
equilibrium in both forms of the game.
