  We quantized the Hawk-Dove game by using the most general form of a pure
initial state to investigate the existence of pure and mixed Evolutionarily
Stable Strategies (ESS). An example is considered to draw a comparison between
classical and quantum version of the game. Our choice of most general initial
quantum state enables us to make the game symmetric or asymmetric. We show that
for a particular set of game parameters where there exist only mixed ESS in the
classical version of the game, however, quantization allows even a pure
strategy to be an ESS for symmetric game in addition to ixed ESS. On the other
hand only pure strategy ESS can exist for asymmetric quantum version of the
Hawk-Dove game.
