Is the essence of a quantum game captured completely in the original classical game?

S. J. van Enk and R. Pike in PRA 66, 024306 (2002) argue that the equilibrium solution to a quantum game isn't unique but is already present classical itself. In this work, we contest assertion by showing random strategy particular (Hawk-Dove) game. other words, one cannot obtain of Hawk-Dove Moreover, provide an analytical $2\times2$ strategic form using randomly mixed strategies. The which describe Pareto optimal with their payoff classically unobtainable. We compare strategies correlated find or Prisoner's dilemma yield Nash solution.