Following \textit{J. Maynard Smith} [Evolution and the Theory of Games (1982; Zbl 0526.90102)], the authors investigate evolutionary games of the Hawk-Dove type. \textit{R. Selten} [Theory Decis. Libr., Ser. C2, 67-75 (1980; Zbl 0658.90102)] has shown that evolutionary stable strategies in the asymmetric game are always pure strategies. This could mean that mixed strategies do not play any role in the analysis of evolutionary games. On the other hand, \textit{J. C. Harsanyi}'s methods [Int. J. Game Theory 2, 1-23 (1973; Zbl 0255.90084)] show that every mixed equilibrium is arbitrarily close to an evolutionarily stable equilibrium (with perturbed payoff). The authors investigate perturbed versions of the Hawk-Dove game and their role-dependent and role-independent equilibria. The role-independent equilibrium approximates the mixed equilibrium of the surface game. The authors interpret this as follows: ``In some games, the return to exploiting role asymmetries [\dots]{} will be small. [They] will then be ignored, allowing equilibria that approximate the mixed equilibrium of the surface game to persist. (p.~215)''.