We consider in this paper the Hawk-Dove game in which each of infinitely many individuals, involved with pairwise encounters with other individuals, can decide whether to act aggressively (Hawk) or peacefully (Dove). Each individual is characterized by its strength. The strength distribution among the population is assumed to be fixed and not to vary in time. If both individuals involved in an interaction are Hawks, there will be a fight, the result of which will be determined by the strength of each of the individuals involved. The larger the difference between the strength of the individuals is, the larger is the cost for the weaker player involved in the fight. Our goal is to study the influence of the parameters (such as the strength level distribution) on the equilibrium of the game. We show that for some parameters there exists a threshold equilibrium policy while for other parameters there is no equilibrium policy at all.