Most of the fighters would not succeed and we could define the costs of losing as large. However, it should be easy to envision a strategy that could invade a population of fighters. They could also eschew all fighting, but try to sneak matings. As long as they were successful sometimes, even though the benefits they received would be different than those of the fighter, they would not suffer any injuries and they might be able to invade. In northern elephant seals things like this happen.
Large males do defend sections of the beach using displays and fights that can escalate to death.
Nonetheless, other males will try to sneak matings, at least during certain parts of their lives. Whether or not this sneaking strategy is an ESS or simply a matter of trying to do the best you can will depend on whether or not the fitnesses are equal. So simple games like Hawk and Dove may help us to learn about some of the factors involved with animal contests, but they need lots of refinement before we can really understand the often highly sophisticated behavior of animals.