Do male orangutans play a hawk-dove game?

Background: (1) The hawk-dove game has been invoked to explain animal fighting. (2) Orangutans (Pongo pygmaeus) have two forms of reproductively competent males: (a) The matured adult male (MA) has wide cheek pads and a well-developed throat sac used for emitting loud cries. The average weight of matured adult males is more than twice that of adult females, (b) The arrested adult male (AA), although it is old enough to be a matured adult male, remains comparable in size to an adult female and lacks the wide cheeks and throat sacs of matured adult males. Matured adult males are behaviourally dominant, whereas arrested adult males are sneakers and forcibly copulate with females. When the population density of matured adult males is low, sub-adult males develop to matured adults by the age of 5-7 years. When the density of matured adults is high, males become arrested adults. Question: Might game-theoretic models similar to the hawk-dove game explain male dimorphism in orangutans? Models: (1) A modified density-independent hawk-dove game. In each, MA is the hawk and AA is the dove. The value of winning (pay-off) for an MA is larger than that for an AA. But only MAs pay a combat cost. (2) A density-dependent hawk-dove game similar to the first but with pay-offs that decline as population size grows. Results: Density-independent: If an MA's combat cost is smaller than its payoff when it wins, then AA males always have less fitness than MAs. There should be no dimorphism. But if an MA's combat cost exceeds its pay-off when it wins, a stable mixed ESS proportion (less than 100%) of males should contain AAs (doves). In the density-dependent model, AAs are part of the ESS even in some circumstances in which the cost is smaller than the pay-off to MA. As population size increases, we see an increase in the breadth of mathematical conditions supporting a stable mixed evolutionarily stable strategy (ESS).