The battle of the sexes over the distribution of male surplus

Female primates carry and nurse the fetus, and thus have the first responsibility for rearing the offspring. Assuming males are at least equally adept at obtaining food, males might either share surplus food with females or consume the food themselves. The distribution of this surplus is the subject of a battle of the sexes. If females succeed in obtaining a large share of the surplus, then there is little size dimorphism between males and females otherwise males might use the surplus themselves to become larger and stronger, and to engage in sexual competition with other males. Besides competing with males, females may compete with each other. Dependency may coincide with sexual competitiveness (sexiness). This paper introduces these ideas in a game theoretic setting and derives a simple bound, called the alpha male condition, on the male 'sexiness'' required for a nonsupportive strategy to be worthwhile.