Pacific Institute for the Mathematical Sciences - PIMS

Females are the choosy sex, their choice being made on the basis of the quality of the males. The benefits they receive from the males for the offspring are either indirect, for example good genes, or direct, such as territories, male parental care and absence of contagious parasites. The presence or absence of attributes as good genes or absence of contagious parasites in a male will determine if he is it a high-quality male or a low-quality male. This interaction between female and male decision rules raises two important questions: Do we expect high-quality males to give less care to the young than low-quality ones? Do we expect females to prefer high-quality males? The problem of how much time to spend with females, for the males, and what males to choose, for the females, is game theoretical. The existence of an optimal Nash strategy for males and females is proven under a general female choice rule. The optimal strategy is then analyzed. Part of this work was done jointly with John McNamara and E.J.Collins