Reducing courtship time promotes marital bliss: The Battle of the Sexes game revisited with costs measured as time lost.

ABSTRACT

Classic bimatrix games, that are based on pair-wise interactions between two opponents belonging to different populations, do not consider the cost of time. In this article, we build on an old idea that lost opportunity costs affect individual fitness. We calculate fitnesses of each strategy for a two-strategy bimatrix game at the equilibrium distribution of the pair formation process that includes activity times. This general approach is then applied to the Battle of the Sexes game where we analyze the evolutionary outcome by finding the Nash equilibria (NE) of this time-constrained game when courtship and child rearing costs are measured by time lost. While the classic Battle of the Sexes game has either a unique strict NE (specifically, all males exhibit Philanderer behavior and either all females are Coy or all are Fast depending on model parameters), or a unique interior NE where both sexes exhibit mixed behavior, including time costs for courtship and child rearing changes this prediction. First, (Philanderer, Coy) is never a NE. Second, if the benefit of having offspring is independent of parental strategies, (Philanderer, Fast) is the unique strict NE but a second stable interior NE emerges when courtship time is sufficiently short. In fact, as courtship time becomes shorter, this mixed NE (where most males are Faithful and the Coy female population is increasing) attracts almost all initial population configurations. Third, this latter promotion of marital bliss also occurs when parents who share in child rearing receive a higher benefit from their offspring than those that don't. Finally, for courtship time of moderate duration, the same phenomenon occurs when the population size increases.