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.

基于属于不同群体的两个对手之间的成对交互的经典双矩阵游戏不考虑时间成本。在本文中，我们建立在一个旧观念之上，即失去的机会成本会影响个人适应度。我们在包括活动时间在内的配对形成过程的均衡分布上计算双策略双矩阵博弈的每个策略的适应度。然后将这种一般方法应用于性别之战游戏，在该游戏中，当求爱和育儿成本通过时间损失来衡量时，我们通过找到这种时间受限游戏的纳什均衡 (NE) 来分析进化结果。虽然经典的性别之战游戏要么有一个独特的严格 NE（具体来说，所有雄性都表现出花花公子的行为，并且所有雌性都是腼腆或所有雌性都快，这取决于模型参数），或者一个独特的内部 NE，其中两性都表现出混合行为，包括求爱和抚养孩子的时间成本改变了这一预测。首先，（Philanderer，Coy）从来都不是NE。其次，如果生育后代的好处与父母策略无关，（Philanderer，Fast）是唯一的严格NE，但当求爱时间足够短时，会出现第二个稳定的内部NE。事实上，随着求爱时间变短，这种混合的 NE（大多数男性是忠实的，而腼腆的女性人口正在增加）吸引了几乎所有的初始种群配置。第三，后一种促进婚姻幸福的情况也发生在共同抚养孩子的父母比不共同抚养的父母从他们的后代中获得更高的利益时。最后，对于中等持续时间的求爱时间，当种群规模增加时会发生同样的现象。