Game theory is frequently used to study conflicting interests between the two sexes. Males often benefit from a higher mating rate than females do. A temporal component of this conflict has rarely been modelled: females' interest in mating may depend on when females become fertile. This sets conditions for male–female coevolution, where females may develop fertility signals, and males may obey the signal, such that they only target signalling females. Modelling this temporal aspect to sexual conflict yields two equilibria: (i) a trivial equilibrium without signals and with males targeting all females, and (ii) a signalling equilibrium where all females signal before ovulation, and where either some, or all, males obey the signal. The ‘all males obey the signal’ equilibrium is more likely if we assume that discriminating males have an advantage in postcopulatory sperm competition, while in the absence of this benefit, we find the ‘some males obey the signal’ equilibrium. The history of game-theoretic models of sex differences often portrays one sex as the 'winner' and the opposite sex as the ‘loser’. From early models emphasizing ‘battle of the sexes’-style terminology, we recommend moving on to describe the situation as non-signalling equilibria having stronger unresolved sexual conflict than signalling equilibria.This article is part of the theme issue ‘Half a century of evolutionary games: a synthesis of theory, application and future directions’.