We present a model of a male–female evolutionary game on mate-locating behaviour. Two major mating systems are considered: “lek polygyny” (in which males aggregate to wait for females searching for males) and “searching polygyny” (in which males search for females emerging or waiting for males). The model predicts that lek polygyny is favoured (i) when male survivorship during lekking is sufficiently higher than that during mate searching, (ii) when female survivorship while visiting a lek is sufficiently higher than at the emergence site, or (iii) when searching efficiency is higher at a lek than at an emergence site. Furthermore, the model shows that a reduction in the reproductive value of females later in the day, which prevents males from performing riskier mate-locating behaviour, can result in a change of mating system. In addition, mixed mating systems can be realized as transient states during this shift.