The optimal coyness game.

In many animal species, females will benefit if they can secure their mate's help in raising their young. It has been suggested that they can achieve this by being coy (i.e. reluctant to mate) when courted, because this gives them time to assess a prospective mate's helpfulness and hence allows them to reject non-helpful males. According to this view, coyness should (i) reflect a trade-off between information gain and time lost on the part of the female, and (ii) be subject to an evolutionary feedback between optimal female coyness and male helping behaviour. Previous theory has considered each of these aspects in isolation. By contrast, here we present a comprehensive game theory model of this situation, leading to qualitatively new insights. We predict that a high degree of coyness should be associated with a high encounter rate during mate search, with an intermediate rate of information gain during mate inspection and with an intermediate dependence of reproduction on male help. Strongly biased sex ratios, however, preclude coyness. Due to the mutual feedback between coyness and helpfulness in our model, alternatively stable evolutionary outcomes (with or without coyness) are possible under broad conditions. We also discuss alternative interpretations of coyness.