"A classical explanation for coy behaviour is the need for the male and the female to synchronize their reproductive physiology. ... Nevertheless it may be advantageous for females to wait activating the reproductive physiology until meeting a male since it might be costly to always be physiologically prepared for reproduction."
"the longer the female stays coy, the more certain she may become of the male's intentions."
The optimal coyness game, McNamara et al.:
"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."