Throughout the animal kingdom, Charles Darwin wrote in 1871, the female is "less eager" for a mate than the male:
“She generally ‘requires to be courted;’ she is coy, and may often be seen endeavouring for a long time to escape from the male.”
An allusion to the same habit, this time in human beings, appears in Pride and Prejudice, which was published a half-century before Darwin's words. While proposing to protagonist Elizabeth Bennett, Mr. Collins makes reference to how he will behave "when we are married." After Elizabeth replies indignantly that she has not agreed to marry him (and cannot do so), Mr. Collins explains that he knows “it is usual with young ladies to reject the addresses of the man whom they secretly mean to accept, when he first applies for their favour; and that sometimes the refusal is repeated a second, or even a third time.” Women, he believes, play hard-to-get.
Despite centuries of changes in social expectations and relations between the sexes, playing hard-to-get remains a relationship strategy not just for women (as famously proposed in The Rules) but for men. Communicating your unavailability and lack of interest---by refusing to answer phone calls, declining to go on dates, or limiting the time one spends with prospective mates, for example---can supposedly increase your desirability to the opposite sex.
There's reason to believe that claim is true. One recent analysis by Peter K. Jonason and Norman P. Li examines how people define playing hard-to-get, their use of the strategy, and how the (un)availability of prospective mates affects their desirability. They found that people's main motives for playing hard-to-get were increasing demand or desirability (a strategy consistent, as the researchers note, with sexual economics) and testing prospective partners' commitment (which is consistent with error management theory).
In a separate study Jonason and Li examined, participants said they preferred highly available members of the opposite sex (those described as often going out with someone they just met) as casual sex partners, but medium- or low-availability mates for committed romantic relationships. And in a third study, participants both male and female indicated that they would spend more time and money on a low-availability potential mate than on a high-availability one.
So it would seem that playing hard-to-get has its rewards in the relationship market. But that doesn't mean we should all adopt it as a strategy: deceit and manipulation seem an unlikely path to a happy relationship characterized by honesty and openness on both sides. There's no honest or kind way to play hard-to-get: it requires falsely indicating a lack of interest, pretending to be busy, cultivating a potential mate's attraction and then deliberately disregarding it later. Presumably no one wants to be on the receiving end of this behavior, so (short of rejecting honesty as a moral principle) how can someone justify adopting it oneself?
And on a societal level, playing hard-to-get only leads to confusion. Think again of Mr. Collins and Elizabeth: So convinced is Mr. Collins of women's habit of false refusals that no matter what Elizabeth says, she cannot convince him that she truly does not want to marry him. Is that a situation anyone wants to be in?