New Delhi, Jan. 17: Long courtships are best — for a woman. Scientists have used the mathematics of game theory to show that a woman who plays hard to get has a better chance of finding a good mate.

In a study that analysed the mating game through a set of mathematical equations, British researchers have rediscovered what they concede is folk wisdom: a woman is best advised not to mate on her first date.

Robert Seymour at the University College, London, and Peter Souzou at the University of Warwick have shown that protracted courtships allow males to signal their suitability as good partners and allow females the opportunity to screen out unsuitable males. The findings of the study, which has modelled courtship as a waiting game in time, appear this month in the Journal of Theoretical Biology.

The researchers set out to explore why courtship is sometimes a long process in some species of birds and in humans. They used tools of game theory — a branch of applied mathematics that seeks to explain behaviour in strategic situations.

“Human courtship can involve a sequence of dinners or outings lasting months or even years,” said Seymour. “There is a significant cost of time to both the sexes which could be spent on other productive activities.”

“Longer courtship is a way for a female to acquire information about the male,” he said.

The model assumes that the male is “good” or “bad” depending on whether he is willing to care for the young after mating. The female gets a positive payoff from mating if the male is good, but a negative payoff if the male is bad.

“We find that a good male never quits, but a bad male quits at some point,” Souzou, a theoretical biologist told The Telegraph in an interview. “The assumption is that a good male values mating more than a bad male — so he waits longer.”

The willingness of a good male to court longer emerges as a consequence of certain assumptions about payoffs in the mating game and what mathematicians describe as the Nash Equilibrium — a concept in which the players pursue the best possible strategy knowing the strategies of other players.

“In our context, when a female's strategy is to wait, the best strategy for a good male is to wait indefinitely, while that for a bad male is to quit at some point in time. And given a situation where a good male waits indefinitely and a bad male quits, the best female strategy is to wait for some finite time,” Souzou said.

The duration of courtship carries information about the male to the female. “Bad males give up at some random time if the female has not by then mated with them, but good males are more persistent and do not give up,” Souzou said.

The researchers have cautioned that human decisions are complex and that “behavioural flexibility is vastly greater than assumed in a simple model.”

People may use a number of signals to assess complex features of potential mating partners over time. In addition, human courtship also takes place within a complex social environment.

Nevertheless, the researchers said, their model does explain the phenomenon of long courtships — and the conventional wisdom: that a woman shouldn’t give in to the charms of a man on a first date.