Psychologists used a test which women completed with an on-screen virtual partner.
The test involved an economic game where the woman had to make an offer to the partner. She had to offer a certain amount and keep the rest for herself.
At the end of the test, the researchers rated the partner's attractiveness on a 10-point scale.
The results of the study showed that women in the fertile stage of the month made smaller offers to attractive women.
On an average, women at the high-fertility stage offered 25 percent less to the most attractive women than they did to the least attractive women.
Women at the low-fertility stage offered 20 percent more to the most attractive women than they did to the least good looking, which according to researchers suggests that low-fertility women are less competitive with attractive women.
According to the study, at Wellesley College in the US, the phenomenon is a hangover from hunter-gatherer days, when a woman had to look after herself and deny resources to other women who might be competing for good male stock.
"What we found supports the idea that, among women, competitiveness during periods of high fertility is linked to the withholding of resources from potential rivals," the Independent quoted Dr Margery Lucas as saying.
"Resource competition is important because women need to acquire products - clothing, makeup, accessories, and so on - to enhance their attractiveness. By offering less to attractive women and keeping more for themselves, fertile women can help to enhance their own appearance and weaken a competitor's ability to do the same.
"Women today should be aware that in, for example, salary negotiations, menstrual cycle phase, along with the attractiveness and sex of the negotiation partner, could interact in complex and potentially costly ways," she added.