Background: I have constructed a game theoretic model of romantic advances. There are a number of Nash equilibria in this model, distinguished by the frequency with which each sex makes romantic advances. I wish to know which equilibrium (if any) might be an accurate description of reality.
Initial research: I've found it surprisingly difficult to find studies of the sort I'm, after. Thus far I have found:
Article in psychology today, with a study showing that men are more likely to have asked for a first date in the last year, and less likely to have received a request for a first date than women - https://www.psychologytoday.com/blog/the-how-and-why-sex-differences/201104/why-dont-women-ask-men-out-first-dates
Data from dating site OKCupid, showing that men send out first messages at roughly 3.5 times the rate that women do - https://www.okcupid.com/deep-end/a-womans-advantage
Question: Does anyone know of any further, 'stronger' studies indicating whether one sex makes romantic advances more frequently than the other? By 'romantic advances' here, I have in mind asking for first dates, requesting contact details, initiating first kiss, initiating first sexual contact, etc.