Women really don't 'pursue' men they want... they just don't make things difficult. A quality attractive woman, who is single will have at least three men chasing after her, likely more. They say yes to dates, they show up, and they are pleasant when you are with them. This is as good as it gets with attractive sane women. Rinse and repeat and if she really wants you, she will make herself scarce with the other dudes and focus on the one she really wants.... this takes time and patience.
I think you are describing a woman with medium interest.
@RangerMIke could be describing a woman with medium interest. At a minimum, that's a woman with medium to medium-high interest.
Doc Love used to have a concept that I first read about when I was in college in the early 2000s. He had this idea that women's interest levels operated on percentages from 0% to 100%. Closer to 100% was high interest. 50%+ interest level was something that was workable.
Women don't pursue in the way that men pursue. Women don't initiate interactions. Women are responsive when men initiate and escalate or they are not responsive. Additionally, women raise objections to initiations and escalations (making things more difficult) when they have lower interest levels. The less interest, the more difficult they make it. When women like you, they make things as easy as they possible can.
Women pursue in the way that they are most responsive to the option they like the best.
A woman might be dating three guys... if they all start off at the same time, she will MOST LIKELY have medium interest in all of them. As she dates them, she will eventually start liking one more that the others. If you happen to be the guy she is very interested in, she will make things easier and easier... will go along and do what you want to do... she will even start reaching out to you more. If you are one of the other two dudes, she will make things harder and harder and hope they take the hint and drift off. If they don't, she'll say "We have to talk.", but she will be disappointed that they didn't take the hint, because at that point she knows those dudes are more interested in her than she is in him.
Only when all the other dudes are out of the picture, will she seriously start to pursue that man she wants.
A scenario like this does happen but usually not exactly at the same time. There's usually some difference in the timelines. It might be something like 1-3 weeks. Not everyone is moving around the exact same time.
If there are 3 men a woman has medium interest in, then there will be scenario where she gets most interested in 1 under the condition she is seeking some sort of exclusive relationship.
It is extremely rare to have a woman just fall for a guy at first sight. Men do this all the time: it is unusual for women to do this.
I agree.
Yes, women have multiple men chasing them, but they do not care about most of these men.
Women today have ridiculous abundance.
Let's compare the situation women have had since the de-stigmatization of tech-based options (mid-2000s to present) as compared to the era before then but after the onset of the Sexual Revolution (1970s - mid-2000s).
In the 1970s - mid-2000s, women would generate interest based on their day-to-day routines in the world. Some women had better routines than others. Some women made me effort to meet men by going to bars more. Some women also had better non-bar routines. A woman with a decent routine might get approached in the real world by 7-15 men in a week depending on her age, looks, and effort in the real world. That's a decent quantity of options.
Since dating from tech methods got de-stigmatized in the mid-2000s, women have far more options than comparable women of the 1970s to circa 2005. A woman's day-to-day routine matters much less now. A woman who has taken a few good pictures on a couple days of her life, owns a smartphone, and has downloaded 1-2 apps now has a constant flow of 200+ new options per week in her swipe queue. This happens while she sits at home and watches internet content and streaming video platform content.
However, most women don't think much of their abundance because most women aren't impressed with the 200+ penises in their swipe queue. They can also add some more options from the social media DMs too.
If a woman fails to find this guy she will either settle with the second best option or just continue being emotionally single in her head. This is why I say anything below high interest is low interest because you run the risk of being instantly dropped for the right type of guy to come along.
A well known internet example of this is content creator Courtney Ryan. Courtney eventually settled for a dweeb with money/status named Teddy Baldassarre after failing to get a commitment from Alpha Chad types. Compared to most women, Courtney had more self-awareness and learned faster. She decided to settle around 23-25 with that dweeb with money option.
It's more common for women to be like the fitness class instructor that I overheard after a fitness class once. At the time, she was 30 years old and telling a female fitness class attendee about how using swipe app had been a disaster for her. This was a 30 year old who was better looking than Courtney Ryan. She had been riding the penis carousel and not getting commitment from the likely higher tier men she wanted a commitment from.
Courtney Ryan is a flight risk for Teddy Baldassarre.
The romanticized notion of tirelessly pursuing the girl of your dreams, as portrayed in Hollywood and popular culture, often falls short of reality. Instead, men would benefit from prioritizing maintaining attraction.
This is good advice for mid-tier men. Mid-tier men on looks/money/status could use their personalities to maintain higher level of attraction with the fewer women that they are able to get. Using personality attributes is free.
, and is much more useful in attraction than being 2.5-sigma in intelligence. 
