I can’t think of any examples of females of other species actively competing for or attempting to entice potential mates. By this I don’t mean things like bees competing to have exclusive reproductive rights or become queens or whatever; I mean women putting on makeup, revealing clothes, acting flirty, etc., in an attempt to attract men. Meanwhile, it almost seems like just being a female in heat is enough to attract plenty of hopeful male suitors in just about every other species. So the first question is, are human females the only ones that put on sexual displays to attract mates?
The second question is, are humans the only animals that put on sexual displays at times with NO intention of actually mating?
Female baboons certainly put on a sexual display, as any 4th grade class on a field trip to the zoo will attest.
As for putting on a sexual display with no intention of mating, I’ve seen male peacocks do it when there were no peahens around, but I think that’s as much a display of dominance as it is sex.
There are some bird species–grebes, for example–where females participate equally in the mating “dance.” I don’t know if they regularly make the initial advance, though.
Three of our mares are known to flirt when in heat. Our third-youngest girl will always flirt whenever she is near our dominant gelding. (Yes, gelding. He’s not receptive. :()
By “flirt,” I mean overtly offering the hind end. Often the mares will simply present themselves, but frequently we’ve seen them rubbing, swiping and backing their rear ends into the males, even across a fence. This often produces an expectant reaction in the mare: toward the end of her flirting, her vagina will open and emit a creamy, yellowish lubricating discharge that has a tell-tale, pungent aroma. This deliberate oil slick is the height of her enticement, in my opinion.
It’s difficult to compare human and equine behavior, though, because flirting human women aren’t always interested (immediately, at least) in conception. I think the real difference is that, if our dominant male weren’t fixed, he’d be taking the offers from any and all of the mares, in descending order of the mares’ aggression. Based on his recovery time, this stallion could mate with each throughout the day, possibly multiple times during each mare’s period of fertility.
As noted previously, virtually any female animal can engage in sex simply by making it known that she’s sexually receptive. What human females are doing is trying to attract a particular male into committing to a long-term or permanent bonding. You’d have to look at the behavior of other monogamous or semi-monogamous species to see if there are comparable instances.
In humans, more than in most other animals, males make significant parental investment. This is the conventional explanation of why human females do/have more sexual display than is typical (breasts are one example). “Unique” is too strong though. In fact among seahorses, in which males do the work of gestating the eggs, the usual roles are reversed: females compete strenuously for males.