…game theory predicts, and empirical studies of auctions bear out, that auctions will often be won by "weak" bidders, who know that they can be outbid and so bid more aggressively, while the "strong" bidders will hold out for a really great deal. You can find a technical discussion of this here. (Be warned: "Bidding Behavior in Asymmetric Auctions" is not for everyone, and I certainly won’t claim to have a handle on all the math.) But you can also see how this works intuitively if you just consider that with a lot at stake in getting it right in one shot, it’s the women who are confident that they are holding a strong hand who are likely to hold out and wait for the perfect prospect.
This is how you come to the Eligible-Bachelor Paradox, which is no longer so paradoxical. The pool of appealing men shrinks as many are married off and taken out of the game, leaving a disproportionate number of men who are notably imperfect (perhaps they are short, socially awkward, underemployed). And at the same time, you get a pool of women weighted toward the attractive, desirable "strong bidders."
Where have all the most appealing men gone? Married young, most of them–and sometimes to women whose most salient characteristic was not their beauty, or passion, or intellect, but their decisiveness.
Here is the full argument. I don’t, however, quite buy this as the explanation of the phenomenon. I view the real world auction as being held — at least if you wish — continuously rather than at discrete times. So the "strong bidding women" can always cave and settle for a "lesser man" after an optimal amount of waiting, yet many don’t. The distinction between period-by-period happiness and overall lifetime happiness also shapes the market. As smart single women mature, their lives get better and better. "Settling" becomes psychologically harder, even if it would make some of the "settlers" happy in the longer run. So settling doesn’t happen; decisiveness become harder to conjure up at the same time that its long-run value is increasing, or in other words behavioral economics is very much at work here.