What are the limits of game theory?

Do you think that they're trying to stretch things a little bit too far? Try this example:

It is a truth universally acknowledged that the available, sociable, and genuinely attractive man is a character highly in demand in social settings. Dinner hosts are always looking for the man who fits all the criteria. When they don't find him (often), they throw up their hands and settle for the sociable but unattractive, the attractive but unsociable, and, as a last resort, for the merely available.

Luckily I can rely on my personality to keep me out of such situations :)

... The problem of the eligible bachelor is one of the great riddles of social life. Shouldn't there be about as many highly eligible and appealing men as there are attractive, eligible women?

Actually, no—and here's why. ... The structure of the proposal is not, "I choose you." It is, "Will you choose me?" ...

... You can think of this traditional concept of the search for marriage partners as a kind of an auction. In this auction, some women will be more confident of their prospects, others less so. In game-theory terms, you would call the first group "strong bidders" and the second "weak bidders." Your first thought might be that the "strong bidders"—women who (whether because of looks, social ability, or any other reason) are conventionally deemed more of a catch—would consistently win this kind of auction.

But this is not true. In fact, 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.)

Is that the limit of this sort of research?

Nope. Consider, for example, a game theory paper entitled On the likelihood of finding the right partner in an arranged marriage or Decision making in arranged marriages with a stochastic reservation quality level.