Most people care a lot more about money than I do, but even so, almost no one wants to be married for their money. It's puzzling. You might say that since marriage is a long-term contract, people only want to be married for traits that they will keep for a long time. But that cuts against the obvious fact that people care a lot about the appearance of their spouse, even though looks generally fade long before money does.
Another possible explanation for the asymmetry is the discrete nature of the marriage contract. Right after someone marries you for your money, they no longer need you for your money, because (prenup aside) they can divorce you and grab a big chunk of your lifetime income. Maybe that's right, but even if you've got a Massey prenup, you still want to be married "for yourself," not your money.
When economics fails, I usually try to supplement it with psychology. Maybe the main reason people don't want to be married for their money is that we don't believe that people can love someone for their money. You can feel strong attraction to someone's personality, looks, intelligence, or success, but not money per se. The catch is that once you start loving someone for one or more of these traits, you often stay in love with them after they fade. You get addicted to the pusher, rather than the drug.
Perhaps this is too much of a man's perspective. It's hard not to feel disgusted at a man who marries for money, but we judge women who do so far less harshly. And the reason, I suspect, is that men almost never fall in love with a women for her money, but some women can fall in love for a man for his money. But that doesn't sound quite right to me. Like George Costanza, "I know less about women than anyone in the world." Still, aren't women much more attracted to success than money? An average guy who inherits millions isn't interesting to women in the same way that a self-made millionaire is.
Whatever the explanation, the fact that people don't want to be married for their money explains some puzzles about the marriage market. For one thing, it explains why people prefer to marry within their social class. If you're rich guy, you would rather marry a rich girl because you know she's not after your money. If disaster struck her family fortune the day after the wedding, you might not care at all about the financial loss, because at least you know that she married you for yourself.
An even bigger puzzle we can explain is why men don't exploit the INS marriage loophole far more than they do. By going to the world market, the typical American man could probably use the lure of citizenship and a First World standard of living to find a wife who is better-looking, younger, and less demanding than he could find in the States. Roll your eyes if you must!
But only an idiot wouldn't wonder "Maybe she's just marrying me for the green card and the green." And that's usually enough to overpower the palpable benefits of casting a wider net.