This is the first time I leave a comment in the Fray. I feel compelled to write this comment because, as someone who has a professional interest in game theory, I am positively shocked by the article. It just seems illogical, to the point of true weirdness. Let me explain why, by going through the author's argument.

Let us be kind to the author and believe his assertion that there indeed is a shortage of appealing, available men. The author makes no attempt to corroborate this statement, and it runs counter to my personal experience. Anyway, I don't think that is the biggest problem with the article, so let us assume it is true.

The first thing that the author does is state that it is the woman who is choosing among the men, not vice versa. Less than obvious (as any woman unlucky in her love life can assert), but let us buy that as well.

It is what follows that really blew me away. The author somehow leaps to the conclusion that search for a marriage partner is similar to an auction, and proceeds with a discussion of how "strong" and "weak" bidders would behave. He warns the reader that the article he is linking "is not for anyone". Well, do have a look at the article, and if you have an elementary knowledge of mathematics and are capable of reading an English text, you will notice that:

1. The auctions that the article talks about are independent private value auctions. In the marriage-market language, that would mean that, for instance, if a woman finds a man attractive, that conveys no information at all as to whether other women would find him attractive. This is clearly not what happens in reality: women's evaluations of a man's attractiveness must be correlated;

2. The author simply does not understand what a "strong" bidder is -- his explanation has nothing to do with the meaning of this term. In reality, a strong bidder is the one who tends to have a higher valuation for the object for sale. I am not quite sure how to translate this into the marriage language, but it clearly has nothing to do with a woman's beauty, intellect, etc.;

3. In theory, it is not necessarily true that weak bidders tend to win more often than strong bidders -- they do tend to bid more aggressively (under some assumptions), but on the other hand, they value the object less. Also, the discussion of why weak bidders are more aggressive ("with a lot at stake in getting it right in one shot, it's the women who are confident...") is simply nonsensical and has nothing whatsoever to do with the real reason for this result;

4. I find the analogy with the auction somewhat contrived, to say the least. What does the author consider to be the payments in this auction? Does the author seriously imagine that there is one man out there, and the women simultaneously submit "bids" (in whatever form) for him (because this is the auction format the linked article talks about)?

Finally, the author finds an "explanation" for the lack of attractive available men -- they all have married early! What this have to do with the discussion of strong and weak bidders remains a mystery.

It is also a mystery to me how this article could have passed any form of editorial control. Not only it has nothing whatsoever to do with game theory -- it is also remarkably illogical. I wish the author consulted anybody who has any knowledge of game theory.

I do think this is related to game theory, because game theory is the study of choices based on perfect and imperfect information. If this isn't game theory, I'd like to hear what your definition of game theory is.

You are right in that the subject itself has to do with game theory (which can be defined as the theory of interactive decision-making). What I meant was that the author's reasoning has little connection with the fact in game theory (i.e. that weak bidders bid more aggressively) he is alluding to or with the article he is linking to. I guess I should have been more clear.

Would you think its closer to chicken in game theory?

The author is completely out of his depth. The whole article was basically mush.

Yes, it's a bad job. The marriage market looks nothing like an auction. It should be a search model. His "intuitive" description could be easily written down formally - but he's going to need some extra assumptions to get the result that he wants. He seems to be suggesting a search model where women get sequential draws and choose the stopping point for a search. That's a standard search model. But women who are "better" will get draws from a better distribution - if not their decision rules would all be identical. This certainly implies that the reservation level of man-quality is higher for the higher quality women, but it does not follow that their mean time-to-marriage will be longer, since they are drawing from a better distribution. You're going to need different shapes of distributions of suitors for different quality women to get that.

Dear A Reader,

I'm considering this more. You're right--I had trouble finding a game theoretic model that would match up perfectly with the very simple auction model I'd want.

I do understand the definition of the strong and weak bidders. But the key here is that in all the models I've seen are based on multiple auctions in each of which bidders can bid up to their private value. So the private value is equal to the maximum bid. In this case bidder with a private value drawn from a lower distribution is the same as the bidder with a lower maximum bid.

If you want to define it more formally, consider an auction with two bidders for an object of type T where T is a number from 1 to 10, with private values PV(1) and PV(2).

PV(1) = T if T<4 or T=4 and PV(1) = 4 if T>4

PV(2) = T if T<9 or T=9 and PV(2)=9 if T>9

This is the equivalent of having two bidders with maximum bids of 4 and 9, bidding on an object with a type (or "desirability") of T. So now we've defined the strong and weak bidders here more formally in terms of a distribution of values.

Am I still cheating here? Yeah. I know I am. For one thing the paper I cite looks at a two bidder case, not a multiple bidder case. I think you should be able to derive an equivalence between the case of two bidders with independent private values and the very simple model I'm using with only one possible bid (the maximum) and a model with multiple bidders with values drawn from a range of distributions. In both cases the decision on whether to bid will be independent of the value that other bidders assign to each object. I would need to think about how to show this more rigorously.

My approach here may be backwards: there may be a way to show this much more simply with a common value model. That might even be trivial, but I haven't seen anything that would apply for that case.

Mark