In the reality show “Beauty and the Geek”, the contestants were first paired off in the following fashion:
7 beauties were located in 1 room and 7 geeks are located in another room and there is a curtain seperating the two. First, a geek would be asked to voulenteer to present himself to the group of beuaties and give a brief speil about who he was. Then, 1 of the beauties would choose to pair up with that geek and they would form a pair. Then, one of the beauties would voulenteer to go over to the geek side and give a brief speil and one of the geeks would voulenteer to pair up with the beauty. This process continues until there is only 1 beauty and 1 geek left and they pair up with each other.
Now, using game theory, is it possible to figure out what would be the optimum strategy for a beauty/geek in order to pair up with the most attractive/intelligent of the opposite kind?
Assume, for the sake of this problem, that all people would rank the attractiveness and intelligence in the same manner, so personal preference has nothing to do with it. Also, assume that a person is aware of his own ranking within his group since he can compare himself with everyone else in the group. But beauties can only compare geeks to the geeks that have been previously presented and geeks can only do the same for beauties.
To me, this seems like some variation on the optimal marriage problem. I’m having problems finding a link to it, but, IIRC, I think either Neumann or Nash or one of the biggies pulled this out as a trivial example of game theory where they managed to prove that a woman should reject all suitors before she is 40 and then marry the first person she meets after the age of 40 which is better than the average of all the suitors who proposed to her before 40. It runs under the same set of arbitrary assumptions but I thought it was quite a neat way to go about the problem.
So, any thought about how to tackle this?
My initial intuition is that you should approach the other group instead of having them come to you and that around 1/2 way through the choosings would be the optimal time. People who start off early on are likely to be rejected in the hopes that someone better will come along later. People later have slimmer pickings of beauties/geeks. I guess it would also depend on your percieved rank within the group. If you rank last, then perhaps it would be better going earlier on so you can exploit the other groups ignorance. Since theres a fixed quantity of attractiveness/intelligence, that makes this a zero sum game which, if I understand the theory correctly, must mean theres a stable optimal solution. I doubt that the theory is advanced enough for us to figure out what it is though.