Jason (jcreed) wrote,

A Nash Equilibrium to All, and to All a Good Night

I feel like overanalyzing and overrationalizing christmas now. It's the kind of thing I do from time to time.

Among other things I got some gift certificates to Borders for christmas. I'm not about to complain, but gift certificates always seem kind of strange to me on a game-theoretic level, because they're worse than cash, and everyone exchanging cash would be just a wash.

Like, apart from the whole aspect of giving gifts to show that you actually care about people, which obviously is an important thing, you hope that in the ideal case the utility the recipient gets from the gift is bigger than what it cost you; because then everyone gets gifts to everybody, and everybody net wins, as if everyone was playing something roughly isomorphic to the Prisoner's Dilemma and all cooperated. This makes sense, because for everything I actually decide to purchase for myself, the utility I expect to get from it exceeds what it costs, because otherwise it wouldn't be worth buying.

So: an exchange of (good) gifts nets everyone positive utility, an exchange of cash nets zero, and an exchange of all gift certificates nets everyone slightly negative, because you've all just turned cash into cash-that-can't-be-used-everywhere.

But the fact that it's merely slightly negative is obviously why people buy them; if I don't think I'll be able to buy someone a gift they like, that means I have some probability distribution I'm estimating in my head (of the utility the giftee is accruing from my gift) that has an upsettingly large standard deviation and negative mean. So I can at least make the spread of the deviation smaller by getting a gift certificate.

The thing that's odd is that this is considered better than not exchanging anything at all. I guess it's that good feeling people get from just participating in the ritual.


Edited to add: nightspore led me to this Surowiecki article that mostly says what I wanted to, but more eloquently. The unfortunate conclusion is that we're all supposed to just spend more time coming up with thoughtful gifts. Dang, that sounds like effort.
Tags: holidays, nngg nerd

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