>Aside from anything else it's an interesting Nash equilibrium -- I want to find a mate with an average-looking face so that we can produce children with average-looking faces who will be the most desirable breeding partners in the next generation.

Isn't it a wrong Nash equilibrium? You should choose a mate with someone on the other side of "average", so your children will have average faces. An average face and your (more likely than not) non-average face do not make average faces.

This "other side of average" effect is to some extent seen with the major histocompatibility complex.