here's a problem from my strategy games class:

(nash equilibrium in a scene from a beautiful mind): you and your close friend thomas are in an eating club in princeton. who should walk in but three women you know (smart, fun-to-be-with female grad students) and their acquaintance, the princeton alum brooke shields. you and thomas must decide very quickly how to 'play' the chance encounter. if both of you fixate on ms. shields, none of the other women ever goes out with you again. on the other hand, if both of you awkwardly ignore ms. shields, your female friends will reject both of you tonight. however, if one of you fixates on her and the other chats up a female grad student, you each get a date tonight - one with brooke and dthe other with your friends. both of you think the the date with the other women is better than spending the evening with a 6'3" supermodel/actress.

what should you do?