Its a standard example of a game that has no Nash equilibrium. But what exactly are the rules of the game? How about these:
You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.
Hmm… maybe it does have a Nash equilbirium. But after reading the article (highly recommended), I am still not sure. I think it comes down to whether or not the players are Turing machines. (Fez flip: The Browser)