MA4264

In the movie, "A Beautiful Mind," John Nash gets the idea for Nash equilibrium
in a student hangout where he is sitting with three buddies. Five women walk in,
four brunettes and a stunning blonde. Each of the four buddies starts forward to
introduce himself to the blonde. Nash stops them, though, saying, "If we all go
for the blonde, we will all be rejected and none of the brunettes will talk to us
afterwards because they will be offended. So let's go for the brunettes." The next
thing we see is the four buddies dancing with the four brunettes and the blonde
standing alone, looking unhappy.

Assume that if more than one buddy goes after a single woman, they will all be
rejected by the woman and end up alone. The payouts are as follows.
Ending up with the blonde has a payout of 4, ending up with a brunette has a payout of 1, and
ending up alone is 0. The four buddies are players in this noncooperative game.

(i) Is the result in the story a Nash equilibrium?

(ii) Find all pure-strategy Nash equilibria for this game.

(iii) Are the Nash equilibria you found better than what Nash suggested?


Lol. Maths for you.