x 8.1: Maybe They’re Just Not That Into You
You have a crush on someone. You know they will be at one of two parties, A or B. You like the
music at party A better than the one at party B.
However: they may or may not be into you to. If they are, then they too hope to show up to the
same party as you. If they’re not, then they hope to show up to the opposite party. Oh, also: their
taste in music is the opposite of yours.
We’ll model this as a Bayesian game. In the first period “Nature” chooses whether your crush likes
you back or not, each with probability 1/2. Then player your crush (player 2) observes nature’s
choice, while you do not. Finally, you each decide which party to go to. Payoffs are as follows:
(Into You) A B (Not) A B
A 2,1 0,0 A 2,0 0,2
B 0,0 1,2 B 0,1 1,0
(a) What are the strategy spaces of the two players?
(b) Draw the Bayesian normal form representation of this game.
(c) Find all the pure strategy Bayesian Nash equilibria of this game.