Economics 111: Intermediate Microeconomics
Spring 2006
Homework 6 Answer Key
Professor: Pedro Dal Bó
1. Football or Movie:
Players 1 and 2 were planned to go see either a football game or a movie but haven’t
decided on one. Now it is time to go to one of the two places but unfortunately they are
not together and have no way of communicating with each other. Each of them must
decide separately. If both go to the movie theater or both go to the stadium they get an
utility of 1 since they are together. Player 1 likes football and gets an additional utility
of 1 from watching the game. Player 2 likes movies and get an additional utility of 1
from watching a movie. If they are alone they get a total utility of zero since they can
only enjoy things when they are together.
a. Write the payo
ff
s of the game in the matrix form.
Player 2
Player 1
F
M
F
2, 1
0, 0
M
0, 0
1, 2
b. Find the pure strategy Nash equilibria.
(F,F) and (M,M).
c. Find the mixed strategies Nash equilibrium (the one with randomizations).
For player 1 must be indi
ff
erent between F and M to be willing to randomize. For
that, the probability
β
that 2 goes to F must be such that
U
1
(
F
) =
U
1
(
M
)
.
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 Spring '08
 DALBO
 Economics, Microeconomics, Game Theory, Perfect Competition, MOE, player, best response function

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