Problem Set 4.
Ben Polak
Econ 159a/MGT522a
Three questions due October 10, 2007
(1) Comparative Statics of Mixed Strategy Equilibria.
Consider the following twoplayer
game.
l
r
U
12
;
2
3
;
9
D
5
;
8
4
;
2
(a)
Find all the Nash equilibria, pure and mixed. Explain how you know you have found all the
equilibria.
(b)
Suppose that the payo° of the column player
u
2
(
D; l
) is reduced from 8 to 6, but all other
payo°s remain the same. Again, ±nd all the pure and mixedstrategy Nash equilibria.
(c)
Compare the mixedstrategy equilibria in parts (a) and (b). Did this worsening in one of player
2’s payo°s change player 2’s equilibrium mixed strategy? Did it change player 1’s? Give some
intuition.
2.
On Her Majesty’s Secret Service.
The famous British spy 001 has to choose one of four
routes
a
,
b
,
c
, or
d
(listed in order of speed in good conditions) to ski down a mountain. Fast routes
are more succeptible to avalanche.
At the same time, the notorious rival spy 002 has to choose
whether to use (\
y
") or not to use (\
x
") his valuable explosive to try to cause an avalanche. The
payo°s to this game are as follows.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 BENJAMINPOLAK
 Game Theory, Nash, Ben Polak Econ, new laser

Click to edit the document details