Due:
Beginning of class
, Tuesday, September 28, 2010
Problem 1 (Find NE 1)
Find
all
of the Nash equilibria of the game in
Table 1. (Hint: start by removing all dominated strategies. Some strategies
may be dominated by mixed strategies.)
E
F
G
H
A
1,2
0,0
2,1
3,1
B
0,0
3,1
1,0
0,1
C
0,2
1,1
0,3
6,1
D
1,2
2,5
2,1
4,1
Table 1: Game for problem 1
Problem 2 (Chasing and Escaping)
Recall the “Chasing and Escap
ing” game from class and from the experimental sets: Player 1 and Player 2
each have to choose a number in the interval [0
,
100]. Player 1 wants to be
as close as possible to Player 2 while Player 2 wants to be as far as possible
from Player 1. Payoﬀ functions are:
u
1
(
s
1
,s
2
) =

s
1

s
2

u
2
(
s
1
,s
2
) =

s
1

s
2

where

x

is the absolute value of
x
, and (
s
1
,s
2
) are the numbers chosen by
Players 1 and 2, respectively.
1. Show that in equilibrium Player 2 will never play a pure strategy, and