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Dr. Huanxing Yang
Econ 601 Game Theory
Homework Assignment 1
Due April 16, Wednesday
1.
Chapter 4, Problem 5
a)
Since
b
is optimal when player 2 uses
x
,
c
is optimal when player 2 uses
y
, and
d
is optimal when player 2 uses
z
, player 1's strategies of
b
,
c
, and
d
are not strictly
dominated. Next note that
a
is strictly dominated by
c
. Thus, the strategies of
player 1 that survive one round of the iterative deletion of strictly dominated
strategies (IDSDS) are
b
,
c
, and
d
. Turning to player 2,
z
is optimal when player 1
uses
a
and
y
is optimal when player 1 uses
b
.
z
strictly dominates
x
. Thus, the
strategies of player 2 that survive one round of the IDSDS are
y
and
z
. The
reduced game is then as shown in Figure SOL4.5.1.
Figure SOL4.5.1
Player 2
1,3
0,2
Player 1
2,1 1,2
0,1 2,4
y
z
b
c
d
For player 1,
c
strictly dominates
b
. Neither
c
nor
d
are strictly dominated. Thus,
the strategies of player 1 that survive two rounds of the IDSDS are
c
and
d
.
Turning to player 2, neither strategy is strictly dominated. After two rounds, the
reduced game is as shown in Figure SOL4.5.2.
Figure SOL4.5.2
Player 2
Player 1
2,1 1,2
0,1 2,4
y
z
c
d
Though neither of player 1's strategies are strictly dominated,
z
strictly dominates
y
for player 2. After three rounds, the reduced game is as shown in Figure
SOL4.5.3.
Figure SOL4.5.3
Player 2
Player 1
1,2
2,4
z
c
d
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View Full Document d
strictly dominates
c
for player 1. We conclude that the IDSDS implies that
player 1 uses
d
and player 2 uses
z
.
b)
The unique Nash equilibrium is (
d
,
z
).
2.
Chapter 4, Problem 8
a)
Figure SOL4.8.1
Sheikh
2468
1
0
1
0,5
0,3
0,1
0,1 0,3
3
5,0
0,3
0,1
0,1 0,3
Sultan
5
3,0
3,0
0,1
0,1 0,3
7
1,0
1,0
1,0
0,1 0,3
9
1,0
1,0
1,0
1,0
0,3
b)
The unique Nash equilibrium is (7, 6).
3.
Chapter 4, Problem 9
The Nash equilibria are (
b, x, A
), (
a ,z, B
), (
c, x, C
), (
c, z, C
).
4.
Chapter 4, Problem 10
(a)
The resulting performance is 1 for player 1, 1 for player 2, and 1 for
player 3 so player 1 wins the promotion. Player 1's strategy is clearly
optimal since he receives the maximal payoff of 1. If player 2 switches
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This note was uploaded on 07/17/2008 for the course ECON 601 taught by Professor Yang during the Spring '08 term at Ohio State.
 Spring '08
 YANG
 Game Theory

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