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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