This preview shows pages 1–2. Sign up to view the full content.
–1–
Prof. William H. Sandholm
Department of Economics
University of Wisconsin
March 13, 2003
Midterm Exam – Economics 713
1.
(10 points)
Let
G
be a two player zero sum game.
Show that if
σ
1
∈
∆
S
1
is a strategy of player
1 which minmaxes player 2, then
1
is not strictly dominated.
2. (10 points)
You and a friend are computing the subgame perfect equilibria of an infinitely
repeated game
G
∞
()
δ
. Your friend suggests that to perform the computation
efficiently, you should begin by eliminating all dominated actions from the stage
game.
Evaluate your friend’s suggestion.
3.
(15 points (5, 10))
A (finite) normal form game
G
is a
potential game
if there exists a function
P
:
S
→
R
(known as a
potential function
) such that
u
i
(
′
s
i
,
s
–
i
) –
u
i
(
s
i
,
s
–
i
) =
P
(
′
s
i
,
s
–
i
) –
P
(
s
i
,
s
–
i
)
for all
s
i
,
′
s
i
∈
S
i
,
s
–
i
∈
S
–
i
, and
i
∈
N
.
(
i
)
Explain in words what this condition means.
(
ii
)
Prove that every potential game has at least one pure strategy Nash
equilibrium.
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.
 Spring '08
 SANDHOLM
 Economics, Game Theory

Click to edit the document details