This preview shows pages 1–2. Sign up to view the full content.
Kaushik Basu
Spring 2008
Econ 367: GameTheoretic Methods
Problem Set 5
1.
Neither John nor George wishes to show up at a public meeting wearing the same colored
hat.
Hats can be R (red), W or B.
Represent the decision problem of John and George as
a game.
That is, selecting some appropriate numbers for payoffs, write down a payoff
matrix to describe this game.
Locate all the Nash equilibria.
2.
Let us define a new equilibrium concept, which I will call the
asymmetric Nash
equilibrium
, for twoplayer games as follows:
(
)
,
*
2
*
1
s
s
is an asymmetric Nash equilibrium
if and only if
)
,
(
)
,
(
*
2
1
1
*
2
*
1
1
s
s
s
s
π
, for all
s
1
≠
*
1
s
),
,
(
)
,
(
2
*
1
2
*
2
*
1
2
s
s
s
s
≥
for all
s
2
(a)
In the game described below, where player 1 chooses between
U
and
D
and 2
chooses between
L
and
R
, locate all Nash equilibria and asymmetric Nash
equilibria
L
R
U
2, 2
4, 2
D
1, 2
4, 4
(b)
If an outcome is an asymmetric Nash equilibrium, does it have to be a Nash
equilibrium?
Briefly explain your answer.
3.
Consider the Traveler’s Dilemma game.
(a)
Is strategy 100 (that is, for a player to write 100) weakly dominated by any other
strategy (that is, writing some other number)?
If so, which ones?
Briefly explain
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
 BASU

Click to edit the document details