Econ 171
Spring 2010
Problem Set 3  Solutions
Due Tuesday, June 1
Important:
hand in only the twostar problems.
There are no onestar problems on this
problem set. The notation a.b denotes problem number b from Chapter a in Watson.
**
Problem 1
Consider a twoplayer Bayesian game where both players are not sure whether they are
playing the game
X
or game
Y
, and they both think that the two games are equally
likely.
L
M
R
T
1
,.
2
1
,
0
1
,.
3
B
2
,
2
0
,
0
0
,
3
X
L
M
R
T
1
,.
2
1
,.
3
1
,
0
B
2
,
2
0
,
3
0
,
0
Y
(a) This game has a unique Bayesian Nash equilibrium, which involves only pure
strategies. What is it? (Hint: start by looking for Player 2’s best response to
each of Player 1’s actions.)
Solution:
The unique BNE is (
B,L
), yielding each player a payoﬀ of 2. Player 1’s
payoﬀs do not depend upon which version of the game is actually being played.
Her best response to
L
is to play
B
and
T
is a best response to
M
or
R
. If 1
plays
T
, then both
M
and
R
give Player 2 an expected utility of
.
15, so her best
response is
L
. Similarly, Player 2’s best response to
B
is
L
. So in
expected
utility,
L
is a dominant strategy for 2, and 1 best responds with
B
.
(b) Now consider a variant of this game in which Player 2 knows which game is being
played (but Player 1 still does not). This game also has a unique Bayesian Nash
equilibrium. What is it? (Hint: Player 2’s strategy must specify what she chooses
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 Fall '08
 Charness,G
 Game Theory, player

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