Professor Rod Garratt
Winter 2011
ECON 210B
Problem Set #3
Due: Friday, March 4 (before section)
1. The following game is called Selton’s horse.
1
C
2
D
3
d
1,1,1
L
R
L
R
3,3,2
0,0,0
4,4,0
0,0,1
Find the pure strategy Nash equilibria. Check whether each pure strategy Nash
equilibrium is also a perfect Bayesian equilibrium.
2. Consider the following game:
(i) Nature determines whether the payoffs are as in Game 1 or as in Game 2, each game
being equally likely.
(ii) Player 1 (the row player) learns whether nature has drawn Game 1 or Game 2, but
player 2 does not.
(iii) Player 1 chooses either T or B, Player 2 observes Player 1’s choice and then chooses
either L or R.
L
R
L
R
T
10, 0
10, 4
T
2, 12
30, 4
B
6, 9
20, 2
B
2, 12
2, 6
Game
1
Game
2
Find all the purestrategy pooling and separating perfect Bayesian equilibria in the
resulting game.
Be sure to specify the equilibrium strategies and beliefs in each case.
3. Once upon a time a signaling game was played between a princesses and a frog. The
frog was the “Sender.” He could either say he was a ‘prince’ or a ‘frog.’ The princess was
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 Fall '09
 GARRATT
 Game Theory, perfect Bayesian equilibria, Professor Rod Garratt, 3,3,2 2 L

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