–1–
Prof. William H. Sandholm
Department of Economics
University of Wisconsin
March 9, 2000
Midterm Exam – Economics 713
1. (20 points)
Suppose that players 1 and 2 play the game below, and that it is common
knowledge between them that both of them are rational.
If we make no other
assumptions about the players' knowledge, what is our best prediction about how
they will play the game?
2. (20 points)
Consider an infinite repetition of the game below, and consider the following
repeated game strategy (which can be used by either player):
"Play
A
in even periods
and
B
in odd periods until someone deviates from this.
Once anyone has deviated,
play
C
forever."
For what values of
δ
is it a subgame perfect equilibrium for both
players to follow this strategy?
3, 3
3, 5
0, 0
0, 0
0, 0
0, 0
1, 1
5, 3
2, 2
A
B
C
ABC
1
2
1, 4
0, 6
5, 2
3, 1
3, 5
7, 3
0, 0
2, 2
3, 1
A
B
C
abc
1
2
d
2, 3
4, 3
3, 2
e
2, 5
3, 3
0, 0