Prof. William H. Sandholm
Department of Economics
University of Wisconsin
March 13, 2008
Midterm Exam – Economics 713
1.
(35 points)
Consider the extensive form game
Γ
below:
1
1
2
2
4, 4
6, 2
0, 0
0, 0
2, 2
R
L
R
L
O
I
T
B
(i)
Compute all subgame perfect equilibria of
Γ
.
(ii)
Compute all sequential equilibria of
Γ
.
(iii) Compute all proper equilibria of the reduced normal form of
Γ
.
(iv) The least demanding concept used in the analysis of games is the elimination of
strictly dominated strategies: no such strategy should ever be chosen by a Bayesian
rational player. Given this fact, it seems natural to seek solution concepts whose
predictions are una
ff
ected when a strategy that is strictly dominated (in the reduced
normal form) is removed from a game. Using your answers to parts (i)(iii), discuss
how subgame perfect equilibrium, sequential equilibrium, and proper equilibrium
fare under this criterion.
2.
(10 points)
An experimenter is evaluating a subject’s preferences over lotteries with prizes in
the finite set
Z
.
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 Spring '08
 SANDHOLM
 Economics, Game Theory, Subgame perfect equilibrium, 0 l, 2 L, Department of Economics University of Wisconsin, ante correlated equilibrium

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