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14.12 Game Theory
Prof. Muhamet Yildiz
Fall 2010
Homework 5
Due on 12/2/2010 (in class)
Youneedtoshowyourworkina
l
lquest
ions
.
1. Consider the following twoplayer game in which the payo
f
s and the actions are as
follows:
LR
U
2
0,0
D
0,0
2
Here,
∈
{
−
1
1
}
and
∈
{
−
1
1
}
are privately known by players 1 and 2, respectively,
and the probability of each
(
)
pair is 1/4.
(a) Write this as a Bayesian game.
(b) Find all purestrategy Bayesian Nash equilibria of this game. Verify that they are
indeed Bayesian Nash equilibria.
2. Two siblings, named Alice and Bob, have inherited a car from their parents. The car
is “peach” with probability
, in which case its value is
ˆ
0
, but it may be a “lemon”
with probability
1
−
, in which case its value is 0. They have equal shares on the car,
but they would rather one of them owned the car. The ownership of the car is decided
as follows. Alice o
f
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