Problem Set 2b

Problem Set 2b - ECON
166A
Fall
2010
 
 
 1)

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Unformatted text preview: ECON
166A
Fall
2010
 
 
 1) Consider
the
following
extensive
form
game
 
 1
 
 
 
 
 2
 2
 
 
 
 
 (2,‐2)
 (‐2,2)
 (‐2,2)
 (2,‐2)
 
 
 a) What
is
the
strategy
space
for
players
1
and
2?
 b) Write
the
normal
form
of
the
game.
 c) Can
you
arrive
at
a
unique
strategy
profile
with
backwards
induction?
If
so,
 what
is
it?
 d) Using
the
normal
form
of
the
game,
apply
iterated
dominance.
Does
the
 procedure
find
a
unique
strategy
profile
that
“solves”
the
game?
If
so
what
is
 it?
 
 Now
considered
the
modified
game:
 
 
 1
 
 
 
 
 2
 2
 
 
 
 (2,‐2)
 (‐2,2)
 (‐2,2)
 (2,‐2)
 
 e) Write
the
normal
form
of
the
game.
 f) Using
the
normal
form
of
the
game,
apply
iterated
dominance.
Does
the
 procedure
find
a
unique
strategy
profile
that
“solves”
the
game?
If
so
what
is
 it?
 
 
 
 2) Harrington
Chapter
3
question
10
 
 
 (GO
ON
TO
PAGE
2!)
 
 
 
 Problem
set
2B
 Sinervo
and
Musacchio
 3) In
Cournot
duopoly,
two
producers
of
an
identical
product
(call
them
firms
A
and
 B)
simultaneously
choose
how
much
of
that
product
to
produce,
say
qA
and
qB,
 between
3
and
7.
For
simplicity,
assume
that
production
cost
is
10
per
unit.
The
 price
p
is
40
–
2(qA

+
qB).
This
is
because
price
falls
as
the
supply
increases.
 Payoffs
are
profit
=
(price
–
unitcost)*quantity,
e.g.,
(40
‐
2qA
‐
2qB
‐
10)
qA
for
 firm
A.
To
simplify
the
game
assume
that
the
only
available
q’s
are
3,
5,

and
7.
 a. Write
out
the
extensive
form
for
this
game.

 b. Now
write
out
the
extensive
form
for
the
Stackelberg
variant
of
this
game,
in
 which
firm
A
chooses
first,
and
firm
B
observes
qA
before
making
its
own
 choice.
 c. Write
out
the
normal
form
for
the
simultaneous
move
version
of
the
game.
 For
the
Stackelberg
version
of
the
game,
what
is
specification
of
B’s
strategy?
 How
big
is
the
table
describing
this
game’s
normal
form?
 d. For
the
original
simultaneous
choice
version
of
the
game,
can
you
identify
 one
or
more
Nash
equilibria?
If
so,
what
is
it
(are
they)?
 
 4)

Harrington
Chapter
4,
question
4
 
 4) Harrington
Chapter
4,
question
9
 
 5)

Harrington
Chapter
4,
question
10
 
 ...
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This note was uploaded on 03/03/2011 for the course ECON 414 taught by Professor Staff during the Spring '08 term at Maryland.

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