Problem Set 4b Solutions

Problem Set 4b Solutions - Econ
166a

 Fall
2010
...

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Unformatted text preview: Econ
166a

 Fall
2010
 
 
 
 Problem
Set
4b
 
 
 Sinervo/Musacchio
 
 1) Harrington
8.7
 
 
 
 
 2) Consider
the
waiting
game
we
studied
in
class
but
consider
two
different
alternatives
for
the
waiting
cost:
 
 a)
the
waiting
cost
is
9*(wait
time)
for
each
player
 1
 2
 1
 2
 1
 2
 (30,20)
 
 
 
 
 
 
 
 (‐15,‐25)
 (‐16,‐6)
 (3,‐7)
 (2,12)
 (21,11)
 (20,30)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1
 2
 1
 2
 1
 2
 (‐15,‐25)
 (‐16,‐6)
 (3,‐7)
 1
 2
 1
 (2,12)
 2
 (21,11)
 1
 (20,30)
 (‐15,‐25)
 (‐16,‐6)
 (3,‐7)
 1
 2
 1
 (2,12)
 2
 (21,11)
 1
 2
 1
 (‐15,‐25)
 (‐16,‐6)
 (3,‐7)
 1
 2
 (2,12)
 1
 (‐15,‐25)
 (‐16,‐6)
 (3,‐7)
 (‐15,‐25)
 (‐16,‐6)
 (‐15,‐25)
 By
BI,
the
only
SPE
is
that
each
player
plays
“gets
in
line”
in
each
of
their
information
sets.
The
 outcome
in
equilibrium
play
is
that
player
1
gets
in
line
in
his
first
turn.
 b)
the
waiting
cost
is

11*(wait
time)
for
each
player
 1
 2
 1
 2
 1
 2
 (30,20)
 (‐25,‐35)
 (‐24,‐14)
 (‐3,‐13)
 (‐2,8)
 1
 2
 1
 2
 (19,9)
 1
 (20,30)
 2
 (‐25,‐35)
 (‐24,‐14)
 (‐3,‐13)
 (‐2,8)
 (19,9)
 (20,30)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1
 2
 1
 2
 1
 2
 (‐25,‐35)
 (‐24,‐14)
 (‐3,‐13)
 (‐2,8)
 1
 2
 1
 2
 1
 (20,30)
 2
 (‐25,‐35)
 (‐24,‐14)
 (‐3,‐13)
 1
 2
 1
 2
 1
 (20,30)
 2
 (‐25,‐35)
 (‐24,‐14)
 1
 2
 1
 2
 1
 (20,30)
 2
 (‐25,‐35)
 1
 2
 1
 2
 1
 (20,30)
 2
 (20,30)
 
By
BI,
the
only
SPE
is
for
player
2
to
wait
until
his
last
turn,
and
then
to
get
in­line.
Player
1
waits
in
all
his
 turns.
 
 3) Harrington
8.12
 
 
 
 4) Harrington
9.3
 
 
 
 
 
 
 5) Harrington
9.11
 
 
 ...
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