ECON 2160 Lecture Notes - Lecture 2: Miniature Golf, Coordination Game, Extraterrestrial Places In The Cthulhu Mythos
2 May 2018
School
Department
Course
Professor
.
Sometimes”amnuyiuvemethmmfleshequbrmloreumpie,saytwolriendsenio'y
sperm
time
touther
but
each
have
a
lavorite
actlvhy
and
one
she
doesn't
enjoy.
Their
pay
off
matrix
is
below
mm‘
type
ol
game
is
called
a
'battle
of
the
sexes“
game
or
a
coordination
game.)
if
you
try
iterated
deletion',
you'll
see
there
are
no
strategies
for
either
player
that
strictly
dominate.
We
go
to
our
best
response
method.
(When
Debbie
chooses
movie,
Shawna
chooses
movve'.
When
Debbie
chooses
mini
golf,
Shawna
chooses
mini
golf.
When
Shawna
chooses
movie,
Debbie
chooses
movie.
When
Shawna
chooses
mini
golf,
Debbie'
chooses
mini
golf)
Shawna
The
game
here
has
two
Pure
Nash
Strategies.
This
game
is
said
to
have
multiple
Nash.
If
they
get
to
one
of
the
Nash,
there
is
not
a
way
to
get
both
players
to
move
to
the
other
Nash.
if
they
both
choose
movie,
Debbie
may
want
to
move
to
mini
golf,
but
Shawna
will
not
move
as
she’d
have
to
grv'e
up
2.
If
you
remember
Dr.
Nash’s
theorem,
he
stated
in
a
finite
game,
with
finite
players
and
complete
information,
there
will
be
an
odd
number
of
Nash.
Wean‘soive'lortlrttud'flashemmn“byusir'probahibty'andfindwhaliscalledamlxed'
strategyormxed’flash.
4:
my
MW}.
lYLb/‘IL
muralpmdmi
and
"mi".
ulnar
mares
.maram
4W;
mime/ms
m:
payoff
of
me.
arm.
mar-Jerri
or!
lilix
l
0
nm
-
r
o
qxjmwc
W
(my
(m‘
r
tail:
),
Shawna
will
pklt
the
movie
with
probabilrty‘
q
and
mini
golf
wtt'h
probability
l-q.
Debbie
will
poc'lt
the
movie
with
probability
p
and
mini
golf
with
probability'
1~p.
To
find
the
mixed
strategy,
we
use
the
players'
expected
utility
grv’en
them
each
playing
their
respectrv’e
.
probabilities
for
each
event.
Shawna's
expected
payoff:
It
is
best
to
think
about
this
as
her
expected
pay
off
when
she
plays
one
strategy
versus
the
other
strategy.
9m
CHOOVS
mat/[Q
mun
“EM
>
5615);?!
\Pkruc
Shawna's
payoff
when
she
plays
"movie"
or
when
q
=1
E(SM)=4p+1(1-p)
(iioquk/i
does
su
g/M-
cl?
p_
E(5M)=3p+1
ch
oi’Kn
alUQS
SW49“
3'“
,PJ
Her
pay
off
when
she
plays
"Mini
golf”
or
when
q
=
0.
E(Sm,~)
=
(-2)p
+
3(1
-
p)
E(SMG)
=
3
"
517
Now
we
can
look
at
when
she’d
prefer
one
outcome
versus
the
other
outcome.
She's
choose
Movie
if
the
expected
pay
off
for
that
choice
is
better
(or
equal)
to
the
choice
of
mini
golf
or
E
(S
M)
>_.
E
(S
MG)
l
3p+1_>3—5p
Quorum
(27:1
8
_>2
"1
420mm
pcq'
1924-
mm
the
m0
are
equal,
SM
uwid
be
irtdifkmm
She
would
choose
mini
golf
if
p
s
:1
What
would
Debbie
do?
Again
we
look
at
her
payoffs
when
she
employs
one
strategy
and
compare
it
to
when
she
employs
the
other.
Debbie'
chooses
movte'
(p
=
1):
Emu)
=
24
+
1(1
‘11)
=
q
+
1
Debbie
chooses
mini
golf
(p20)
:
E(DMG)
=
"1.4+4U‘Q)
5(1),“):
#8117»
524}
Ll-uq/:—-6q/f¢l
Again,
since
Debbie
is
a
rational
agent,
she’ll
choose
movie
when
her
expected
pay
off
from
that
is
greater
than
her
expected
pay
off
from
choosing
mini
golf.
((+12
M
-Gq/fl—l
71:60.3
Wfizfg
)p:'
p30
And
Debbie
will
choose
mini
golf
when
q
3%
7-”;
I
If
we
graph
the
best
responses:
basncally
h’Lc
pam
of
W
/L—ycu
Moose
what,
a
grapnoF
flraiegie/s
1
(
1/4
((1.
I;
0
Lin/01194.1:
When
p=0,
q
_<
2—
and
when
p
=
1,
q
_>
2-,
