ps8s Duopolies

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For
 ‐10
,
‐10
 0
,
‐10
 Congressman
Beans
 Vote
Against
 ‐10
,
0
 20
,
20
 
 b. What
is
the
Nash
equilibrium
to
this
game?
 The
Nash
equilibrium
is
for
both
Congressmen
to
vote
against
the
 proposed
law.
 
 
 1
 c. Now
assume
that
each
Congressman
gets
a
further
utility
of
Ci
(that
is,
CF
for
 Frank
and
CB
for
Beans)
for
going
along
with
the
party
leadership.

CF
and
CB
 will
be
delivered
to
each
Congressman
in
the
form
of
money
for
a
reelection
 campaign,
should
they
vote
for
the
law.

Re‐write
the
normal‐form
game
with
 these
C’s
included.
 
 Congressman
Frank
 Vote
For
 Vote
Against
 Vote
For
 ‐10
+
CF
,
‐10
+
CB
 0
,
‐10
+
CB
 Congressman
Beans
 Vote
Against
 ‐10
+
CF
,
0
 20
,
20
 
 d. Derive
an
expression
for
each
C
that
describes
the
minimum
utility
that
the
 party
leadership
has
to
offer
to
get
Frank
and
Beans
to
vote
for
the
law.

In
 other
words,
the
party
leader
wants
to
set
CF
and
CB
such
that
the
Nash
 equilibrium
is
for
each
Congressman
to
vote
for
the
law.
 There
were
two
ways
to
approach
this
problem.
 
 1.

Dominant
strategy:
find
the
solution
where
each
congressman
will
 vote
for
...
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