Solutions to Chapter 15 Exercises
SOLVED EXERCISES
S1.
(a)
In the purethreat case, the union’s expected payoff is 50(1 –
p
) – 100
p
= 50 – 150
p
. The
union’s expected payoff goes to zero for
p
= 1/3 and is negative for
p
> 1/3. Thus the pure threat is too big
from the union’s perspective. There may be scope for brinkmanship in this case.
(b)
Diagram is below.
(c)
The union sets up a situation in which there is some risk, with probability
q,
that the
company’s defiance will lead to a damaging strike.
(d)
If brinkmanship is used, a profitable company is better off conceding to the union
demands if 50 > – 100
q
+ 100(1 –
q
), or
q
> 1/4. This is the effectiveness condition. With brinkmanship,
the union’s expected payoff is 50(1 –
p
) – 100
qp
. Brinkmanship is acceptable to the union if this payoff is
positive, or if
q
< (1/2)(1 –
p
)/
p
. This is the acceptability condition. The union will use the pure threat (
q
=
1) for
p
< 1/3. For values of
p
between 1/3 and 2/3, the union can successfully use brinkmanship. For
values of
p
> 2/3, the union uses no threat at all.
S2.
(a)
This scene makes the escalation of risk inherent in brinkmanship explicit. If both players
continue on their set paths—the army officer in raising the helicopter and the gunman in refusing to
provide information—they raise the risk that the gunman dies on the next push out of the helicopter. Then
neither side gets what it wants. As in other examples of brinkmanship, each is feeling the other out for his
level of risk tolerance.
(b)
In this film, the FBI agent makes explicit a probabilistic threat that spending any of the
found ransom money may lead to Hank’s arrest. Given this information, Hank must determine his own
Solutions to Chapter 15 Solved Exercises
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View Full Documentwillingness to spend the money, knowing that increases in spending increase the risk that his crime will
be discovered. Although the threat is presumably acceptable to the FBI, it remains to be seen whether it
will be effective in deterring Hank’s spending the money.
S3.
The examples described in this exercise (and in Exercises
S4
and
S5
) do not have unique,
mathematically correct answers; their purpose is to get students thinking about realworld issues using game
theoretic perspectives. Each is so complex and rich in factual detail that setting the stage completely would
take several pages. Therefore we offer only the basic facts of each, with some suggestions for your further
analysis. Each topic can develop in many different directions and can benefit from factual information or
experience that you may be able to contribute.
(a)
T
HE
U
RUGUAY
R
OUND
OF
T
RADE
N
EGOTIATIONS
General trade liberalization brings overall economic benefits to all countries. But within each
country there are gainers and losers; people whose incomes are tied to the export sectors gain as more and
bigger markets open up for them, and those whose incomes are tied to the import sectors lose as they
must face stiffer competition from other countries’ products. Thus almost no country can present a clear
and unified front for trade liberalization; each must resolve its internal conflict over the gains and losses.
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 Spring '08
 Charness,G
 Republic of China

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