Economics 109 Midterm Examination
Prof. Watson, Fall 2001
You have one hour and twenty minutes to complete this examination. You may
not
use your
notes or any books during the examination. Write your answers in the spaces provided on the
answer sheet that has been distributed separately. When you have
f
nished the examination,
submit your answer sheet.
Basic Questions
1.
Write your name in the designated space on the answer sheet.
2.
Consider the following strategic setting. There are three people: Amy, Bart, and Chris. Amy
and Bart each have two cards, one of which has “K” (for King) written on it and the other has
“Q” (for Queen) written on it. That is, Amy and Bart both have a King and a Queen.
At the beginning of the game, Amy must place one of her cards (either K or Q) into an envelope
and then give the envelop to Bart. Bart sees the card that Amy placed into the envelop and then
he places one of his cards (either K or Q) into the envelop as well. The envelop is then given to
Chris, who has
not
observed the moves of Amy and Bart. Chris opens the envelope. Therefore,
Chris sees the two cards inside, but she does not know which card was placed there by Amy and
wh
ichcardwasdepos
itedbyBart
.
After observing the contents of the envelope, Chris selects “yes” (Y) or “no” (N). If Chris
selects Y and Amy had put a King in the envelop, then Amy and Bart each get a payo
f
o
f0and
Chris gets 1. If Chris selects N and Amy had put a Queen in the envelop then, again, Amy and
Bart each get a payo
f
of 0 and Chris gets 1. In all other outcomes, Amy and Bart each get a
payo
f
o
f1andChr
isgets0
.
Represent this game in the extensive form (draw the game tree).
3.
Convert the following extensive form game into the normal form (draw and label the matrix):
4.
For each of the normal form games pictured on your answer sheet,
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5.
Consider a game between two
f
rms who simultaneously and independently select advertising
levels. Let
a
1
denote
f
rm 1’s advertising level and let
a
2
denote
f
rm 2’s advertising level. Assume
that the advertising levels are between 0 and 24. That is,
S
1
=[0
,
24] and
S
2
=[0
,
24]. Firm 1’s
payo
f
(pro
f
t) is
u
1
(
a
1
,a
2
)=20
a
1
+
a
1
a
2
−
a
2
1
and Firm 2’s payo
f
is
u
2
(
a
1
,a
2
)=20
a
2
+
a
1
a
2
−
a
2
2
.
(a) Calculate and graph the
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 Fall '08
 WATSON
 Economics, Game Theory, ........., Nash

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