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Unformatted text preview: Eeo 122: Game Theory
Summer Session II, lllﬂll
Professor David Lang Exam [
20 August 2W3 NAME: k E I I. Multiple Choice Qaestiens
For each ofthefot'lowlng. cheese the best tamer. Each question will be worth 3 points. Be sure to write the sewers in the boxes provided to the fell areas}:
question. For questions 13, consider a game between a husband and a wif e in which the couple will choose to go to a baseball game or to the opera. The payoffs are listed in the table below, where
the husband’s payoffs are listed ﬁrst. 1. Identity the pure strategy equilibrium:
a. e” Husband plays Baseball; Wife plays Baseball b. Husband plays Baseball: Wife plays Opera
E es" Husband plays ﬂpera; Wife plays Opera ii {El and [bl
(£3 {at and be
2. In a mixed strategy equilibrium w “FE: FUE : t Uh
a. Husband plays Baseball with probability lift P. m ; " ' ‘5 _ I
b. Husband plays Baseball with probability iii 1:) H Pap (“l P)
e. liasbaati plays Baseball with probability in {D F ~
Husband plays opera with probability is P —_~ 1/3 e. None of the above 3. In a mixed strategy equilibrium, .— a. Wife plays aassbaii with probability lt'ﬁ HuskMal ' 5: Up = E Up
b. Wife plays Baseball with probability “3 _ _ e. Wife plays Baseball with probability is 21 013  ' ‘11 + U a a)
ti Wife plays IIlpera with probability EH (5 1 1 @ None of the above It as 2/5 For questions 45. Use the following table, in which Bush's payoffs are listed ﬁrst, New Mexico Iowa
63: “In? Eli31m
.er
 4. Which of the following snatcgies represent a Nash Equilibrium?
:1. Ohio, Colorado b. Florida, Colorado
c. Pennsylvania, Colorado
{at} Pennsylvania, New Mexico c. None of the above 5. Which of the strategies remain after using iterated elimination of dominated strategies?
:1. Ghio, Colorado F: .
E Fluﬁdlcﬂlumdﬂ g Chib‘iﬂ Aﬂoﬁl‘lﬁj’ﬂ HaulIAN“
ﬁ o c. PennsyltAania, Colorado @J ? “in $9me In}: Lyn11
Pennsylvania. Newbiesico emu; Jwﬁm Hal; _.H A 115 E} 
n. Home of the above [ED Um yMQmm 593w“. Lm’ NW“ For questions 153: Suppose that in the US, society can be represented as two people — yourself
and an average person named “Either”. Each of you drives a car and can choose to put a
pollution control device on your car, at a cost of$1ﬂﬂ to the car owner. which would provide a
beneﬁt in the form of cleaner air that is worth STD to each person. Thus, each of you has 2 possible actions — Install or Not Install. Suppose that this scenario is a simultaneous, onetime
garner partially represented as the table below: m Not Install as a. When each person plays install1 what is the net beneﬁt in dollars to you? a. 100 if: 33 70+70 ~lco: HO
a. o
e. do T. When you ehoose blot install but Other ehooses Install, what is the net beneﬁt in dollars to you?
a. [ﬁt]
(t? to
d. t}
e. 3tl 3. Listing your strategy ﬁrst, determine the Nash equilibrium {equilibria) of this ante:
a. Install, Install 3: h. Net Install. Install
:2. Install, Not Install
Not Install, Not Install : wt and to 9. Suppose that you can model a simultaneous, Zerosum game between 2 players by using a
standard game tablefmatris. Then, any purestrategy Nash equilibrium outcome must he the number in that column of the mania and the number in that row
of the matrix.
a. smallest: largest
{ED largest; smallest
e. smallest; smallest
d. largest: largest
e. {a} or {b} Fer questions ltll 1, use the following information: The sales for Firm t and Firm 2 depend on
both its own priee and the competing ﬁtm's price, and can be represented as 01:2]  'i' Q; = 27  {1.7591 + DJ!" Where P. is the price charged by Firm 1, Q; are the sales by Firm 1, and P1 and Q1 are deﬁned
similarly for Finn 2. The eost of produetion is constant at 6. “1 Given the priee from Firm 2, what is the best response ftmetion for Firm i'?
l P=tlill4jp}+ I? t? tests: TITCiQCE‘O'TSR+03?!) a. P1=(2JBJP2+21 311,;
E Noneot'theaboye “5:7; :: Zl~0.75ﬁ+8.5P1—ﬂ,'7§fl+t[Egﬁ
LSQ : 2‘35 +03% PF igP, +17 1]. Listing the price efFirrn 1 ﬁrst, determine the Nash Equilibrium prices. a. 9. it]
1}. “3,9 l _
(a. 2323'] BIC?! + *" d. 3H. 32 . »
e. 32,32 (Lia after adswars} i Mi Flap1c) twee?? FEEdeﬁieh 12. Pepsi and Cake play a game where they must decide whether te advertise er net. When
the game is played simultaneeusly, it can he represented in the table helew with Ceite's
paveth listed ﬁrst. _E'_
Advertise Net Advertise
[ﬁlmﬁli t nae If the game is really.r played sequentially, which ef the fellewing is true?
Cake has a ﬁrst mever advantage if it moves ﬁrst Pepsi has a ﬁrst mever advantage if it meves ﬁrst
Celte has a seeend mever advantage ifit nteves sewed a.
h.
e.
6.3;] {a} and {h} Jﬁuarddﬁrii e‘t‘t‘tcﬁi'l} deratmdt‘l— "Fur _‘ Nene ef the aheve .
ardar 1H,: Flap M15 Mr hm Fer questiens 13‘ 14., use the tellewing interrrtatien: pizzeria 1 and pizzeria 2 play a simtdtaneeus
game in ﬁnish they decide what prices to eharge fer their pizzas. The game is represented in the
table heiew with the paveft‘s ef pizzeria 1 listed ﬁrst. —_
__ menstrual
Pizzeria l “SEEM 13. Listing the strategy ef pizzeria 1 ﬁrst, determine the pure strategyr Nash equilibrium.
High, High 3. h. Meditun. Medium
C (E) Lew. Lew d. Medium, High E3. Nene ef the aheve 14. Listing the strategy of pizzeria 1 first, determine the mixed strategy equilibrium in order
of the probability of playing Low, the probability of playing Medium, and the probability
of playing High. a. b.
a: (.525 15. Compare the following two games {13, 1!}, LG}; (US, US, U3]
[HI4, 132, “4): [ii1, “2. U4]
(“3, 1E3, 1H}; UM, U2, 1M}
[HEEL 1325).;(13'5, 2193,15}
None oftbeaboye “Higgit” 5+Fia‘H7‘ domt'aarimi
by “Plasmas”! gym Fio‘fﬁﬁ Fﬂhbiirl‘ixf
Ere—Fe? on “ﬂap,” Which of the following is true in mixed strategy equilibrium? Castor’s probability of playing W is higher in Game 1 relative to in Game 2
Castor’s probability of playing W is lower in Game 1 relative to in Game 2
Pollux's probability of playing "'1' is higher in Game 1 relative to in Game 2
(a) and [C]
(bl and {Cl ﬁiiﬁ‘mlﬁ {is m'i’ gn _A£L'+{ﬂr rial {:ﬁLﬁ‘i'ﬂ't'xé a“? WeJrqlnﬂ MK (ValeI5 ouci' assumes ﬂab}&nm 2)!
Con lkﬁw Leiarelating. Faibyls 5%? in. Fatwa +6 cooPirm Cr?) 15, “Ha. Mﬁwef.’ ’EUw army as we?) = P* litF) s P“: s; l]. FreeResponse Questions
Far sash afrhefaﬂawing. be sure m 531014: :21! war}: Parrim' credit may be awarded Fur quesﬁnns 1—4. rsfer m the following simultaneous game batman Bruce and Ralph. 1. Find any and all pure and mixed strategy squsihris in this slmulmnenus game. Discuss
yuur methodnlugy as you go. [20' points] ’2. F1
lm4wa asmgmsm 75.) F q" W Y 4
l 1:
i PC m EON :3)? “3? 3p + (FF): '2; + Hot?) 2. {In a single graph‘ shew the bust rcspnnse curves far bum Emma and Ralph and indicate
the Equilibria. [15 paints] 3. Suppoac the game were played put Sﬂqmnﬂﬂlly rather than simultanenusly. What wuuld
be the Suhgamt: Perfcct Equilibrium if Ralph plays ﬁrst?I How about iantce plays ﬁrst?
[Iii paints] 3:4 Eaipin 5m Qté‘i‘ 1 Raipitiﬁ‘ grum‘j M mag RalfLIE w A 9?? @ﬁﬁ‘mws (Waxy) 4. mushate — but DO NUT SDLVE — the original simtﬂtaneeus game in extensive ferm
ramer than in its payoff matrix. [I I] paints] Bruce.
A E e. D
_ ":_' __E@: “b “I *1 a "'4'" ,1 1%
3. ‘f E " 7’ 1 '3 ‘2 5 '3’ I
I G ‘5 I 1.11?
i 7' O ‘5 Li 6 3
HGTE'i PM [35me my be agaﬂmdv 7113 +ng ...
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This note was uploaded on 10/15/2009 for the course ECON 122 taught by Professor Bonanno,g during the Summer '08 term at UC Davis.
 Summer '08
 Bonanno,G

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