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**Unformatted text preview: **Economics 109 Midterm Exam
Prof. Buzard, Summer 201 1 You have 70 minutes to complete this examination. You may not use notes, calculators, or any books
during the examination. Write your answers, including all necessary derivations, and nothing more, in the spaces provided. You may use the scratch paper that has been distributed for all other work but will
not turn it in. To receive full credit, you must fully justify your answers (except where noted). Proper justiﬁcation may
consist of showing your work in attaining the answer, if your work reveals the reasoning that supports
your answer. Excess verbosity will not help your grade. Even if your answer is correct, citing incorrect
or irrelevant justiﬁcations will reduce your grade. If a question has multiple correct answers, you must
(at a minimum) identify all of them to receive full credit. Identifying incorrect answers will reduce your
grade even if you also identify all the correct answers. Partial credit may be given for correct reasoning
and explanation, even if your ﬁnal answer is incorrect, and is awarded at the discretion of the grader. 1. Consider the following normal form game,
\ a0 V CB a) Calculate BR2(91) Where 01= (1/3, 1/2. ,1/3).
F ua(eu)b)- #515l+3-©7%
(Adena) 2 4+2-s+-2-1=8/2 anaemia} Ma (9») P3 :é‘béswéri : t/g b) Name the Pareto efﬁcient strategy proﬁles (answers only) QX\ b) (E E\ C C F5
c) Determine the rationalizable set. A 1/3 dwwrxmai Nag 58+:Q Once {\de bu) W
E M 6M1 (Va moor/1m ijtimkep‘) (4‘07 1 370
H9, ”’1 a 373w utilgommmagwou M co
R {BCBX XSEE} d) Show analysis of best response on the normal form and report all pure strategy Nash equilibria. (3 mm (c F) e) Compute any mixed- -strategy equilibria of the game. If none exist, explain why. We Can Auljxlxak outta (\wa to Wu family): M‘(B)%\ : ui(()%> “a (PJEB:£&9(P)F
395*“1, : ”$9933 3P*“\>= PM“?
QCLJA _ Q, 3% thL 1 4-39 HSME : (<33 93B
5 z . ) '
‘4ng P \mﬁb 12/ We 6.: "of/2%) other you choose but you must clearly state your
choice). . . . i f: A 3, 0, 3
2. ConSIder the extensrve form game on the right. .<:
a) How many strategy proﬁles are there in this game? S R 0‘ 2. 1
(answer only) ‘ G
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b) Draw the normal form for this game (payoffs are in ,‘<:
the order B,G,F; you may list them in this order or any N I,” Q 0, 23 1
F ’ C 1 SM = Monitor Kids
"P a) Show an analysis of best response on the above normal form.
b) Name all pure strategy Nash equilibria of this game. SM = Chores
" P The/Fe am 013mg. 0) There is a mixed-strategy Nash equilibrium of the game in which B and S each play N with
probability 1/2. Clearly state an indifference condition that is sufﬁcient to determine the
probability with which their mother must monitor them in this equilibrium and solve it. ugCN)‘/1)P3 ‘ ”‘8 (ENE (Cl “30””) 5"“3G'79193
~- tsp wbvga-s help dank? + ngp) | .1 ”SI‘g‘P 339*23‘23? Co -2 3 l) ‘ a “WMWW_W-W~M
Emu—2 mm PmbWH mam/3kg 4. Consider the following normal form game.
31 = [0.11.52 = [0,1], 111691.32) = 351 _ ZSISZ _ 28%, andu2(51, S2) = 52 + 28182 " 23g _ Find the following.
a) The best response functions (the solution 1s interior so you can use calculus). 1* W 331 $599,933 my $9’W9S5- -3193
\ S s ‘ y- _ '1 \‘WDS 43*: 3&39' s —o - 1 ug:i§* $”**
b) The Nash equilibri W
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S1 L1 531 1‘1 8 L1$[-8 *3 .7 gs. 35‘s: A 911“"; 9f»; ‘iﬁé‘ﬁlﬁfa ’1 Nb-C5,g) ts c) The set of strategies tha 1 :31 3 .~-\_ 1 -
R‘ 3: $53. 3:1:{0‘1 \ g9. 4*33, S.eEO,1](subscripts forrounds,
~ - 3 3 S‘Vv’yo >L su erscrl tsfor la ers
g .1. -1 9 ‘+ ‘1 P ‘P R13 3’
1 ‘18-0 (f g‘Ll4JL-(13e R1: L :3. :Ce}?
3,} 1.19 ‘3 42— q 1 13.1 11,4
12 ,- 3. l- 5 L- 9 ‘L 5‘ ‘1 3 a 5 a
3'1-1'“? R1 m 1.1.3-5 R1: : 1 R2: - £3
3 $22,134.91 431112 2 ”J8 ‘518
1'4 5'71'8 d) From player 1’ 5 point of View, are S: ands, complements or substitutes? What about from player 2’s point of v1ew? :1: in mm C3 (1%“ £0“ $325
3 {NW (s9 Feed-11¢ (in °ES\
e) What IS the socially efﬁcie t outcome? How does it differ from your answer to part (b) and how does this relate to your answer to part (d)? 1 D 1
mm 11‘ +uQ : 33‘~Qg\33/33?+33+ 33133'3-39 = 35"93. 15.34932 S\)Sg ’
3U‘*M3 ‘
I5~S:O= :3 BMW - _ -1
33‘ LL‘ 731 11 x5; = \Hsawo A sg-q s
wwm Maw 6‘4).§'WW+FD)_ 1/1 5. Consider a two—player contractual setting in whimhe players must decidew
in a joint project. The underlying technology of the relationship 15 represented by the following normal form:
a) Draw the normal form for the induced game with limited veriﬁability. b) If veriﬁability is limited, can a contract achieve the efﬁcient outcome? Why or why not? Lo 7 8
ck) I W W (1’1)wa Wﬁmm5>b+o< Omol
61%‘201 (Wm dVngmmWedojt’ﬁuWhma ﬂaw 0) Would the players jointly be willing to pay to transform the setting to one of full veriﬁability of“? m
’U 8 their investment decisions? Why? If so, what 5 the maximum they would pay? g0 W
Mew w Wt£1ww 11101115131111 WEI/v3 14161 W
(:17 N) M113 wt) (ﬂuk‘ﬂ admruvd. Mum
mMwannwpa wmﬂiiwﬁw Om ﬁﬁaj {NINE ofﬂmijgww 130111212101 Mupﬁ ’L‘ 6. (Circle the correct answer) We can only perform the iterated dominance procedure if players have
a) common knowledge of rationality.
b) at least one dominated strategy.
0) common knowledge of the game. .aand c. 7. (Circle the correct answer) In a two-player game, if a strategy is undominated, it must be a best
response to how many of the opponents strategies?
a) all strategies.
b) at least half the strategies. @ at least one strategy.
d) no strategies. e) not enough information. 8. (True or false) A socially efﬁcient strategy proﬁle must also be Pareto efﬁcient. If true, explain
Why, based on the two deﬁnitions of efﬁciency. If false, give a counterexample; i.e., construct a
normal form game in which the claim is false. “Ynez %OL ntmmryrdﬁn ta mt PM ngtw jaw WW dill/Mom” HMX’MW “Wax/[WWW
Wm )LN GMCX‘S. {N ‘bm big SEW 1 (£1 eke/ﬂ
am 0:3 9. (Short answer) Why is it possible for the Nash equilibrium outcome to differ from the socially
efﬁcient outcome? /\)ru 31>me W Wt Wﬁm Pia/6%)
. Lnobu/LOL
tmﬁsmﬂm Mm (30.31%; {NM (,0 mm ﬁww
/W WW OWL “be hr WLmAPm‘
10. (Short answer Describe one strategic tensioriS-Aat contgzgwn elp remedy. ...

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