01-05 mid sol.

01-05 mid sol. - Economics 109 Midterm Examination Answer...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 109 Midterm Examination Answer Sheet, Fall 2001, Prof. Watson 1.Y0urname ........................................................................................... .. 50/446045 ‘4 N l,l,0 2. Extensive form diagram: K r ’ ) [1 1,0 N 0,0,: 6 ‘I 62 Y 7 l, 1,0 Cg ,‘o,l 3. Normal formmatnx: {\L‘X ,A‘ , X Y 1 A0 A t o L- “WNW!!! W IMEME :0 ¢ ' \‘v 4. R= R= R: 5 (a) am; ‘_ :2 ram ~ 20 43-240 -0 I i l . BR1(‘12)= loll-Ea?— BR2(al)= /0 +3’ 0" (graph on other side) 5. (continued) (b) UDl= {JO/1L1 Sakhalin 4D 90/“ aesexaamfsmm), (c) Io+—LL(/o+¢;a.)=a‘ 2) /0+5+%Muwi.s 6:0 = 3a. at: 20 = a1 Nash a1*= ZO (12*: L0 (d) Is the Nash profile efficient? Circle one: YES “LG/0,2101): 4-00 god" Mifl. (164' (A; (14/7/43 7, 48*0 I w Sb, wk para M Amp, 6,7,4 my; (24%) (e) Efficient, non-rationalizable strategy? Circle one: Y1}? NO (14114) M My?! (2‘ 6. x = y = 7. Enough information? Circle one: @ NO ’5} mats-1L 1M W M,CA, 0-7,) = 43 so +- O_;(Y) ’0 4’ ‘O : ‘f' --—-> Ifyes,02(X)= %_ 8. If f/u part—bf 07, mag, WW 53;;11‘5‘0 IS muck 7" J] (rod/ch)? '7. “19+” in ‘f/Q Submit/S} 77% 101st [91 fire h ~4nvlzzo Suburbs W’va mf 13K facsfres 4 e ‘ (n+z)®‘a=o m*=‘f' If m Maw TM an Kama/J47 mm 50mm“ 14m M “MA/4f , Mtg/we §nvml+sv n*=é Profits: 4'4 aaLC/L Economics 109 Midterm Examination Answer Sheet, Fall 2002, Prof. Watson 1.Yourname ................................................................................... .. SO/bt‘i'lo'hf Version: 2. Extensive form diagram: L . l,o,o >< &1<Z’O'Z 1 g \/ z 1 0,0,0 : x I f ‘ 70,0,0 Y 5‘ 0,2,2 ‘/ 0,1,0 3. Normal form matrix: 4. R: R: R: 5. (a) Payoff functions: - “10): (’2 ' 3-171) ?v " 2%. u1(q1,q2)= (I1- 3,, 31) g,- 23.) mg) = (/2- g; 397.; +5.2 u2(q1,q2)= (/2— z, — 5;) 31-4542 5. (continued) (b) 92 ‘53:“: l'O”Z‘3~'—~Z,LEO A I BR1(q2)= b _ z Z»L BR2(q,)= 4 - 247., (3%) is Wail/ML => no [mfg/iqu fin/x, I ,Q 90,“:ch 6. (4;) .‘s ermm ’7 7(34 ( , . W x=4 \leBKz J- 4) =7 W W M “LOA'IY)=32 “lg/(02):?)(51't‘2 21L 7. l , 5- C(O'WImal—CS |,3, 7, Dual 6] (rm 190M w I. 3,7, W’ q ave Purim/{J (“4+ Mimi g. fim’mmalcs l/4( g, M R= {(5,5)} [\1 8. X (a) The game matrlx forn=2: \I Z, O ? O, l (b) Nash equilibrium forn =2? Circle one: YES @ (c) Nash equilibrium forn= 11? Circle one: @ NO Luck PM 61 cm {In wl—icL ‘Huz Flair/V1, .r i ' ‘ +14 saw '5 W pm WM IfYES,number0f “ a ’9 7° Nash equilibria: h mfdm- Y=2x=3§ a no N F I I a 213 3.2 ’ 2:23 (®)‘(Z)-z4ezdo : 6:: flisan {Tl 6fme/M‘Z‘,3SMX,MZSMY Economics 109 Midterm Examination Answer Sheet, Fall 2003, Prof. Watson 1.Yourname ................................................................................... .. SO/VHLWMS 2. Extensive form diagram: 1 X 7’lo/o X 74% 210/2 ‘ l \l l 7,. i ‘I ' 0,0,0 Y L O,L,Z V 0,1,0 3. (a) BR2(p.1)= {gig} (b)Circleone: 0 19$ 4 5 6 7 8 9 (0) Circle one: Yes (d) Circle one: (9 1 2 3 4 5 6 7 8 9 (e)R= {v.%]x{€«gi 4. Condition on x: @ Supporting logic: Ned: u.(z,13 > 14.0.!) 53> 30> 40+% E 5‘0, w»: M Mm) > um») ® 40+%>>< “((2,3) > 04.03) (=3 +rwz Z ' (Adam!) > (1.03)) é?) W 5. The probability that player 1 selects X is: {J— 6 We N“, MX f} f) /-9 my §Jo+Z(/'p)= O-p+3(',-,f) Mica/11 ($134”; g—QLZ’Z) / 422: [0+ $2 3‘31: 6/3231 r iii: 5—“é(/z)= ‘1' Nash equilibrium: q‘* = 4- The rationalizablesetR= {C0, 0/ 0, 0, 0, 0/ O, 0/ 0/0)} Your reasoning: N511 flu} a; u,0=(a—10«—I)s,o M f/M a—// < OW 0%wa MIG-W/p/aym/oMms'/%/G (AW/W Siva/213?, O, ’ MM #44, bvf lz/mw a {2sz J64 427‘ Mm‘ 9 (% Maw/don MW [75ng MW/O), Tim/ 234567Total 1. 2. 3. 4. 5. 6. Economics 109 Midterm Examination Answer Sheet, Fall 2004, Prof. Watson Your name ................................................................................... .. 3 0/01 +7 How many strategies does player 2 have (circle one): 1 2 3 Q3 5 6 7 8 10 16 64 256 Is M dominated? Circle one: @ NO If so, name a strategy that dominates it: l ’32; I 0) W is, % K, % L If not, name a belief to which M is a best response: The set of rationalizable strategies: R = {C . B} )6 { C, B Y (a) The NaSh CCIUilibria arei (W119) 0"! (Y! c) (b) The efficient ones are: (‘11 c) (c) BR1(|_L2) = { wl x] (d) X weakly congruent? Circle one: YES (a) Best-response functions 73%: [0+ Sf'zsi 5‘0 =7 8;: 5+ésJ- BR1(52)= gvl'é‘SZ BR2(51)= 54' “£3, (b) Nash equilibrium §u£§ln4ule M Fw- S": 5+éSL 51: 5+é(5’+és¢) sl*-" IO 45;: 20 +10 + S; 33;: 30, sl=lol s,:/o 52*_ ’0 (c) Is the Nash equilibrium efficient? Circle one: YES Explain: buffalo) : ~100 Uo‘fi HM (0/0) [4— W «:4. (/o,/o>/ “(MW (15(0/0) = O 7. Calculate the set of rationalizable strategy profiles. &u, _ W _ ax =Zy~2x=09xly aul : ’2 50 = 32X 37 ‘fx 7 7 Y EXafzf M 74d MLLM )<>4—) 7=Zx~ [’4 MW& (y mus+b¢ s 8); m (144)—ng OFWV=8‘ So, BRO/3:7 BRAXP ix 3? X54 {3 115 x>‘l' T+emld ClOW(;mmc,L ; l. S‘lYn-RfiM/bp 4’ W ({VWI;AW‘6YF/fi Z, (W WW 25’ 5'2 Wow“, Ins/ATM awfflw 5;. 4Lwa W 4- M478") 2. W P/wflq L} swag?» La—o/aw 4’ an: C(d'W/zmw, LA 3. 7m fl/aym z£~ 9m Law 3’ a g“? 7:37 is mfukaf/M ,L. W! ml? x=87 I; ra-HJMme f/‘Lafl/r/ M may, aannannnma nuanaannmu IIIIIIII- 1. Yourname ................................................................................... .. /W+'ZWI 2. Extensive form diagram: y / Economics 109 Midterm Examination Answer Sheet, Fall 2005, Prof. Watson 1 / ‘7 1 ’ 0,0,! I A- N \ <1! \ \N >110 SI \\ I C)IOI’ k 1 L IN “'10 l / N ><IIIIU 3 N 0,0,I 3. Normal form matrix: b éminau by, P I~P an c} Mum peg”). y a any «use; R: WW} R= Z“{C}’<{Yt%l 5. Circle one: NO Explanation: Fm {y‘fitfjnisfztg‘f 1"» LA WE? (Lt/MW] M W Sfé “ll/uh fife EKrC/A’ZL S; ee-Ezgum M 576’; e—EKZx-Q/ulg/ W JAM/ti; elsfsf‘tcr} ami/Awfl‘fe AZS‘I‘l/cf‘k. m is W 6W #1 W151 Wk, am 52‘, M; M.{ M {355, 42h», Mod/vac Na»! 15” M4 Mm”, 6. (a) Nash equilibria: szx (,C, Y )1 M (C13) (b) Efficient Nash equilibria: CC I E") (c) 3121012) = (b, a} 7. (Adz): (34‘271“%)21—4’3/ “1(q1’q2)= (Z4 ’ Zg'l—Zzb>37~4g‘ A?“ = 24~4g_l—Z;Z~4 Eo BR1(q2)= 53%;; t Z: :7 4'3_I=ZO—Zgz ,. UD1= [0/5] I sat 3‘ = 5—2 z 5 Z‘ 8. jmdt#Wm Wei/19%: % W M W YWifl /M.;(/ q OfyPtzoiz [5mm d“ chooses XJ #— Z- PrvLLno an em W x] = bow—i . wt m1 Lzz-rx“ =7 é:=x““ __L\ <>7 o< = Ci)“ ~_\__ H73)“ 9. (a) Description of rationalizable strategies: A’H 0+ #4 ar‘c Via-MM . I223. Ii; 7c Sela/‘93 6—, S/Ac 24/13 i. 3?? 5/44 P? s/‘Lc yfi Zia/lit:— G. % a u w " MM 3.x - ( a ~ ~ a}, F_ Is there a symmetric Nash equilibrium? Circle one: @S/ NO If so, description: .. , - - WWMWNaY‘L%./mmx WM (b) Description of rationalizable strategies: “ 7/— ?fififlj‘ ’ il'PW Fly/{Ad'— ZM—ZK. NW W risi. Tat—1L (5 ram! {77' 5f must fit 015 (#4 [MW i7 dwosc F aim VZGHCL +091 M3 x “at ZW—Zx<t MN #54 m 6—dowikut1u/F.71u4(&eM {'5 x> W—I‘i_ m meanJWCk {’44 M71 FM) ma yT,‘ M4. dcmmdb?‘2L_ .. f. . ._A”F+MWVW3(WWWG'UW0%%L (c)Descr1ptlono rationalizable strategiewf ~ NW 5 W W907 m Mm dcsmgfiéigm ‘1 . - » a741,) smWaZ/AWWW, fi/r E’Ma’w ...
View Full Document

This note was uploaded on 02/11/2009 for the course ECON ECON 109 taught by Professor Watson during the Fall '08 term at UCSD.

Page1 / 10

01-05 mid sol. - Economics 109 Midterm Examination Answer...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online