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

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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 ...
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