Ec101F09practiceExam1

Ec101F09practiceExam1 -...

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Unformatted text preview: Thisisthepracticeexam.Youhave1htosolveit.Theeasyquestionsare1,4,6,7,8,9,10,12,14; mediumare2,5,13;thedifficultonesare3,11.Goodluck! (Questions35)ItisduringtheColdWarandRussia(USSR)andAmerica(US)areplayingnuclear dtente.TheUSisconsideringattackingRussia.IftheUSdoesnotattack,thegameisover.If theUSdoesattack,Russiachooseswhethertoretaliate.Ifitdoes,theworldends.Ifitdoesn't theUSwins.Thegametreewithpayoffsisdisplayedbelow US US 0 USSR 0 1 1 2 2 Notattack Attack USSR Notretaliate Retaliate 3.WhichofthefollowingarethepurestrategyNashEquilibriainthisgame? a. (attack,notretaliate|attack),(notattack,retaliate|attack) b. (attack,retaliate|attack),(notattack,retaliate|attack) c. (attack,notretaliate|attack),(notattack,notretaliate|attack) d. (attack,notretaliate|attack) 4. WhichofthefollowingaretheSubgamePerfectNashEquilibriainthisgame? a. (attack,notretaliate|attack),(notattack,retaliate|attack) b. (attack,retaliate|attack),(notattack,retaliate|attack) c. (notattack,retaliate|attack) d. (attack,notretaliate|attack) 5. Nowimaginethegameisplayedsimultaneously,i.e.,allplayersmoveatonce.Whichof thefollowingisamixedstrategyequilibriuminthisgame?(Hint:itmayhelptodrawthe gameinnormalform...) a. (1/2attack+1/2notattack,1/2retaliate|attack+1/2notretaliate|attack) b. (attack,1/2retaliate|attack+1/2notretaliate|attack) c. (attack,1/3retaliate|attack+2/3notretaliate|attack) d. (notattack,1/3retaliate|attack+2/3notretaliate|attack) (Questions67).Alexhastwokids,BritneyandChris.BritneyandChriscleanedahouse togethertogetanallowanceof$90.BecauseAlexdoesnotknowwhoworkedharder,she suggeststhefollowingstodividethemoneybetweenthem.BritneyandChriswritedown howmucheachdeservestogetonapapersimultaneously,andgiveittoAlex.Theycan chooseamong$0,$30,$60,and$90.Alexwillgivetheamounteachwrotedownifthesum ofthenumberdoesnotexceed$90,butkidswillgetnothingifthesumexceeds$90. 6. WhicharetheParetooptimaloutcomesofthegamebetweenBritneyandChris? (a) (30,60),(60,30) (b) (0,0),(90,0),(0,90) (c) (0,90),(30,60),(60,30),(90,0) (d) (0,90),(30,60),(60,30),(90,0),(120,120) 7. HowmanypurestrategyNashequilibriaexistinthisgame? (a)0 (b)1 (c)2 (d)3 (e)4 8. Twoneighborswanttobuildawallbetweentheirhousesforprivacy.Thecostis100 whilethebenefitforeachis80.(thewallisapublicgood.)Neighbor1suggestsfirst aboutifshewanttosharethecost,andthenneighbor2willchooseheractionafter observingneighbor1'saction.Theywillbuildthewallaslongasatleastonepersonsays Yes,butonlytheonewhoansweredYeswillpaythecost.IfbothsayYes,theysharethe costevenly.Thefollowinggametreesummarizesthesituation. WhatisthecorrectdescriptionofsubgameperfectNashequilibriumofthisgame? (a) BothoftheneighborssayNo. (b) Neighbor2choosesthesameactionwithneighbor1inanycase,andneighbor1says Yes. (c) Neighbor1saysNo,andneighbor2choosestosayNoregardlessof1'sdecision. (d) Neighbor2takestheoppositeactiontoneighbor1inanycase,andneighbor1says Yes. (e) BothsayYes. 9. IsthesubgameperfectNashequilibriumoutcomeofthisgameParetooptimal? (a)Yes,becauseitmaximizesthesumofplayers'utilities. (b)Yes,becausenobodycandoanybetter. (c)No,becauseoneplayercanimprovehisutilitybymakingtheotheroneworse off. (d)No,becausetheycouldbothbemadebetteroff. 10.Supposetherearefouryears,andthediscountfactoris=0.5.Thepresentdiscounted valueofobtaining$2everyyearis (a)8;(b)6.5;(c)11/2;(d)23/3;(e)Noneoftheabove 11.Supposeplayer1andplayer2movesimultaneouslyinthegamebelow.Howmany Nashequilibria(considerbothpurestrategyNEandmixedstrategyNE)arethere? (A)3;(B)2;(C)1;(D)0;(E)Noneofabove (Player1istherowplayer,player2isthecolumnplayer.) A B 12.Thereare3firmsinamarketforashtrays.Theyeachhaveaproductioncostof$1/ashtray. Thereisoneconsumerinthismarket(abarowner)whoiswillingtobuythefirstashtrayfor $100,thesecondonefor$99,andsoonheiswillingtobuythe101stashtrayfor$0.Whichof thefollowingstatementsarecorrect(youmaychoosemorethanoneanswer)? (a)Ifthefirmscollude(forexample,whenthesituationisrepeated)thentheprice equalsthemonopolistprice 13.AsubgameperfectequilibriumisaNashequilibriumthat a.cannotpersistthroughseveralperiods. b.involvesonlycrediblethreats. c.consistsonlyofdominantstrategies. d.isunique. (b)Iftwofirmscompetebysettingpricesthenthepriceis$25 (c)Ifthethreefirmscompetebysettingpricesthepriceis$16.66 (d)Ifthethreefirmscompetebysettingpricesthepriceis$1 (e)Noneoftheabove. C 3,3 4,2 D 2,1 3,4 14.InthePrisoner'sdilemma, Confess NotConfess Confess 1,1 0,3 NotConfess 3,0 2,2 (Notconfess,Notconfess)canbedescribedas a.nonParetooptimalandunstable. b.Paretooptimalandunstable. c.nonParetooptimalandstable. d.Paretooptimalandstable. ...
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This note was uploaded on 12/09/2009 for the course ECON 101 taught by Professor Buddin during the Fall '08 term at UCLA.

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