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Practicequestions2  1.InaNashequilibrium: a.Allplayersadopttheirbeststrategies,giventhestrategiesadoptedbyallotherplayers. b.Thestrategychosenbyeachplayermustbeadominantstrategy. c.Surplusisnevermaximised,eventhougheachplayeradoptstheirbeststrategygiventhe strategiesadoptedbyallotherplayers. d.Alloftheabove. e.aandbarecorrect.   2.ConsiderthefollowinggameinvolvingSonyandNintendo.Eachhastodecideonanewplatform foritsnewgenerationofgames.Inthenormal‐formgamebelow,thefirstpayoffisforSonyandthe secondisforNintendo.WhatisSony’spreferredoutcome?WhatisNintendo’spreferredoutcome? WhataretheNashequilibriumorequilibriaofthegame?Explainyouranswer.  

Nintendo

 Platform 1



Platform 2

  

Platform 1

(20, 20)

(5, 7)

Platform 2

(8, 2)

(30, 30)

Sony

     3.HPandEPSONarebothconsideringsimultaneouslywhethertouseaNEWtechnologyintheir nextprinter,orwhethertocontinueusingtheOLDtechnology.IftheybothoptforNEW,thepayoffs are2toeachfirm.IfbothfirmsinsteadoptfortheOLDtechnology,thepayoffsare1toeachfirm.If HPchoosesNEWandEPSONoptsforOLD,thepayoffsare20toHPand4forEPSON.Finally,ifHP optsforOLDandEPSONchoosesNEWthepayoffsare7toHPand5toEPSON.WhatistheNash equilibrium(orequilibria)ofthegame?(ThefirststrategyisHP’s,thesecondisthestrategyof EPSON.)

a.(OLD,NEW) b.(NEW,OLD) c.(OLD,NEW)and(NEW,OLD) d.(NEW,NEW)and(OLD,OLD) e.NoneoftheaboveareNashequilibriaofthegame.  4.Twofirmsplaythefollowinggameconcerningtheadoptionofanewtechnology,ornot.  Firm2

Old

Old

New

0,0

0,0

0,0

50,50

Firm1 New

  WhataretheNashequilibria?Relateyouanswertofirmsbeingtrappedina‘bad’outcome.  5.Explainwhyalldominant‐strategyequilibriaarealsoNashequilibria,butnotallNashequilibria aredominant‐strategyequilibria.Illustrateyouranswerusingexamples.    6.AppleandSamsungareconsideringlaunchinganewversionoftheirrespectivehandsets.The choicesforeachfirmaretoEnterortoWait.Thetwofirmsmakethesechoicessimultaneously.The payoffsareasfollows.IfbothfirmschoosetoEnter,thepayoffis9toeachfirm.Ifbothfirmschoose toWait,thepayoffsare7toAppleand5toSamsung.IfAppledecidestoWaitandSamsungEnters, thepayoffsare8toAppleand4toSamsung.Finally,ifAppleEntersandSamsungWaits,thepayoffs are6and7toAppleandSamsung,respectively.WhataretheNashequilibriaofthegame? a.(Enter,Enter),wherethefirststrategyisthestrategyofSamsungandsecondisApple’s. b.(Enter,Wait)and(Wait,Enter) c.(Enter,Enter)and(Wait,Wait)

d.(Wait,Wait) e.(Enter,Wait)  7.OnapeacefulSundayafternoon,MalcolmandAnguseachsimultaneouslydecidewhethertogo toGreystanes(G)orRootyHill(RH).IfbothchoosetogotoGreystanestheyget5each.Ifbothgoto RootyHilltheyeachgetapayoffof1.IfMalcolmchoosesGreystanesandAngusRootyHillthe payoffsare(3,2)toMalcolmandAngus,respectively.IfMalcolmgoestoRootyHillandAngus Greystanes,thepayoffsare0toeachparty.Whatis/aretheNashequilibriainthisgame?Isthisalso adominantstrategyequilibrium?  8.ConsiderthefollowinggameinwhichSallycanplayTorBandJohnchoosesbetweenLorR.Each playermakestheirchoicesimultaneously.IfSallychoosesTandJohnchoosesL,Sallygetsapayoffof 5andJohnhasapayoffof4.IfSallyplaysTandJohnR,Sally’spayoffis8andJohngets3.IfSally ChoosesBandJohnL,thepayoffsare3toSallyand2toJohn.Finally,ifSallychoosesBandJohnR, thepayoffsare7toSallyand0toJohn.Whichstatementistrue?  a.TheNashequilibriumis(B,R);thisisaprisoners’dilemma b.TheNashequilibriumis(T,R);thisisaprisoners’dilemma c.TheNashequilibriumis(T,R);thisisnotdominantstrategyequilibrium d.TheNashequilibriumis(T,L);thisisadominantstrategyequilibrium e.Noneoftheabove  9.CoopersandBoagsaretwobrewersthatchoosetolaunchasummerale(SA)ornot(NOT).The payoffsareasfollows:ifbothbrewersoptforSABoagsgets8andCoopersgetsapayoffof5;ifboth firmsoptforNOT,Boagsgets4andCoopersgets7;ifBoagschoosesSAandCoopersNOT,the payoffsare5toBoagsand3toCoopers;andifBoagsoptsforNOTandCoopersforSAthepayoffs are6toeachfirm,respectively.Drawthenormalformofthegame.WhatistheNashequilibrium?   10.DellandHPmustbothsimultaneouslypricesfortheirnewlaptops.Theycanbotheitherchoose tosetaLoworHighprice.Thepayoffsareasfollows.IfbothfirmssetaLowprice,Dellgets5andHP  6.IfbothfirmssetaHighprice,thepayoffsare7toDelland8toHP.IfDellsetsaHighpriceandHP choosesLow,thepayoffsare3toDelland10toHP.IfDellsetsaLowpriceandHPoptsforHigh,the payoffsare9toDelland1toH.WhatistheNashequilibrium? a.(Low,High),wherethefirststrategyisDell’sandthesecondHP’s. b.(High,Low),wherethefirststrategyisDell’sandthesecondHP’s. c.(High,High),wherethefirststrategyisDell’sandthesecondHP’s.

d.(Low,Low),wherethefirststrategyisDell’sandthesecondHP’s e.Noneoftheabove...