GameTheoryTheProblemofStrategicBehaviorWhatIdodependsonwhathedoesand…ViceversaWhatVonNeumannWasTryingtoDoAgeneralsolutiontostrategicbehaviorhoweachplayershouldplayAndwillplay,beingrationalAndassumingtheotherplayersareAsolutionthatwouldcoverEconomicsPoliticsforeignpolicypoker,…ButwhatheactuallydidwasTwoPlayerFixedSumGameFixedSum:WhathelpsmehurtsyouStrategy:AfulldescriptionofwhatIwilldoinanysituationIncluding“flipacoin,ifheadsdoA,iftailsdoB”Consider”scissorspaperstone”wherebeingpredictablelosesSolutionconcept:ApairofstrategiessuchthateachisbestagainsttheotherDoesnotincludethebenefitofstealingcandyfrombabiesVonNeumanndemonstratedhowtofindthesolutionforanysuchgameProvided,ofcourse,thatyouhaveunlimitedcomputingpowertodoitwithScissorsPaperStoneThesolution:Rolladieoutofsightofyouropponent1-2scissors,3-4paper,5-6stoneWhateveryourstrategy,Iwin1/3rd,lose1/3rd,tie1/3rdAveragepayoutzeroIfyoufollowthesamestrategy,whateverIdogetsthesameaveragepayoutSoaVonNeumannsolutionAnditdoesnotmatterifyouknowmystrategyAslongasyoucan’tseethedieAndsimilarlyifIknowyoursWhichistrueingeneralofaVNsolutionManyPlayerNotFixedSumVNSolutionconcept:Asetofoutcomes(whogetswhat)SuchthatanyoutcomenotinthesetisdominatedbyoneinthesetWhereoneoutcomeisdominatedbyanotherifThepeoplewhopreferit(getmoreinit)Aresufficient,workingtogether,togetitTheremaybemanydifferentsolutionsEachcontainingmanyoutcomesSoa“solution”inaveryweaksenseThreePlayerMajorityVote:Allocating$1Solution:(.5,.5,0),(0,.5,.5)(.5,0,.5)ConsideranyotherallocationofthedollarThereisalwaysoneofthesethattwopeoplepreferSoeveryotherallocationisdominatedbyoneoftheseSolution:(.1,x,.9-x)forallvaluesof0>x>.9Alsoasolution,butonethatincludesAninfinitenumberofallocationsTrytofindanallocationthatisn’tdominatedbyonememberofeitherthefirstorthesecondsetofallocationsBilateralMonopolySellinganapplePuttingachildtobedADoomsdayMachineTheHumanDoomsdayMachineDefertomeorIbeatyouupAfighthurtsbothofus,but…Youdon’twanttobehurt,soIdon’thavetobeatyouupHawk/DovegameEquilibriumnumberofhawksWhycrimesofpassioncanbedeterredEconomicsofViceandVirtueEconomicsofvice:ThebullystrategyEconomicsofvirtueWhyaretherepeoplewhowon’tstealEveniftheyaresurenobodyislooking?Whatifyourutilityfunctionwaswrittenonyourforehead?ThecosttomeofhiringsomeonewhowillstealfrommeIsgreaterthanthebenefittohimofstealingfrommeSoIwillpaythehonestmanmorethanenoughmoresothathonestypaysYourutilityfunctioniswrittenonyourforeheadWithafuzzypencilSohonestypaysUnlessyouareaverytalentedconmanImplicationoftheeconomicsThebullystrategyonlyworksforinvoluntaryinteractionsIfyouannounceattheemploymentinterviewthatyoubeatpeopleupiftheydon’tdowhatyouwantYoudon’tgetthejobThevirtuestrategyonlyworksforvoluntaryinteractionsSoasocietywheremoreinteractionisvoluntarywillhavelessviceandmorevirtue.NicerpeoplePrisoner’sDilemmaMikeConfessSayNothingJoeConfess2years,2years3months,5yearsSayNothing5years,3months6months,6monthsDominanceasasolutionconceptifchoiceAisbetterformethanchoiceBWhatevertheotherplayerdoesThenAdominatesB“Confess”dominates“SayNothing”forbothcriminalsSotheyget2yearseachinsteadof6monthseachRepeatedPrisoner’sDilemmaWithafixednumberofplaysBothCriminalsknowtheywillbetrayonthelastroundSo…AgoodreasonnottogetintothatgameConsiderPleaBargainingasaRealPrisoner’sDilemmaIfmostdefendantscopapleaTheD.A.canspendlotsofresourcesonthosewhodon’tWhichraisestherisktothosewhodon’tWhichmakesthosewhodowillingtoacceptworsetermsTheymightallbebetteroffgoingtotrialSincetheD.A.doesn’thavetheresourcestoconvictthemallSomeMoreApproachestoSolvingGamesNashEquilibriumEachplayerisactingoptimally,givenwhateveryotherplayerisdoingThisassumeswecanfreezetheotherplayerswhileIadjustmystrategyButwhatdoes“freeze”mean?ConsiderOligopoly:AfewfirmsincompetitionWhenIincreasemyoutputTheotherfirmscannotkeepbothpriceandquantityfixedBecausealargerquantity(duetomyincrease)impliesalowerpriceIfweassumetheyholdquantityfixedwegetoneequilibriumIfweassumetheyholdpricefixed,adifferentequilibriumSotheoutcomedependsonhowwedefineastrategySubgamePerfectEquilibriumAsequentialgameFirstImakeachoicethenyoumakeachoicethenCouldbemorethantwoplayersAndeachsequenceofchoicesendswithapayoffforeachplayerGotothelastchoice,assumethechoosertakesthebranchthatgiveshimthehigherpayoff.Crossofftheotherbranch.NowthegameisonestepshorterRepeatasyougobackupthediagramBut…TheTantrumGameCommitmentStrategiesMatterAndkidshavethemtooImplicationsWehavesolvednothingharderthanscissorspaperstoneButlearnedsomeusefulwaysofthinkingaboutstrategicbehaviorCommitmentstrategiesmatterBilateralmonopolywithawiderangemaybeexpensiveCrimesofpassionaretosomedegreedeterablePleabargainingmaymakeaveragesentenceshigherTheValueofLifeWemeasurevaluetoyoubyourchoicesYouwouldnotsellyourheartforamilliondollarsNotevenabillionDoesthatmeanthatthevalueoflifeisinfinite?Ifso,ornot,whataretheimplications?ForbuildingbridgesandhighwaysPayingformedicalproceduresAwardingdamagesfortortiouslossoflifeAndlivingInfiniteRelativetoWhat?Relativetosomethingofvalue,noOrwewouldallhavemuchsaferlivesthanwedoAlsomoreboringRelativetodollarstoadeadman,yesTheissueisnotmultiplyingbyinfinityButdividingbyzero1,000,000/0=∞

HowMightWeMeasuretheValueofLife?IncomepremiumforariskofprofessionPricepeoplewillpayforadditionalsafetyWhatifthebestsurgeoncostsmorethanthegoodsurgeon?MeasuredbyrevealedpreferenceThechoiceswemakeHowMightWeUsetheInformation?HighwaydesignDeathpanels–WhatMedicarewillpayforFDAdrugapproval?Tradeoffs:Morelife,lessmoney,risksTortdamagesfortortlossoflifeHowwenowdoitBasedonthevalueofyourlifetoeveryonebutyouHowweshoulddoit—standardPigouvianargumentHedonicdamagesTortDamagesforLossofLife:TheProblemAdamagepaymentplaystworolesThedisincentivetotheinjurerCompensationtothevictimThereisnoreasontoexpecttheoptimalsumtobethesameforbothInthecaseoflossoflife,“compensation”islifeinsuranceThefactthatIdon’twantany(nowifeorchildren,orIamalreadywealthy)DoesnotmeanthatmylifeisofnovaluetomeThesolutionBasedamagesonthevalueofmylifetomeandLetmeselllifeinsuranceonmyselfIcanthenspendthemoneyinthefuturewhereIamnotkilledSothevalueismeasuredindollarswhenIamalive,andfiniteAMarketinInchoateTortsWhatIamsellingisonlylifeinsuranceifIamtortuouslykilledSoitisreallymytortclaimforatortthathasnotyethappenedTherearetworeasonswhythiscan’tbedoneatpresentDamagesawardedarenotbasedonthevalueofmylifetomeAndtortclaimscannotbesoldinadvanceOrsoldatall,saveinafewlimitedcasesContingencyfeeforalawyerSellingtheclaimtothedefendant—anoutofcourtsettlementOtherAdvantagestoMakingTortClaimsMarketableProtectingthepoor—whocannotaffordalawyerThatwasthesysteminsagaperiodIcelandWhereallprosecutionandenforcementwereprivateKillsomeone,hisrelativessueyouOurlegalsystemisonlyathousandyearsbehindtheirsFindingtherightlawyerThepoorplaintiffmightfindafirmtotakethecaseonacontingencybasisButhowdoesheknowwhichfirmwilldothebestjob?TheonethatoffersthehighestpriceforhisclaimMoreadvantagestobediscussedlaterDamagesforInjuryLosingyourvisionlowersbothYourutilityandYourabilitytoturndollarsintoutilesFullycompensatingyouexpostMaybeimpossibleAndtransfersfromhighMUItolowMUITheblindbillionaireproblemButwecouldfullycompensateexanteJustaswithlossoflifeBylettingyousellasmuchofthedamagesasyouwantinadvanceKeeptherestasinsuranceDamagesforInjuryinJewishandIslamicLawHowmuchisyourrightarmworth?WhatweneedisamarketAndtheyhadoneHowmuchwouldyoubeworthifsoldasaslavewithbotharms?Howmuchlesswithonlyonearm?ThedifferenceisthedamageforthelosstoyouofthearmMaimonidesincludedatermforpainandsufferingIfcondemnedtohaveyourhandcutoffHowmuchwouldyoupaytohaveitdoneunderdrugs(opium?)That’sho