Principal-agentModeling

責任代理模式

1Principal-agentModeling

責任代理我請您們考慮一些問題Asmallmedicalinsurancescenario一個醫療保健的問題

Whenyouhaveasmallillness,doyounormallyseeyourdoctor?

當你有小病的時候，你會不會自費看醫生？

Whatabout,ifyourfirmpayforyourexpense?

但是，如果是單位付錢呢，那又怎樣？2我請您們考慮一些問題Asmallmedicalinsu我請您們考慮一些問題Acarmaintenancescenario一個汽車維修的問題

Yourcarisbeingrentedfor2months.Supposedly,itneedsoilingeverymonth.Howlikelyyouwillremembertodoso?

你的汽車是租來用兩個月的，它需要每月潤滑上油一次。你會不會依時地去上油？

Howaboutifthisisyourowncar?

如果這是你自己的汽車，你又會不會去做？3我請您們考慮一些問題Acarmaintenancesc我請您們考慮一些問題Amedicalinsuranceproblem自費醫療保險的問題

Whenwepurchasemedicalinsurance,theinsurancecompanyusuallyrequiresthatyoudiscloseyourmedicalhistory.Pre-conditionsareusuallyexcludedfromthecoverage.

購買保險的時候，它們通常要求你列出你的病歷。但是如果你有大病的話，很可能保險公司不愿意受保。4我請您們考慮一些問題Amedicalinsurance我請您們考慮一些問題

Ifyoudoinfacthavesomemajormedicalproblemsthatrequireexpensivetreatments,wouldyoudisclosetheseproblems?

如果你真的有大病,你會不會真實地上報？

Whatdoallthesetellusaboutcertainhumanbehavior?

這些問題表明了一些什么的人性行為？5我請您們考慮一些問題 IfyoudoinfacthAgencyProblemsandBehavior

代理人的行為與問題Amoralhazardproblem(道德危機問題)

whenanindividualhasanincentivetodeviatefromthecontractandtakeself-interestedactionsbecausetheotherpartyhasinsufficientinformationtoknowifthecontractwashonored.

醫療保健雖然我知道我與雇主的契約明確列出我不要浪費公司的資源。但是用公司的好過用我的嘛！而且公司又不會知道我未能遵守契約。6AgencyProblemsandBehavior

代AgencyProblemsandBehavior

代理人的行為與問題Ahorizonproblem水平界線問題

Ifoneparty’sriskorcompensationisnotthesameastheotherparty’s,theonewithashorterhorizonwilltendtosecretlymaximizetheshort-termbenefits,attheexpenseoftheotherlonger-termparty.

汽車維修我明白汽車不維修壽命不會長。但是，兩個月以后這車子變成怎么樣與我無關了吧。7AgencyProblemsandBehavior

代AgencyProblemsandBehavior

代理人的行為與問題Anadverseselectionproblem逆向選擇問題

Thetendencyofindividualswithprivateinformationaboutsomethingthataffectsapotentialtradingpartner’sbenefitstomakeoffersthataredetrimentaltothetradingpartner.

自費醫療保險:雖然我知道保險公司需要知道我的病歷從而決定保險費。但是誠實的代價是較高的費用。此外，我不說，誰知道。8AgencyProblemsandBehavior

代誰是代理人？什么是代理成本？Anagentissomeonewhohascertainspecialexpertisethatisdesiredbytheprincipaltouseforhis/herbenefits.Theagentisusuallyriskadverse,hasdecisionrightstomanage,butdoesnotown,theorganization’sassets.

代理人(agent)是任何人在公司有決策權力，但是并非產權的最終所有者。代理人通常有較佳的專長，更好的資訊，和對風險抱保守的態度(riskadverse)。9誰是代理人？什么是代理成本？Anagentissome誰是代理人？什么是代理成本？Therearethree(3)typesofagencycosts.代理成本有三類：設計限制性契約的成本(bondingcosts)建立監督制度的成本(monitoringcosts)剩餘的損耗(residualloss)Notethatsomecostsareborntbytheprincipalbutsomeareborntbytheagent.

注意的是，有時這些成本是由委托人(principal)負擔。不過有時這些成本是由代理人自己負擔的。10誰是代理人？什么是代理成本？TherearethreeAgencyCostsBondingcosts–costsincurred,beforeenteringthecontract,toconvincetheprincipalthatsuchagencyrelationshipwillnotresultintheabove-mentionedagencyproblems.Examplesare:reputationbuilding,3rdpartyguarantor,etc.11AgencyCostsBondingcosts–coAgencyCostsMonitoringcosts–costsincurred,afterenteringthecontract,toensurethatsuchagencyproblemswillnotarise.Examplesincludeauditingandinspectioncosts.12AgencyCostsMonitoringcosts–AgencyCostsResidualloss–lossunavoidablyarise,despitethebondingandmonitoringcosts,thecontractstillcannotyieldtheutmostbenefits,because:theagencyproblemsdoarise,orduetothesuspicionoftheagencyproblems,theprincipalrefusestopaytheagentcompensationsthatfullyreflecthis/herefforts.13AgencyCostsResidualloss–loExamplesofthePrincipal-agentModelEffortlevelProbabilitiesandpayoffsfor4differenteventsS1=0.3S2=0.3S3=0.2S4=0.2E1=6$55,000$55,000$55,000$40,000E2=5$55,000$55,000$40,000$40,000E3=4$55,000$40,000$40,000$40,00014ExamplesofthePrincipal-agenExamplesofthePrincipal-agentModelAgent’sUtilityFunction:Xa?-e2

100where: Xa=agent’scompensations e=theeffortlevelusedbytheagent Question1:Ifyouweretheprincipalinenteringthecontract,whichlevelofeffort(e1,e2,ore3)wouldyoudemand?Question2:Ifyou,theprincipal,cancloselymonitorandobservetheagentatalltime,whataretheamountandconditionofpayment?And,whatistheexpectedpayofffortheprincipal?15ExamplesofthePrincipal-agenNow,let’sassumethatyoucannotmonitorandobservetheagentdirectly.Whatwouldyou,astheagent,do?Now,canyouseetheagencyproblemshere?EffortlevelExpectedutilityoftheagentE1=618,496?-62=100E2=518,496?-52=111E3=418,496?-42=112Isitlikelytohavethe“adverseselection”problem?Howaboutthe“moralhazard”problem?And,thehorizonproblem?Residualloss?16Now,let’sassumethatyoucanWhatcanwesay,uptothispoint?Underconditionofunobservability(incompleteinformation),fixedpaymentstoagents(i.e.workers,employees)mostlikelydonotwork.Whatarethenthealternatives?Wecangivetheprincipalafixedpaymentinstead.Or,wecancomeupwithan“incentivecompatible”conditionalcontract.17Whatcanwesay,uptothispoFixedPaymenttothePrincipalConsiderthisnewcontractunderwhichtheprincipalgets$32,750nomatterwhathappensandtheagentkeepstherest.Willthiswork?EffortlevelExpectedpayofftotheagentE1=6[(55,000?x0.8+40,000?x0.2)-32,750]-36=100.36E2=5[(55,000?x0.6+40,000?x0.4)-32,750]-25=98.56E3=4[(55,000?x0.3+40,000?x0.7)-32,750]-16=88.3518FixedPaymenttothePrincipalFixedPaymenttothePrincipalThus,numericallythiswillworktoensurethattheagentgivesthehighesteffort.However,thereisnonethelessalosstotheprincipal(33,504-32,750)=754whichisinasenseamonitoringcost(maximumcosttopayforaninformationsystemtorevealtheagent’seffortlevel).Butthemostfundamentalproblemisthatthistypeofcontractsviolatesthe“riskadverse”natureoftheagent.Nowtheagentbecomestheprincipal!19FixedPaymenttothePrincipalIncentiveCompatibleContract–ProblemSetupMaximize(55,000–R55)Φ55(e1)+(40,000-R40)Φ40(e1)Subjectto:R55?Φ55(e1)+R40?Φ40(e1)-e12=100 R55?Φ55(e1)+R40?Φ40(e1)-e12R55?Φ55(e2)+R40?Φ40(e2)–e22R55?Φ55(e1)+R40?Φ40(e1)-e12R55?Φ55(e3)+R40?Φ40(e3)–e3220IncentiveCompatibleContractIncentiveCompatibleContract–SpecificSolutionsMaximize(55,000–R55)0.8+(40,000-R40)0.2Subjectto:R55?(0.8)+R40?(0.2)-36

=100 R55?(0.8)+R40?(0.2)-36

R55?(0.6)+R40?Φ40(0.4)–25R55?(0.8)+R40?(0.2)-36

R55?(0.3)+R40?(0.7)–16Solutions: R55=21,609 R40=

8,464Expectedpayoffs: Principal = 33,020 Agent = 18,98021IncentiveCompatibleContractSummaryofDifferentContractsEventundere1Principal’sPayoffsAgent’sPayoffObservableFixedRenttoPrin.IncentiveCompat.ObservableFixedRenttoPrin.IncentiveCompat.55,000(p=0.8)36,50432,75033,39118,49622,25021,60940,000(p=0.2)21,50432,75031,53618,4967,2508,464ExpectedPayoffs33,50432,75033,02018,49619,25018,98022SummaryofDifferentContractsWhatdoweknowfromthese?Thebestcasescenariofortheprincipaliswhenhecanobservetheagent’seffortleveldirectly.Theworstcasescenariototheprincipalappearstobesimplychargingafixedrent.Thedifferencebetweenthetwo($754)representsthemaximumamounttopayforaninformationsystemtorevealtheagent’seffort.Themiddle,2ndbestsolution(incentivecompatiblecontract)maynotalwaysbethenextbestthingthough!23Whatdoweknowfromthese?TheLet’ssaythatwesetthetwovariables,R55andR40,tobe18,769and11,449respectively.EffortlevelExpectedutilityoftheagentE1=6(18,769?)0.8+(11,449?)0.2-6?=95E2=5(18,769?)0.6+(11,449?)0.4-5?=100E3=4(18,769?)0.3+(11,449?)0.7-4?=100Now,theprincipalistellingtheagentNOTtoworkhard!The$33,159isactuallybetterthanthe$33,020under“incentivecompatible”contract!EffortlevelExpectedutilityoftheprincipalE1=6Notafeasiblesolution,agent’sutility<100n/aE2=5(55,000-18,769)0.6+(40,000-11,449)0.4

=33,159E3=4(55,000-18,769)0.3+(40,000-11,449)0.7

=30,85524Let’ssaythatwesetthetwoAFewCautionaryRemarksThismodelpresentedhereisasingle-periodmodel.Multiple-period(repeatedgames)cangiveverydifferentanswers.Therecanbemultipleprincipalsaswellasmultipleagentsinthemodel.Suchmodels,however,becomeextremelycomplex.Informationsystemsarenotconsideredhere.25AFewCautionaryRemarksThismConcludingRemarksThePrincipal-agentmodelistheoreticalelegantbutmathematicallytedioustouse.Empirical(real-life)evidenceseemstosupportthemodelwell.Thechallenges,inmyopinion,include:tocomeupwithuseful,testablehypotheses;toextendthemodeltomorecomplex,butrealbusinesssituations;toencourageresearcherstoteachnewcomersthebasicskillinunderstandingthemodelratherthansimplytopublishin“ivory-tower”typeofjournals.26ConcludingRemarksThePrincipaPrincipal-agentModeling

責任代理模式

27Principal-agentModeling

責任代理我請您們考慮一些問題Asmallmedicalinsurancescenario一個醫療保健的問題

Whenyouhaveasmallillness,doyounormallyseeyourdoctor?

當你有小病的時候，你會不會自費看醫生？

Whatabout,ifyourfirmpayforyourexpense?

但是，如果是單位付錢呢，那又怎樣？28我請您們考慮一些問題Asmallmedicalinsu我請您們考慮一些問題Acarmaintenancescenario一個汽車維修的問題

Yourcarisbeingrentedfor2months.Supposedly,itneedsoilingeverymonth.Howlikelyyouwillremembertodoso?

你的汽車是租來用兩個月的，它需要每月潤滑上油一次。你會不會依時地去上油？

Howaboutifthisisyourowncar?

如果這是你自己的汽車，你又會不會去做？29我請您們考慮一些問題Acarmaintenancesc我請您們考慮一些問題Amedicalinsuranceproblem自費醫療保險的問題

Whenwepurchasemedicalinsurance,theinsurancecompanyusuallyrequiresthatyoudiscloseyourmedicalhistory.Pre-conditionsareusuallyexcludedfromthecoverage.

購買保險的時候，它們通常要求你列出你的病歷。但是如果你有大病的話，很可能保險公司不愿意受保。30我請您們考慮一些問題Amedicalinsurance我請您們考慮一些問題

Ifyoudoinfacthavesomemajormedicalproblemsthatrequireexpensivetreatments,wouldyoudisclosetheseproblems?

如果你真的有大病,你會不會真實地上報？

Whatdoallthesetellusaboutcertainhumanbehavior?

這些問題表明了一些什么的人性行為？31我請您們考慮一些問題 IfyoudoinfacthAgencyProblemsandBehavior

代理人的行為與問題Amoralhazardproblem(道德危機問題)

whenanindividualhasanincentivetodeviatefromthecontractandtakeself-interestedactionsbecausetheotherpartyhasinsufficientinformationtoknowifthecontractwashonored.

醫療保健雖然我知道我與雇主的契約明確列出我不要浪費公司的資源。但是用公司的好過用我的嘛！而且公司又不會知道我未能遵守契約。32AgencyProblemsandBehavior

代AgencyProblemsandBehavior

代理人的行為與問題Ahorizonproblem水平界線問題

Ifoneparty’sriskorcompensationisnotthesameastheotherparty’s,theonewithashorterhorizonwilltendtosecretlymaximizetheshort-termbenefits,attheexpenseoftheotherlonger-termparty.

汽車維修我明白汽車不維修壽命不會長。但是，兩個月以后這車子變成怎么樣與我無關了吧。33AgencyProblemsandBehavior

代AgencyProblemsandBehavior

代理人的行為與問題Anadverseselectionproblem逆向選擇問題

Thetendencyofindividualswithprivateinformationaboutsomethingthataffectsapotentialtradingpartner’sbenefitstomakeoffersthataredetrimentaltothetradingpartner.

自費醫療保險:雖然我知道保險公司需要知道我的病歷從而決定保險費。但是誠實的代價是較高的費用。此外，我不說，誰知道。34AgencyProblemsandBehavior

代誰是代理人？什么是代理成本？Anagentissomeonewhohascertainspecialexpertisethatisdesiredbytheprincipaltouseforhis/herbenefits.Theagentisusuallyriskadverse,hasdecisionrightstomanage,butdoesnotown,theorganization’sassets.

代理人(agent)是任何人在公司有決策權力，但是并非產權的最終所有者。代理人通常有較佳的專長，更好的資訊，和對風險抱保守的態度(riskadverse)。35誰是代理人？什么是代理成本？Anagentissome誰是代理人？什么是代理成本？Therearethree(3)typesofagencycosts.代理成本有三類：設計限制性契約的成本(bondingcosts)建立監督制度的成本(monitoringcosts)剩餘的損耗(residualloss)Notethatsomecostsareborntbytheprincipalbutsomeareborntbytheagent.

注意的是，有時這些成本是由委托人(principal)負擔。不過有時這些成本是由代理人自己負擔的。36誰是代理人？什么是代理成本？TherearethreeAgencyCostsBondingcosts–costsincurred,beforeenteringthecontract,toconvincetheprincipalthatsuchagencyrelationshipwillnotresultintheabove-mentionedagencyproblems.Examplesare:reputationbuilding,3rdpartyguarantor,etc.37AgencyCostsBondingcosts–coAgencyCostsMonitoringcosts–costsincurred,afterenteringthecontract,toensurethatsuchagencyproblemswillnotarise.Examplesincludeauditingandinspectioncosts.38AgencyCostsMonitoringcosts–AgencyCostsResidualloss–lossunavoidablyarise,despitethebondingandmonitoringcosts,thecontractstillcannotyieldtheutmostbenefits,because:theagencyproblemsdoarise,orduetothesuspicionoftheagencyproblems,theprincipalrefusestopaytheagentcompensationsthatfullyreflecthis/herefforts.39AgencyCostsResidualloss–loExamplesofthePrincipal-agentModelEffortlevelProbabilitiesandpayoffsfor4differenteventsS1=0.3S2=0.3S3=0.2S4=0.2E1=6$55,000$55,000$55,000$40,000E2=5$55,000$55,000$40,000$40,000E3=4$55,000$40,000$40,000$40,00040ExamplesofthePrincipal-agenExamplesofthePrincipal-agentModelAgent’sUtilityFunction:Xa?-e2

100where: Xa=agent’scompensations e=theeffortlevelusedbytheagent Question1:Ifyouweretheprincipalinenteringthecontract,whichlevelofeffort(e1,e2,ore3)wouldyoudemand?Question2:Ifyou,theprincipal,cancloselymonitorandobservetheagentatalltime,whataretheamountandconditionofpayment?And,whatistheexpectedpayofffortheprincipal?41ExamplesofthePrincipal-agenNow,let’sassumethatyoucannotmonitorandobservetheagentdirectly.Whatwouldyou,astheagent,do?Now,canyouseetheagencyproblemshere?EffortlevelExpectedutilityoftheagentE1=618,496?-62=100E2=518,496?-52=111E3=418,496?-42=112Isitlikelytohavethe“adverseselection”problem?Howaboutthe“moralhazard”problem?And,thehorizonproblem?Residualloss?42Now,let’sassumethatyoucanWhatcanwesay,uptothispoint?Underconditionofunobservability(incompleteinformation),fixedpaymentstoagents(i.e.workers,employees)mostlikelydonotwork.Whatarethenthealternatives?Wecangivetheprincipalafixedpaymentinstead.Or,wecancomeupwithan“incentivecompatible”conditionalcontract.43Whatcanwesay,uptothispoFixedPaymenttothePrincipalConsiderthisnewcontractunderwhichtheprincipalgets$32,750nomatterwhathappensandtheagentkeepstherest.Willthiswork?EffortlevelExpectedpayofftotheagentE1=6[(55,000?x0.8+40,000?x0.2)-32,750]-36=100.36E2=5[(55,000?x0.6+40,000?x0.4)-32,750]-25=98.56E3=4[(55,000?x0.3+40,000?x0.7)-32,750]-16=88.3544FixedPaymenttothePrincipalFixedPaymenttothePrincipalThus,numericallythiswillworktoensurethattheagentgivesthehighesteffort.However,thereisnonethelessalosstotheprincipal(33,504-32,750)=754whichisinasenseamonitoringcost(maximumcosttopayforaninformationsystemtorevealtheagent’seffortlevel).Butthemostfundamentalproblemisthatthistypeofcontractsviolatesthe“riskadverse”natureoftheagent.Nowtheagentbecomestheprincipal!45FixedPaymenttothePrincipalIncentiveCompatibleContract–ProblemSetupMaximize(55,000–R55)Φ55(e1)+(40,000-R40)Φ40(e1)Subjectto:R55?Φ55(e1)+R40?Φ40(e1)-e12=100 R55?Φ55(e1)+R40?Φ40(e1)-e12R55?Φ55(e2)+R40?Φ40(e2)–e22R55?Φ55(e1)+R40?Φ40(e1)-e12R55?Φ55(e3)+R40?Φ40(e3)–e3246IncentiveCompatibleContractIncentiveCompatibleContract–SpecificSolutionsMaximize(55,000–R55)0.8+(40,000-R40)0.2Subjectto:R55?(0.8)+R40?(0.2)-36

=100 R55?(0.8)+R40?(0.2)-36

R55?(0.6)+R40?Φ40(0.4)–25R55?(0.8)+R40?(0.2)-36

R55?(0.3)+R40?(0.7)–16Solutions: R55=21,609 R40=

8,464Expectedpayoffs: Principal = 33,020 Agent = 18,98047IncentiveCompatibleContractSummaryofDifferentContractsEventundere1Principal’sPayoffsAgent’sPayoffObservableFixedRenttoPrin.IncentiveCompat.ObservableFixedRenttoPrin.IncentiveCompat.55,000(p=0.8)36,50432,75033,39118,49622,25021,60940,000(p=0.2)21,50432,75031,53618,4967,2508,464ExpectedPayoffs33,50432,75033,02018,49619,25018,98048SummaryofDifferentContractsWhatdoweknowfromthese?Thebestcasescenariofortheprincipaliswhenhecanobservethe