# Spillovers, Investment Incentives and the Property Rights Theory of the Firm

**ABSTRACT** This paper examines the property rights theory of the firm when a manager's relationship-specific investment can be partially appropriated by the owner of an asset even if cooperation breaks down. The investments of non owners may then be devalued, but are seldom wholly lost to the owner. With such spillovers, the outside-option principle can be incorporated into the Grossman-Hart-Moore framework without implying that ownership demotivates. Enriched predictions on the determinants of integration emerge. Copyright Blackwell Publishing Ltd. 2004.

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**ABSTRACT:**We apply the property rights theory of Grossman-Hart-Moore in the music industry and study the optimal allocation of copyright between the artists who create music and the labels who promote and distribute it. Digital technology opens up a role for new intermediaries. We find that entry of online platforms occurs only if they are sufficiently more productive in distribution than the incumbent label. Furthermore, entry leads to a change in bargaining positions and it can become optimal for the copyright to be shifted from the label to the artist.SSRN Electronic Journal 10/2004; - SourceAvailable from: David de Meza[Show abstract] [Hide abstract]

**ABSTRACT:**Exclusive contracts prohibit one or both parties from trading with anyone else. Contrary to earlier findings, notably Segal and Whinston (2000), we show that investments that are specific to the contracted parties may be encouraged. Results depend on the nature of the investments and whether the bargaining is cooperative or non-cooperative. The major part of the analysis show that exclusive contracts designed to 'assure' the supply of essential inputs promote investment. Infinite penalties for breach, even if ex post renegotiable, may result in excessive investment, in which case a finite penalty for breach achieves the first-best outcome.The RAND Journal of Economics 07/2004; · 1.49 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper pinpoints optimal vertical arrangements in settings characterized by incomplete contracting and resale of an intermediate input (a "widget"). In the Grossman-Hart-Moore property rights theory, we conclude that sometimes strictly complementary assets should be owned separately to permit the emergence of a secondary market. In a richer model where the parties choose specific and nonspecific investments, vertical separation may also dominate joint ownership. The article then examines the profitability of three integration forms when the proposed bargaining model substitutes random-order values (e.g., the Shapley value). The conclusions differ markedly from existing claims. (JEL C70, C78, D23, L42) The Author 2008. Published by Oxford University Press on behalf of Yale University. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.Journal of Law Economics and Organization 01/2009; 25(1):211-234. · 1.02 Impact Factor

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SPILLOVERS, INVESTMENT INCENTIVES AND THE

PROPERTY RIGHTS THEORY OF THE FIRM?

DaviddeMezaw

BenLockwoodz

This paper examines the property rights theory of the firm when a

manager’s relationship-specific investment can be partially appro-

priated by the owner of an asset even if cooperation breaks down. The

investmentsofnonownersmaythenbedevalued,butareseldomwholly

lost to the owner. With such spillovers, the outside-option principle can

be incorporated into the Grossman-Hart-Moore framework without

implying that ownership demotivates. Enriched predictions on the

determinants of integration emerge.

I.INTRODUCTION

Whether for good or ill, managers often have influence well beyond their

tenureinajob.Examplesaresonumerousastobecommonplace.According

toChandler[1977],theAmericanrailroadnetworktookitsmodernformby

the 1880s and ‘ysalaried career executives played a critical role in the

system building of the 1880s’ (p. 167). A theme of Peters and Waterman

[1982]isthateffectivemanagersinculcateanenduringculture.Typicalisthe

quote of Richard Deupree, former CEO of Procter and Gamble, ‘William

ProcterandJamesGamblerealizedthattheinterestsoftheorganizationand

its employees were inseparable. That has never been forgotten.’ (p. 76).

The common element here and much more generally is that a firm may

continue to benefit from an employee’s past efforts even when they part

company. This feature evidently affects employees’ bargaining positions

with employers and hence the incentives of both parties to make non-

contractible investments in the relationship. The underlying perspective is

thepropertyrightstheoryofthefirm(PRT).Thisisaboldattempttoexplain

patterns of industrial organization by the incentive effects of asset

ownership. The seminal papers are Grossman and Hart [1986] and Hart

and Moore [1990], henceforth GHM. They argue that costly verification of

rBlackwellPublishingLtd.2004,9600GarsingtonRoad,OxfordOX42DQ,UK,and350MainStreet,Malden,MA02148,USA.

229

THE JOURNAL OF INDUSTRIAL ECONOMICS

Volume LII

0022-1821

No. 2June 2004

?We greatly appreciate the exceptionally helpful comments of the referees and editor.

wAuthors’ affiliations: Interdisciplinary Institute of Management, London School of

Economics, Houghton Street, London, WC2A 2AE, U.K.

email: d.de-meza@lse.ac.uk

zDepartmentofEconomics,UniversityofWarwickandCEPR,Coventry,CV47AL,U.K.

email: b.lockwood@warwick.ac.uk

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relationship-specific investment means that contracts are necessarily

incomplete and can always be renegotiated. Eventual payoffs, and

consequently the ex ante incentive to invest, are therefore determined by

ex post bargaining. As ownership of non-human assets affects bargaining

power, ownership ultimately influences the ex ante incentive to invest. The

boundary of the firm (that is, the extent to which assets are under common

ownership) is thus determined by the ownership structure that provides the

best bundle of investment incentives.

The concern of this paper is with the neglected but pervasive feature that

one party’s investment often creates benefits for the other even if the

relationship breaks down. This is particularly likely to apply when the asset

is work in progress or reputational capital, but can also easily arise with

other assets. The remainder of the paper shows that such spillovers have

major implications for the PRT.

PerhapsthecentralresultofGHM’sformulationisthatapartyacquiring

additional assets does not suffer a decrease in its investment incentives1. To

see this, suppose that there are two parties, A and B, and one asset. All that

canbecontractedoverisownershipoftheasset.2GHMassumethatthefinal

surplusissharedexpostaccordingtotheNashbargainingsolution,i.e.,each

party gets its disagreement utility3plus half of the difference between total

surplusandthesumofthedisagreementutilities.Thus,50%ofthemarginal

return of the investment stems from the effect of the investment on total

surplus,whileanother50%stemsfromitseffectonthedisagreementutility.

Now, if A owns the asset, the marginal return of her investment outside the

relationshipwillbehigherascomparedtothesituationwhereBcontrolsthe

asset. Therefore, her investment incentives will be higher.

However, this key qualitative prediction of PRT does not appear to be

especially robust. Two recent papers, Chiu [1998] and de Meza and

Lockwood [1998], note that the Nash bargaining solution obtains in a non-

cooperative alternating-offer game only if the disagreement utilities are

interpreted as inside options, that is, they can only be consumed during

negotiations. For example, the parties may be in paid employment which

they will quit once agreement is reached. In practice, the disagreement

utilities relevant for PRT may be outside options. That is, they are payoffs

achievable by taking up some alternative offer which scuppers the existing

relationship.

As emphasized by de Meza and Lockwood, under these circumstances

extra asset ownership may demotivate managers. When parties can

irrevocably break off bargaining and take up some new opportunity (and

1This result is formally stated and proved as Proposition 1 below.

2The more general case with n managers is dealt with by Hart and Moore [1990].

3Disagreement utilities are the payoffs available to the two parties while negotiations over

the division of the surplus take place.

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under an additional assumption on the sequential order of moves) the

subgame-perfect equilibrium of the bargaining game satisfies the outside-

option principle. This principle says that if the outside-option utility of one

party is larger than 50% of the total surplus from cooperation, then this

party will only get its outside option utility, while the other party will get all

of the additional social surplus. It is easy to see that with the outside-option

principle,GHM’sconclusionfails.Supposethattheoutside-optionutilityof

whoever owns theasset does exceed halfofthesurplus.Then,ifA owns, she

will get only her outside option, so 100% of her investment incentives stem

from theeffectoftheinvestmentontheoutsideoption.GivenGHM’saddi-

tional assumption that the marginal impact of the investment on the total

relationship surplus is higher than on the outside option, it is clear that A’s

investmentincentivesarelowerifsheownstheassetthanifshedoesnotownit.

This paper presents a result below (Proposition 2) which shows that the

foregoing argument applies quite generally4; under some weak assump-

tions–which together imply that a manager’s outside option binds when he

owns both assets, i.e., that outside options are sufficiently valuable–a

manager’s incentive to invest is maximized when owning no assets.

Although there may be occasions where ownership demotivates, it is

implausible that this is the norm. Since in many contexts the relevant

alternatives appear to be outside options and alternating offers a natural

bargaining protocol, there is a puzzle. This paper offers a solution. It is

shown that if managers’ investments augment the value of the physical

asset(s) as well as their own human capital, the conclusion of the earlier

property rights literature (namely, that asset ownership motivates) can be

restored even when the outside option principle applies.5This is because the

value of investments in physical assets can be appropriated by the owner of

the asset whether or not he works together with the agent who made the

investment.

The mechanism at work is the following: If the team breaks up, the

subsequent revenue generated by the owner of the asset depends on the

investment made by the non-owner, insofar as that investment is embodied in

4De Meza and Lockwood [1998] show that with outside options, increased ownership

motivates only under rather special conditions, namely: (i) if the manager’s outside option is

already binding before he is given the asset; or, (ii) if the outside option is initially not binding

oneithermanager,butbecomesbindingontherecipientfollowingtransferoftheasset,andthe

recipient’s outside option is relatively sensitive to investment (i.e., the return on investment in

theoutsideoptionismorethanhalfthereturntoinvestmentinteamproduction).SeealsoChiu

[1998] for similar results. Both (i) and (ii) require some asymmetry in the model. In particular,

although both these cases involve the manager gaining the asset investing more, the manager

losing the asset does not invest less (and in the second case invests strictly more). So even here

the investment incentives of one of the managers is at a maximum when they own no assets.

5Noldeke and Schmidt [1998] allow investments to augment physical assets but work in a

Nash bargaining framework and are concerned with different issues. There are also spillovers

in the contracting problems of Che and Hausch [1999] and Segal and Whinston [2000] but

implications for asset ownership are not examined.

SPILLOVERS, INCENTIVES AND THE PROPERTY RIGHTS THEORY

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the physical asset. In this paper, we call the (marginal) impact of an agent’s

investment on the individual revenue of the other agent a spillover. To

illustrate the qualitative significance of spillovers for the property-rights

theory, suppose the outside option of an asset owner is binding at the

bargaining stage so the non-owner is the residual claimant. With spillovers,

the non-owner’s marginal return to investment is now the increase in team

revenuelesstheboostintheowner’soutsideoptionduetothespillover.The

spillover thus weakens the non-owner’s investment incentive since, to the

extent investment augments asset value, it merely serves to strengthen the

owner’s bargaining power. Consequently, if the spillover is large enough,

ownership may once more motivate (see Proposition 3 below).

The key ingredient of our approach, that the value of the owner’s outside

option depends on the investment of the other agent(s), is natural and

realistic in many settings. For example, consider a vertical production

relationship such as that between a carmaker and component supplier.6

Supposethatoneoftheassetsisapressformakingpartsofthecarbody,and

that the manager of the component firm has invested some time making

improvements to that machine. Then, if the manager of the carmaker owns

this asset, in the event of individual production, (i.e., the managers do not

agree to produce the car together), the manager of the car-making firm

obtains some benefit from the other manager’s time investment7. The

situation is similar when an employee makes organizational improvements,

orwhenascientistmakesadiscoverybutthecompanyownsthepatent8.The

ownershipissuecouldalsoinvolvewhohastherighttoworkinprogress,the

value of which generally depends on the contribution of all team members.

In all these cases, even in the presence of outside options, ownership may

enhance incentives.

II.AN EXAMPLE

Toillustratetheseideas,considerHartandMoore’s[1990]exampleofachef

andskippercombiningforcestoofferaluxurycruise.Theyfirstdecidewhich

6TheclassicexampleisFisherCarBodyandGeneralMotors.Klein,CrawfordandAlchain,

[1978] Williamson [1985] and Hart [1995] argue that the takeover of Fisher by GM, completed

by 1926, was to mitigate hold-up problems. This is disputed by Casadesus-Masanell and

Spulber [2000], Coase [2000] and Freeland [2000] who cite transaction cost savings and

coordination benefits. The picture is mixed though. Coase reports that prior to 1926, many

plants were owned by GM and leased to Fisher. This suggests that hold-up may have been an

issue.Inaddition,themergerwaspromptedbytheconcernofGMthatFisherBrothers‘ypaid

lessattentiontotheneedsofGeneralMotorsthanGeneralMotorswouldhaveliked’(Coase,p.

23). This indicates that the ownership change was designed to change incentives.

7This variant of Hart’s model is discussed in detail in Section 3.

8All these examples assume that the investment of the non-owner augments the physical

capital of the owner of the asset. However, a similar effect might arise if the investment is in

human capital. For example, suppose an engineer trains an assistant to repair the machine

before he leaves.

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of them should own the yacht. Next the skipper can make an unverifiable

investment which raises total cruise revenue. We suppose that this involves

researching charts to provide a particularly suitable itinerary. At this stage,

with prospective team revenue determined, the chef and skipper negotiate

how it should be divided. The protocol is alternating-offers bargaining, but

theoutcomeofthenegotiationdependsontheopportunitiesthetwoparties

face. One possibility is that both are currently employed in other jobs. Once

theyreachagreementtheywillquitthesejobsandlosetheincomeflowsthey

generate. Instead, each obtains the agreed share of cruise income. In this

case, income from the current jobs represent inside options. Bargaining then

resultsintheexcessofcruiserevenueoverthesumoftheinsideoptionsbeing

equally split between the parties.9

Another possibility is that neither chef nor skipper is currently employed,

but each has alternative opportunities he or she could take up. Perhaps the

chefcouldsignupforadifferentvoyagewhilstayacht-owningskippercould

just set sail and combine both jobs. If either of these options is taken, the

original cruise is cancelled. Now the bargaining involves outside options.

Bargaining then results in cruise revenue being either equally split or, if one

party has an outside option worth more than half cruise revenue, this is the

payoff and the other party receives the remainder of the cruise revenue.10

Resumingthedetailoftheexample,supposethattheskipper’sunverifiable

investmentraisestotalcruise revenue from 80 to 100but involves a personal

costof11.Iftheskipperownsthevesselbutworksindependently,heearns60

if the investment has been made and 50 otherwise. Without the yacht, the

skipper’sinvestmentiswastedandheearns20.Ifthechefownstheyachtbut

she works independently she earns 50, but only 20 if she does not own the

yacht. So, fornow,if theteam dissolves,theindividualrevenue ofthechefis

independent of the skipper’s investment (i.e., there are no spillovers).

Now consider investment incentives if the independent payoffs are inside

options in the post-investment bargaining. First, suppose the skipper owns

the yacht. If he invests, his payoff is 60þ0.5(100?60?20)570 whereas

without investment, the payoff is 50þ0.5(80?50?20)555. So, as

70?55411, the investment is undertaken. When the chef owns, the

skipper gets 20þ0.5(100?20?50)535 if he invests, and if he does not, he

9This is the outcome under the assumptions that the time interval between bargaining

rounds goes to zero, and both parties discount the future equally. Both these assumptions are

made throughout this paper.

10Thoughourpreferredinterpretationisthatthedifferencebetweenthecasesisthenatureof

theopportunitiesopentotheagents,itcouldbethebargainingprotocolthatdetermineswhich

equilibrium prevails. Suppose that there is a genuine outside option available to each agent.

The bargaining is take-it-or-leave-it but each agent has an equal chance of being the proposer.

Nowexpectedpayoffsequaltheinsideoptioninterpretationofthetext,ortheNashaxiomatic

outcome. So outside options could be consistent with the GHM results though the bargaining

protocolrequireddoesnotthoughseemparticularlyeasytojustify.TheNashsolutioncanalso

emergewithoutsideoptionsifthereisasmallexogenouschancethatnegotiationsbreakdown.

SPILLOVERS, INCENTIVES AND THE PROPERTY RIGHTS THEORY

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gets only 20þ0.5(80?20?50)525. In this case, his gain from investment

is less than 11 and he does not invest. So the efficient investment only takes

placeiftheskipper,thesolepartywithaninvestmentchoice,istheowner.As

incometransferscanbemadeexante,thisownershipstructureistheonethat

will be agreed at the outset. This first case illustrates the original GHM

theory of the firm.

Nowconsiderhowmattersturnoutiftheoutsideoptionprincipleapplies,

as in de Meza and Lockwood [1998]. When the skipper owns the yacht, his

outside option is binding at the bargaining stage, as it is worth more than

50% of team revenue whether or not he invests. Hence, the skipper gets 60

withinvestmentand50without,andconsequentlydoesnotinvest.Whenthe

chef owns, her outside option binds, and so the skipper gets 80?50530

without investment and 100?50550 with, implying that the skipper now

wishes to invest. It is now efficient for the chef to own, because only if the

skipper does not own is he sufficiently motivated to invest.

Finally, retain the outside option principle, but suppose that when the

skipper invests, in addition to researching charts (which augments only

the skipper’s human capital), he also supervises modifications to the keel

of the yacht to allow easy access to more ports on the itinerary (which

augments the value of the physical asset). This additional work11raises the

skipper’s investment cost by 5 taking it to 16. In the event negotiations

breakdown irretrievably, the gain from easier port access is worth 10 to

whoever owns the yacht. There are now spillovers, i.e., the skipper’s

investment augments the value of the yacht to the chef.

So, if the chef owns and the skipper invests, the chef’s outside option

increasesfrom50to60.Therefore,withoutsideoptions,whenthechefowns,

the skipper’s gain from investing is now only (100?60)?(80?50)510,

less than the cost of investment of 11þ5516. On the other hand, when the

skipper himself owns, investment raises his outside option from 50 to 70,

more than the investment cost of 16. So, even with outside options, we are

back to the original GHM conclusion, i.e., the skipper can only be

sufficiently motivated to invest if he owns the asset.

III.THE MODEL

Our model can be thought of as an extension of Hart’s [1995, ch. 2] widget

model,toaccommodatespillovers.Therearetwomanagersi ¼ 1;2engaged

in a vertical production relationship using two indivisible assets a1;a2.

Specifically, 2 works with an asset a2to produce a widget which is then

passed to 1 who works with a1to produce a final output (interpret a1;a2as

machines (or factories) that make the final product and the widget

11Wesupposeforsimplicity thatinvestment isstillbinary,i.e.,either theskipperundertakes

both the keel adjustment and the chart research, or neither.

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respectively). Investments at levels e1;e2;0)ei<1; are made by managers

1,2 at date 0 and the widget is supplied at date 1.

Following Hart, we interpret investments e1;e2as being money or time

spent improving the efficiency of the relevant manager’s operation. There is

uncertaintyaboutthetypeofthewidgetmanager1requires,whichisresolved

atdate1;consequently,aneffectivelong-termcontractisimpossible.Rather,

at date 1, the parties negotiate about the widget price and type from scratch.

Finally, both parties are risk-neutral and have unlimited wealth so that it is

feasible for each party to own any asset that is it efficient for him to own.

The first possibility is that the managers trade a ‘specialized’ widget, an

event we refer to as team production. In this case, manager 1 gets payoff

Rðe1Þ ? p?, where p?is the price – negotiated at date 1– at which they trade,

and R is the revenue from the sale of the widget. Similarly, manager 2 gets a

payoff p?? Cðe2Þ; where C is the cost of producing the widget. So, the total

profit (ignoring investment costs) from team production is P ¼ R ? C: We

assume that R is strictly concave and differentiable in e1and C is strictly

convex and differentiable in e2:

The second possibility is that the two managers do not agree to trade, an

event we call individual production. Let the payoffs to individual production be

p1;p2:Itiscentraltothepropertyrightstheorythatp1(resp.p2Þdependalsoon

the set of assets that manager 1 (resp. manager 2) owns12. Following Hart

[1995], we consider two possible allocations of assets between the managers:

non-integration, where manager 1 owns a1, and manager 2 owns a2; and

integration, where one manager owns both assets (there are obviously two

possibilities here). Formally, an asset allocation is a pair ða1;a2Þ where ai2

f;;faig;fa1;a2ggisthesetofassetsownedbyi ¼ 1;2:Letthesetofallpossible

asset allocations13be A. So, we write piðe1;e2;aiÞ to denote the value of

individual production to i under different asset allocations.

Inmodellingindividualproduction,wewishtocapturespillovers.InHart

[1995], there are no spillovers, i.e., p1is independent of e2, and p2is

independent of e1. One way of interpreting this is the following. Hart

assumesthatthetwomanagershaveanadditionalinputtoproductionother

than the non-contractible investments, which he calls ‘human capital’ (Hart

[1995], p. 36). It is an implicit assumption in Hart that in the absence of 2’s

human capital, 1 simply cannot produce a widget, and similarly, in the

absenceof1’shumancapital,2simplycannotproducethefinalproduct.So,

withindividualproduction,thereisnowayformanager1tobenefitfromthe

investment e2that manager 2 has made in improving the efficiency of the

asset a2which is used to make the widget (and vice-versa).

12Recallthatintheexamplediscussedintheprevioussection,theindividualrevenueofeither

the skipper or the chef depended on whether that agent owned the yacht.

13Obviously, all assets are owned by one or other of the agents (a1[ a2¼ fa1;a2g), and no

asset is jointly owned (a1\ a2¼ ;).

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SPILLOVERS, INCENTIVES AND THE PROPERTY RIGHTS THEORY

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Here, we relax this assumption. Specifically, we will assume that if

manager1ownsa2aswellasa1,hecanmakeawidget,andthusbenefitfrom

2’s investment e2in asset a2(and symmetrically, if manager 2 owns both

assets,hecanmakethefinalproduct,andthusbenefitfrom1’sinvestmentin

thefirstasset).Thisimpliesthatwithintegratedassetownership,therewillbe

spillovers, but not otherwise. A more general formulation is that spillovers

occur even under non-integration. For example, the team members may

work in close proximity so that an innovation introduced by one may be

observedandapplicablebytheother.Thenmanager1’sinvestmente1would

improve the efficiency of asset a2as well as that of asset a1; and similarly for

manager2.AswenoteafterProposition3,thisextensiondoesnotupsetour

main results, but to avoid clutter we work with the simpler case.

The details are as follows. We will suppose that the investments e1;e2

consistinpartofmodificationstotheassets(machines)a1;a2,andwedenote

by 0)l2<1 the fraction of 2’s investment that is embodied in the widget-

making machine (perhaps 2 has made some improvement to the speed or

reliability of the machine) and similarly denote by 0)l1<1 the fraction of

1’s investment that is embodied in the machine that produces the final

product.So,intheeventthatteamproductiondoesnottakeplace,manager

1 has ‘access’ to investment l2e2of manager 2, and similarly for manager 2.

Parameters l1;l2are crucial in what follows.

Now suppose that team production does not take place. If 1 owns both

machines,hehasthreeoptions.First,hecanbuyastandardwidgetatpricep

and produce final output. Second, he can produce a standard widget with

machinea2,anduseitinconjunctionwitha1toproducefinaloutput.Third,

he can produce his own specialized widget with machine a1, and use it in

conjunction with a2to produce final output.

Denotetherevenuesfromthesecondstageofindividualproductionusing

specialized and standard widgetsby rðe1Þ; ~ r rðe1Þrespectively. Also, fromthe

definitionofl2above,thecoststo1ofproducingaspecializedandstandard

widgetwithasseta2arecðl2e2Þ; ~ c cðl2e2Þ:Itisnaturaltoassumethatrevenue

is higher if aspecialized widget is used, and that such awidget is more costly

to produce (i.e., r>~ r r, c>~ c cÞ, but neither of these assumptions is necessary in

what follows. All we assume is that if 1 owns both assets, he prefers to

produce thespecialized ratherthan thestandardwidget,no matter whatthe

investment levels.14

Second, if 1 has only asset a1, he can only buy a standard widget and

produce the final good using this widget, or remain inactive. Finally, we

suppose that without either machine, agent 1 can produce nothing.15

14Formally, we assume rðe1Þ ? cðl2e2Þ>~ r rðe1Þ ? ~ c cðl2e2Þ; all e1;e2:

15This assumption seems very weak; the discussion in Hart [1995] makes it clear that in the

model, assets are to be thought of as necessary for team production, so we simply assume the

same of individual production.

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Aconvenientsimplifyingassumptionisthat ~ r rð0Þ>p>~ c cð0Þi.e.,itisalways

betterformanager1tobuyastandardwidgetandproducethefinaloutputif

he owns a1, rather than remain inactive, and for manager 2 to produce and

sellthestandardwidgetifheownsa2;ratherthanstayinactive.So,usingthe

above assumptions, the net revenue to manager 1 in these three cases is:

ð3:1Þ

p1ðe1;e2: a1;a2

p1ðe1;e2: a1

p1ðe1;e2: ;Þ ¼ 0

Bysimilararguments,wecanwritedownthenetrevenueformanager2in

theeventthat no team production takes place. Ifhe has no assets, he cannot

produce anything. If he only has the second asset, it is both feasible and

optimal for him to produce a standard widget for sale to the spot market. If

hehasbothassets,hehasthesamethreeoptionsasmanager1didinthesame

case, the only difference being that 2 only benefits from fraction l1of 1’s

investment.Also,weassumethatif2ownsbothassets,hepreferstoproduce

a specialized rather than a standard widget.16So, we have:

f

f gÞ ¼ ~ r rðe1Þ ? p

gÞ ¼ rðe1Þ ? cðl2e2Þ

ð3:2Þ

p2ðe1;e2: a1;a2

p2ðe1;e2: a2

p2ðe1;e2: ;Þ ¼ 0

f

f gÞ ¼ p ? ~ c cðe2Þ

gÞ ¼ rðl1e1Þ ? cðe2Þ

Finally, we assume that r;~ r r are increasing and strictly concave, and c;~ c c are

decreasing and strictly convex, in their arguments.

We now turn to the key issue of spillovers. As remarked above, with

integrated ownership, there are spillovers as long as l1;l2>0, i.e.,

ð3:3Þ

@p1ðe1;e2;a1;a2Þ

@e2

¼ ?l2c0ðl2e2Þ>0;

@p2ðe1;e2;a1;a2Þ

@e1

¼ l1r0ðl1e1Þ>0

On the other hand, with non-integration, there are no spillovers.17When

agent 1 owns only asset a1, he must buy a widget from the spot market at

16Formally, we assume that rðl1e1Þ ? cðe2Þ>~ r rðl1e1Þ ? ~ c cðe2Þ; all e1;e2:

17Of course, it is possible to envisage situations where there are spillovers even with non-

integration.Inoursetting,thiswouldoccurwhentheinvestmentofeitheragentaugmentedthe

productivity of both assets. The main results of the paper extend to this case, because the main

mechanism at work would not change, i.e., an increase in investment by the residual claimant

would still increase the outside option of the other agent by more, the greater the number of

assets owned by the other agent.

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price p, (and similarly for 2) and so the payoff to manager i from individual

production is independent of j’s investment. So, we have the important

observation that in a fully specified model, spillovers are determined

endogenously by the structure of asset ownership.

Finally,notethatwhenl1;l2¼ 0;ourmodelisalmostthesameasthatof

Hart [1995].18More generally, when 0)l1;l2)1, any differences are

superficial, in the sense that the key assumptions made by Hart are also

satisfiedinourmodelundersimple andplausiblerestrictionsontherevenue

and cost functions. The assumptions on P;p1;p2made in Hart-Moore

[1990] and Hart [1995], and also in what follows, are19:

Assumption 1.

ða1;a2Þ 2 A:

Pðe1;e2Þ>p1ðe1;e2;a1Þ þ p2ðe1;e2;a2Þ;

alle1;e2, all

Thisassumption implies thatteamproductionwill alwaystakeplace.For

Assumption 1, it is sufficient that RðeÞ ? Cðe0Þ>rðeÞ ? cðe0Þ; all e;e0: The

justificationforthisisthesameasinHart[1995],namelythatwithindividual

production, manager i no longer has access to J’s human capital.

Assumption 2.@Pðe1;e2Þ

@ei

>@piðe1;e2;a1;a2Þ

@ei

*@piðe1;e2;aiÞ

@ei

*@piðe1;e2;;Þ

@ei

*0; all e1;e2:

This says that the marginal return to investment in individual production is

(weakly)increasinginthenumberofassetsowned,andisalwaysstrictlylessthan

the marginal return to investment in the relationship. Also, at least one of the

weak inequalities in Assumption 2 should hold strictly for the PRT to be non-

trivial. For Assumption 2 to be satisfied, we require that r0ðeÞ*~ r r0ðeÞ*0;

c0ðeÞ)~ c c0ðeÞ)0, i.e., investment by manager 1 has a higher marginal return if

thefinalproductismadeusingaspecializedwidget,andsimilarlyinvestmentby

manager 2 has a higher marginal return if the specialized widget is produced.

Theassumptionsmadesofarimplythefollowingusefulintermediateresult.

Lemma 1. The payoff to individual production piis non-decreasing in the

number of assets owned by i.

This result follows directly from (3.1)–(3.2) and the assumption that ~ r rð0Þ>

p>~ c cð0Þ:

18Thereareonlyinessentialdifferences.InHart,agentsengagedinindividualproductionare

assumed to transact on the spot widget market, whatever assets they own. By contrast, in our

model, (i) when an agent owns both assets, he finds it both feasible and profitable to make the

specialized widget and use it as an input, and (ii) an agent with no assets cannot produce at all.

19Our Assumption 1 corresponds to part of Assumption 2 of Hart-Moore [1990], and

Assumption 2.1 of Hart [1995]. Our Assumption 2 corresponds to Assumption 6 of Hart-

Moore [1990], and Assumptions 2.2 and 2.3 of Hart [1995].

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The order of events is as follows. First, the non-contractible investments

e1;e2are made. Then, once investments are made, agents bargain over the

revenue from team production. Finally, production and consumption take

place.Wesolvethemodelbackwardsintheusualwaytolocatethesubgame-

perfect equilibrium.

IV.BARGAINING

The way in which the revenue from team production is divided up depends

on the assumed bargaining protocol, i.e., the rules of the bargaining game.

One way to think of the two alternatives studied in this paper is to regard

both as bargaining games whose basic structure is alternating-offers. In

GHM,aprotocol is assumed which effectivelytreats p1;p2asinside options.

Thatis,eachagentgetspiperperiodwhilebargainingoverthedivisionofP.

The interpretation of this is that the two agents can engage in individual

production whilst bargaining; this may be an appropriate assumption in

some cases.

In this case, in the limit as the discounting goes to zero, it is well-known

(e.g., Sutton [1986]) that the equilibrium payoff for each party is the inside

option payoff plus half the net gain from trade;

ð4:1Þ

v1ðe1;e2Þ ¼ p1þ1

2P ? p1? p2

?

?

?

?

ð4:2Þ

where we have suppressed the dependence of v1;v2on ða1;a2Þ for

convenience.

Bycontrast,morerecentworkbydeMezaandLockwood[1998]andChiu

[1998] assumes a bargaining protocol where p1;p2are outside options. Here,

it is assumed that agents cannot engage in individual production while

bargaining.Rather,inanybargaininground,therespondermayirrevocably

leave the bargaining process and commence individual production. In this

case, it is well-known (Binmore, Shaked and Sutton [1989], Sutton [1986]),

that in the limit as the common rate of discounting goes to zero, the

equilibriumpayoffsatthebargainingstagemaybecharacterizedasfollows.

Given some arbitrary investment levels (e1;e2Þ; and asset ownership

structure a1;a2

ð

Pðe1;e2Þ

2

v2ðe1;e2Þ ¼ p2þ1

2P ? p1? p2

Þ, say i’s outside option is binding, if

<piðe1;e2;aiÞ

Then, if neither outside option is binding, each manager gets P=2. If 1’s

outsideoptionisbinding,thenhegetsp1,andmanager2getsP ? p1,i.e.,2is

‘residual claimant.’ If 2’s outside option is binding, then he gets p2, and

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manager 1 gets P ? p2, i.e., 1 is ‘residual claimant.’ By Assumption 1, these

are the only possibilities. Let these payoffs just described be written

w1ðe1;e2Þ; w2ðe1;e2Þ:

V. RESULTS ON INVESTMENT AND ASSET OWNERSHIP

We begin with the inside-option case. At date 0, managers 1 and 2choose e1

and e2 respectively to maximize their payoffs net of investment costs,

v1ðe1;e2Þ ? e1, v2ðe1;e2Þ ? e2 (we have set the unit cost of each type of

investment to unity for convenience). Note from inspection of (4.1), (4.2)

and the properties of P;p1;p2that the optimal e1is independent of e2and

vice versa.So, for each asset allocation,by thestrictconcavity ofr;~ r r;R; and

the strict convexity of c;~ c c;C; there will be a unique pair of optimal

investments e?

allocation.

Asremarkedabove,Hart’s[1995]widgetmodeliseffectivelyaspecialcase

of our model without spillovers (i.e. l1;l2¼ 0). In that case, we know that

whenthe payoffs from individual production are inside options, investment

is increasing in the number of assets owned (see e.g., de Meza and

Lockwood, [1998]). This result20extends straightforwardly when spillovers

are introduced.

1;e?

2. Note also that–crucially–e?

1;e?

2depend on the asset

Proposition 1. With inside options, manager 1’s (resp. 2’s) investment e?

(resp. e?

spillovers are present. Moreover, the larger the spillovers l1, l2the lower is

investment by the non-owner under integrated ownership.

1

2Þ is (weakly) increasing in the number of assets he owns, even when

This result shows that the most basic implication of the inside option

bargaining protocol is that asset ownership motivates, and moreover, this

conclusionis robust totheintroductionofspillovers.Notethatthehigher is

l1or l2; the lower is the investment by the non-owner. Intuitively, with a

spillover, more investment by the non-owner simply increases the owner’s

inside option, and therefore his bargaining power, and the stronger the

spillover, the stronger is this loss of bargaining power for the non-owner.

We now turnto thecase ofoutside options. In thiscase, thepayoffs inthe

investment stage are w1ðe1;e2Þ ? e1; w2ðe1;e2Þ ? e1. Contrary to the inside

option case, there is strategic interaction at the investment stage in that

optimalinvestmentfor1dependson2’sinvestmentandvice-versa(deMeza

and Lockwood [1998]). We will assume throughout that there is a unique

pure strategy Nash equilibrium, e?

on a given asset allocation. Building on results of de Meza and Lockwood

[1998],weshowinAppendixBthatasufficientconditionfortheexistenceof

1;e?

2; to this investment game, conditional

20The proofs of all propositions are in Appendix A.

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a unique pure-strategy Nash equilibrium is that if the asset allocation is one

in which an agent’s outside option can bind, at the investment level chosen

when it does, themarginal effectofinvestmenton theoutside option should

be not too different from half the increase in the value of joint production.

This ensures that the discontinuity in the best-response function is not too

great at the boundary at which the agent’s outside option ceases to bind.

Say i’s outside option is binding in equilibrium if in the equilibrium of the

investment game,

Pðe?

1;e?

2

2Þ

<piðe?

1;e?

2;aiÞ

Of course, which, if either, outside option is binding in equilibrium depends

on the asset allocation. We now make one more assumption:

Assumption3.Foreithermanager,thereexistsanassetallocationsuchthathis

outside option is binding in equilibrium.

This is quite a weak assumption. It rules out (i) a trivial case, where neither

manager’s outside option ever binds, in which case asset ownership can

never affect investment, or (ii) the case where the model is highly

asymmetric. Under these assumptions, we can now get the following

general result about the effect of asset ownership on investment:

Proposition 2. Suppose Assumptions 1–3 hold and there are no spillovers

(l1;l2¼ 0).Withoutsideoptions,theinvestmentofeithermanagerisstrictly

higher when he has no assets than when he has two assets, and weakly higher

when he owns no assets rather than one.

This is themost general possible formulationof theidea thatwith outside

options, asset ownership may demotivate. This result consolidates Proposi-

tions4and5ofdeMezaandLockwood[1998],andextendsthemtothecase

of relatively productive outside options21.

Propositions 1 and 2 together indicate that without spillovers, the nature

of alternative payoffs p1;p2ð i.e., inside or outside options) is critical for

whether ownership motivates or not. We now investigate whether, with

spillovers, asset ownership motivates when p1;p2are outside options.

Proposition 3. Suppose Assumptions 1–3 hold and that the return to investment

in individual production is relatively high

?0:5C0ðeÞ; all eÞ. Then, with outside options, when spillovers are sufficiently

ðr0ðeÞ>0:5R0ðeÞ; ?c0ðeÞ >

21This occurs when the marginal product of investment in individual production is at least

half the marginal product of investment in team production. For a more formal definition, see

Section 4 below.

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strong (1 > l1;l2>l0; for some l0<1), the investment of either manager is

strictlyincreasinginthenumberofassetsowned,exceptinthespecialcasewhere

manager i already owns aiand is given ajand initially, j’s outside option is

binding. In this case, manager i’s investment falls.22

So,withspillovers,therathergeneralresultthatinthepresenceofoutside

options asset ownership demotivates is partially reversed; when spillovers

are sufficiently strong, giving additional assets to a manager will strictly

increase that manager’s investment, except in the special case identified in

theProposition.23TakingPropositions1and3together,itfollowsthatifthe

hypotheses of Proposition 3 hold, therefore, the effect of transferring

ownership of additional asset(s) to a manager is usually to induce him to

invest more, irrespective of the precise bargaining protocol.

Can the hypotheses of Proposition 3 all be satisfied, and are they also

consistent with the conditions for existence and uniqueness of pure strategy

Nash equilibrium in the investment game, as discussed above? In Appendix

C, an example is presented which shows the mutual consistency of all these

assumptions.24

Finally, note another novel implication of spillovers. Introducing

spillovers creates the possibility that diversified ownership may be optimal

even with a binding outside option.25Suppose that agent 1 works with asset

a1andagent2withasseta2.Leteachagent’sinvestmentincreasethevalueof

the asset he or she workswith but have no effect on theotherasset. Suppose

initiallythat1ownsbothassetsandheroutsideoptionbinds.Nowasseta2is

transferred to manager 2, but this still leaves 1’s outside option binding.

Since the spillover is eliminated, 2’s investment increases whereas 1’s is

unaffected. Diversified ownership therefore dominates both assets being

owned by manager 1. Were ownership concentrated in 2’s hands it might be

that2’soutsideoptionbinds,inwhichcasehisinvestmentfallsrelativetothe

22Ifspilloversariseevenundernonintegration(investmentbyonepartyaugmentsthevalue

ofthemachineownedbytheother)theexceptionmaynotapply.Thespilloverlowersmanager

i’sincentivewhen owningonly aianddoesnotreduceincentives whenalsoowning aj:None of

the other cases are qualitatively affected by the more general treatment of spillovers.

23Inthisspecialcase,withnon-integration,onemanager’soutsideoptionisbinding(say2’s)

and thus manager 1 is residual claimant. As there are no spillovers with non-integration, the

marginal return to 1’s investment in that case is R0ðe1Þ and is thus as high as it can be. When 1

gets an additional asset (integrated ownership by 1), then 1’s marginal incentive to invest must

fall.

24Ifspilloversoccurevenundernonintegration,thisdoesnotupsetProposition3.Spillovers

havenoeffectifoutsideoptionsarenotbindingundernonintegrationwhilstunderintegration,

all that matters is the total spillovers and not the decomposition across machines.

25In de Meza and Lockwood [1998] it is noted that without spillovers, the agent with a

binding outside option should own all the assets. Notice also that spillovers augment the case

for joint ownership which may now boost the non-owners’ incentives as well as the owners’.

Halonen [2002] has an alternative explanation for joint ownership as the regime which, in a

repeated game framework, maximises the punishment for deviation from efficient investment.

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diversified solution. Whether 1 invests less depends on the effect on team

productivity relative to the impact on his outside option, but whatever

happens to 1’s investment, diversified ownership may be best even though

there is a binding outside option.

VI.CONCLUSIONS

GHM explain the pattern of asset ownership by means of an incomplete

contractingframework.Ownershipmattersforex-anteinvestmentdecisions

becauseofitsinfluenceonex-postbargaining.Theirdetailedanalysisismost

naturally interpreted in terms of the effect of ownership on inside options.

Yet in many instances, it is the threat of outside options being exercised that

drives ex-post bargaining. That is, the consequences of team members’

committing to alternative employment arrangements is the key factor in

negotiations. As ownership enhances a manager’s opportunities, it may

make the threat to break up the team credible, in which case the owner’s

payoffisdeterminedbytheoutsideoption.Theowner’sincentivetoraisethe

value of his own firm is therefore dulled. The striking implication is that

there is certainly one manager, and usually both of them, whose investment

incentives are maximized when no assets are owned.26

This paper shows that the demotivating effect of ownership relies on the

assumption that a manager’s outside option only depends on her own

investments. In many cases this is unrealistic. An owner typically has the

right to continue with a project even if the team dissolves. The investment

thatthenon-ownermadetoenhanceproductivitymaythenbedevalued,but

isnotnormally whollylosttotheproject.Indeed,theleadingexampleinthe

property rights literature, the widget model, naturally exhibits the spillover

propertyunderintegratedownership.Thismatters,forifatleastsomeofthe

worker’sinvestmentis available totheownereven without cooperation, the

bargaining power of the non-owner is weakened, diminishing her incentive

to invest. Moreover, if the owner’s investment is complementary with the

non-humanassets,theinvestmentsshemakesmaybelargelypreservedifthe

teambreaksup.So,intherealisticcasethatspilloversarepresent,theGHM

property that ownership motivates may extend to the case of outside

options.

In the paper we have investigated the case in which investment enhances

nonhuman asset value and shown how this implies that, even with outside

options, it may be appropriate to give ownership to the party whose

investmentmost influencesteamsurplus. This allocationcanalsoarise if,as

is possible, investment decreases asset value. For example, in the skipper-

chef story, investment could involve work on the keel of the boat which

26Anexampleofonemanager’sinvestingmorewhenowningsomeassetsisgiveninfootnote

4. Note that this case violates Assumption 3 so is consistent with Proposition 2.

SPILLOVERS, INCENTIVES AND THE PROPERTY RIGHTS THEORY

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