vankoten_ legal unbundling and auctions in vertically integrated _utility_ markets_ postprint

8/11/2019 VanKoten_ Legal Unbundling and Auctions in Vertically Integrated _Utility_ Markets_ POSTPRINT

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1

Legal unbundling and auctions in vertically integrated (utilities) markets.

Silvester van Koten

Loyola de Palacio Chair, RSCS, !"#, $lorence

C!R%!&!#'

POSTPRINT of European Journal of Law and Econonomics

DOI 10.1007s10!"7#011#$%!$#0

&''p(lin).sprin*er.comar'icle10.1007s10!"7#011#$%!$#0+null

bstract

his aer addresses the e**ectiveness o* auctions and legal unbundling as regulatory measures to

tender a vertically integrated industry more cometitive. Seci*ically, # analy+e i* imlementing

auctions and legal unbundling can counter market oer in an industry here a -ertically

#ntegrated Cororation (-#C) has a monooly osition in an essential, scarce ustream activity and

also ons one o* the *irms active in the cometitive donstream activity. #n an earlier aer, -an

Koten (/11), # shoed that in this con*iguration the -#C, by having its donstream *irm bid more

aggressively, can 0 through increased auction revenue 0 increase its ro*it, hile disadvantaging

donstream cometitors and loering e**iciency. ere # analy+e the regulatory measure o* alsolegally searating the donstream *irm *rom the -#C. # sho that such a measure may only be

artially e**ective2 the -#C can *ormulate a simle comensation scheme that does not violate

restrictions tyically imosed by legal searation but induces the manager o* the -#C&oned

donstream *irm to bid more aggressively. his increases the ro*its o* the -#C, decreases

e**iciency, and disadvantages donstream cometitors.

Keywords: regulation, vertical integration, competition, electricity markets, strategic delegation.

JEL classification code: L22, L43, L!, L"4, L"#.

Corresondence address3 -ia 4occaccio 151, 5/166 $iren+e, #taly. !&mail3 silvester.vankoten7eui.eu,slvstr7gmail.com. el. 869 6:5 ::11 :1: . $a;3 869 /55 :>/.'

C!R%!&!# is a ?oint orklace o* the Center *or !conomic Research and %raduate !ducation, Charles"niversity in Prague, and the !conomics #nstitute o* cademy o* Sciences o* the C+ech Reublic.


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1. In'roduc'ion

his aer addresses the e**ectiveness o* auctions and legal unbundling as regulatory measures

to make a vertically integrated activity more cometitive. # analy+e a setu in hich an unregulated

ustream roducer sells scarce access rightsto a bottleneck netork that connects to a distant,

suer&ro*itable market. he access rights are scarce in the sense that they are in e;cess demand.

he ustream roducer is vertically integrated into a -ertically #ntegrated Cororation (-#C) ith a

donstream *irm (hence*orth @the donstream integrated *irmA) that cometes ith the other

indeendent donstream *irms in the auction *or the scarce access rights. $igure 1 shos the basic

setu.

,i*. 1 -ompe'i'ion for access ri*&'s / independen' and in'e*ra'ed downs'ream firms

Legally SeparatedLegally Separated

Independent

Downstream

Firm

Super-Profitable

Distant

Market

Vertically Integrated Corporation (VIC)Vertically Integrated Corporation (VIC)

Legally SeparatedLegally Separated

Integrated

Downstream

Firm

AccessAccessUpstream

Firm

Bid in auctionBid in auction

n e;amle o* such a setu can be *ound in the !" electricity market.1he ustream roducer

is a netork *irm that oerates an unregulated cross&border transmission line that can e;ort

electricity to a *oreign country. Such transmission lines are called interconnectors. Bonstream

*irms are domestic electricity generation *irms that comete *or access to the interconnector. he

electricity market in such a *oreign country is, *rom the oint o* vie o* domestic *irms, a suer&

ro*itable, e;clusive market hen the e;ected clearing rice is high and the interconnector

caacity scarce. here is indeed a dramatic shortage o* interconnector caacity beteen the !"

countries, hich, most o* the time, revents rice convergence beteen di**erent !" countries

(!uroean Commission //>2 !uroean Climate $oundation /1/). s a result, access rights *or

e;ort on the interconnector mostly have a ositive value. !lectricity generators may also be able to

roduce *or a domestic donstream market here they do not need to obtain scarce access rights to

1his art dras on -an Koten (/11) and -an Koten and rtmann (//=), here a more detailed account can be

*ound.


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interconnector caacity, but instead to gain access to a regulated national transmission netork. Dy

analysis does not address the allocation o* caacity on national lines. $or such analysis see, amongst

others, -ickers (1995), 4iglaiser and Be%raba (//1), E*ler and Kran+ (//>), and $oros, Kind F

SGrgard (//>)..

4ecause o* the shortage o* interconnector caacity beteen the !" countries, ne !" las

allo *irms, conditional on aroval by the national regulators, to build and oerate unregulated

interconnectors *or ro*it. Such *or&ro*it lines are called merchant interconnectors. !" las ill

robably in most cases reHuire merchant interconnectors to allocate caacity non&discriminatorily

(!uroean Commission //:, art. 19 and art. 6:2 //92 CR! /1/, .:). n auction is the most

straight*orard manner by hich to imlement a non&discriminatory allocation o* caacity in the

electricity industry (!R%!% //9). t the moment, not many merchant interconnectors have been

built yet, but robably many more ill be built in the *uture, esecially by cororations that are alsoactive in electricity generation (de auteclocHue and Rious //92 -an Koten /11). s a result, a

vertically integrated cororation may on a merchant interconnector (the ustream roducer) and

an electricity generation *irm (the donstream integrated *irm), and thus be cometing in an auction

*or access to its on interconnector (the scarce ustream good).

4urkart (1995) and -an Koten (/11) sho that in such an auction the donstream integrated

*irm ill bid more aggressively, leading to ine**icient and discriminatory outcomes. he integrated

*irm is more likely to in the auction and the ro*itability o* the cometing donstream *irms is

decreased. -an Koten (/11) shos that the legal unbundling o* the ustream roducer, hile

guaranteeing that the auction is *air, does not remediate the negative e**ects o* ine**iciency and

discrimination. he negative e**ects are caused by the donstream integrated *irm ma;imi+ing the

?oint ro*it made by itsel* and the ustream roducer, and thus bidding more aggressively to

increase the auction revenue. # there*ore e;amine the e**ectiveness o* an additional remedy that

aims to neutrali+e the incentive o* the donstream integrated *irm to bid more aggressively3 the

remedy o* legally searating the donstream integrated *irm *rom the -ertically #ntegrated

Cororation (-#C) that ons both the ustream roducer and donstream *irm.# use legal

searation as seci*ied in the !" (!uroean Commission //9, article 1:). Ihile the -#C retains

the onershi o* the donstream integrated *irm, and is thus the residual claimant o* its ro*it, it is

not alloed to intervene in the day&to&day decision making o* the donstream integrated *irm. nd

hile the -#C has the right to eriodically (e.g. bi&annual) set er*ormance criteria and bonus

Legal searation is sometimes also called legal unbundling.


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schemes, these criteria and schemes may deend only on the outcomes o* the donstream *irm (and

not on the outcomes o* other J ustream J activities o* the -#C). 6

he assumtion that legal searation can be en*orced by the regulator and that the -#C can thus

be revented *rom giving day&to&day instructions to its a**iliated donstream *irm is central to this

analysis. #* legal searation cannot be en*orced, then the -#C can instruct the donstream *irm

directly to ma;imi+e the total -#C ro*its. Such a setting has been analy+ed in -an Koten (/11).

oever, legal searation o*ten *igures as a olicy measure, hich suggests that 0 at least in olicy

circles 0 there is a strong belie* in its e**ectiveness. his study may also be o* value to those ho

are more sketical o* the e**ectiveness o* legal searation, as the results sho that eveniflegal

searation can be en*orced, it ill likely not be very e**ective3 he -#C has alternative ays to

in*luence its a**iliated donstream *irm to act in a ay that aro;imates the ma;imi+ation o* the

-#C ro*its.Ihen intervention in day&to&day decision making is outlaed, the -#C must delegate decision

oer to the manager o* the no legally indeendent donstream *irm. he -#C can, hoever, still

in*luence the managers decisions by setting an e;&ante comensation scheme. he literature on

strategic managerial delegation has shon that hen an oner must commit to a comensation

scheme, he has incentives to set the comensation *or his manager as a linear combination o* ro*it

and revenue (-ickers 19=52 $ershtman and udd 19=>2 Sklivas 19=>). # modi*y such a

comensation scheme *or use in an auctions setting and sho that it ould be ro*itable to o**er this

comensation scheme to the manager o* the legally searated donstream *irm.:he comensation

scheme # consider resects the legal indeendence o* the donstream *irm2 comensation is based

on er*ormance indicators o* the donstream *irm only. # assume that the other cometing

indeendent donstream *irms are ma;imi+ing ro*its, as their oners are not able to commit

credibly to a comensation scheme other than that o* ma;imi+ing ro*its.

!arlier aers e;amine the e**ects o* the vertical integration o* an ustream monoolist ith a

*irm in the cometitive donstream market. -ickers (1995), 4iglaiser and Be%raba (//1),

Mystein, Kind and SGrgard (//>), and E*ler and Kran+ (//>) e;amine the e**ect o* the ustream

rice on outcomes in the donstream market. utcomes in the donstream market are determined

by Cournot cometition (-ickers 19952 Mystein, Kind and SGrgard //>), by cometition on a

otelling line (4iglaiser and Be%raba, //1), or are J *or ma;imum generality J le*t unseci*ied

(E*ler and Kran+ //>). Mystein, Kind and SGrgard (//>) assume that a non&discrimination

6his is a realistic reHuirement3 the !uroean Commission, *or e;amle, insects hether er*ormance schemes *or

managers in legally searated electricity and gas netork comanies (both ustream activities) are indeendent o* the

other activities o* the -#C (%Nme+&cebo F Pombo bogados, S.L. and Charles Russell LLP, //5, 5 &>).:#t is ossible to consider more general *orms o* comensation schemes, e.g. non&linear ones, but the comensation

scheme under consideration su**ices to sho that the holding comany can increase its ro*its this ay. Doreover,linear comensation schemes seem to be idely used (Bi;it, //).


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regulationcould a**ect the internal organi+ation o* the integrated donstream *irm in such a ay

that the donstream *irm acts as i* it ere an indeendent *irm that *aces the same net costs o*

urchasing the ustream inut as other donstream *irms. Mystein, Kind and SGrgard (//>) do not

seci*y the mechanisms that imlement non&discrimination and ho these mechanisms may a**ect

or interact ith the behavior o* the *irms. #n contrast, # e;amine the seci*ic mechanisms o* legal

searation3 outlaing day&to&day instructions and reHuiring comensation schemes to be based on

the er*ormance o* the donstream integrated *irm only, and # sho ho these mechanisms may

interact ith the behavior o* the -#C and the donstream integrated *irm.Legal searation is the

most rigorous remedy J short o* onershi searation J*or imlementing non&discrimination.

#n the above aers, it is sho that the e**ect o* vertical integration is that donstream

integrated *irms have a cost advantage over their indeendent cometitors. Ihen urchasing the

ustream inuts, donstream integrated *irms *ace a net cost eHual to the (lo) marginal cost o*roduction and not the higher regulated rice. s a result o* this cost advantage, donstream

integrated *irms roduce more than their indeendent cometitors. Dy aer is similar in that it is

shon that the donstream integrated *irm, due to the vertical integration, does not *ace the same

net costs as other *irms hen buying the ustream inut. #n the above aers, outcomes *or the

ustream market are trivial3 the rice o* the ustream inut is given e;&ante by a regulator and the

ustream inut is in abundant suly3 he *ocus o* the analyses in the above aers is on the

outcomes in the donstream market. #n contrast, my *ocus is on outcomes in the ustream market.

he rice o* the ustream inut is determined by the cometing donstream *irms bidding in the

auction. # *urther assume that the donstream *irms *orm a rational e;ectation o* the rice in the

distant, suer&ro*itable market and that they have the same e;ectation o* the rice. he rice in

the distant, suer&ro*itable market is determined in a rational ay, taking in account the e;tra

suly resulting *rom the bottleneck netork. $or ease o* e;osure, # ill assume that is done by

er*ect cometition. #n the e;amle o* merchant interconnectors, the rice in the *oreign country

(the distant, suer&ro*itable market) is determined by cometition among the *oreign donstream

roducers, taking into account the given, *i;ed imort o* electricity over the interconnector. See

osko and irole (//5) *or an e;amle o* such a setu. hese assumtions ensure that both

donstream *irms ill value access to the distant market and ill thus make ositive bids in the

auction *or access.

he comensation scheme # use *or the manager o* the donstream integrated *irm J a linear

combination o* ro*it and revenue J as originally roosed by -ickers (19=5), $ershtman and

udd (19=>) and Sklivas (19=>) and is here modi*ied *or alication in an auctions setting. #n

-ickers (19=5), $ershtman and udd (19=>), and Sklivas (19=>), the incentive *or the -#C to o**er

his manager a comensation scheme is to create a strategic interaction e**ect. his e**ect is absent in


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) also aly the strategic delegation *rameork o* -ickers

(19=5), $ershtman and udd (19=>), and Sklivas (19=>) and assume that oners o* all *irms, both

integrated and indeendent, can imlement comensation schemes.5his is, hoever, not a realistic

assumtion. ners may have the incentive to announce a comensation scheme, but they also

have the incentive to secretly instruct their manager to ma;imi+e ro*its. Iithout a commitment

device to @tie their handsA, indeendent *irms cannot commit to a comensation scheme

(Beatriont 19==2 Kat+ 19912 Iilliamson 19=6). he legal searation o* *irms, veri*ied and

en*orced by a regulator, is a commitment device.his assumtion allos me to derive closed&*orm

e;ressions. # *urther assume that a -#C *ully ons the donstream *irm and a art o* the

ustream *irm that organi+es the auction.

o tyes o* bidders articiate in the auction. he *irst is a donstream *irm oned by the

-#C, labeled as integrated bidder -. #n the analyses there is only one, uniHue integrated bidder -.

5# use the term @comensation schemeA, *or comensation schemes ith a strictly ositive eight on revenues. # use the

term @ma;imi+ing ro*itA *or comensation schemes ith a +ero eight on revenues and a ositive eight on ro*its.See -an Koten (/11) *or e;amles o* the !" and "S electricity industry here bidders have randomly distributed

values in transmission caacity. See also SchEne (//9) and Parisio F 4osco (//=).


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he second tye is a donstream indeendent *irm, labeled as indeendent bidder O. Ihen

analy+ing outcomes in the second rice auction, # ill allo *or any number no* indeendent

bidders O. #n the *irst rice auction, hich is mathematically more comle; than the second rice

auction, # ill allo *or only one indeendent bidder O, so as to be able to derive a closed&*orm

solution. he bidding *unction o* integrated bidder - is determined by its manager, re*erred to as

manager -m. Danager -mreceives remuneration according to a comensation scheme set by the

-#C. he other tye o* *irm, O, is indeendent and the *irm oner cannot credibly o**er its manager

(@OmA) incentives that di**er *rom ro*its ma;imi+ation (Beatriont 19==2 Kat+ 19912 Iilliamson

19=6). s a result, the bidding incentives o* a manager @OmA and his *irm O are identical, and # ill

thus not distinguish beteen the to and ill re*er to the indeendent *irm tye as an indeendent

bidder O.

#n line ith the literature, # assume that there e;ists a di**erentiable, strictly increasing biddingstrategy Q$% ( Q&% ), that mas a bidders reali+ed value [ ]/,1$u ( [ ]/,1&u ) into its bid Q$ $% v

( Q&% ).=#t *ollos *rom this that the bidding strategy Q$% ( Q&% ) has an inverse Qv ( Q ) such

that [ ] Q =$ $ $v % u u ( [ ] Q =& & &' % u u ).

he -#C ants to ma;imi+e the ?oint ro*it *rom its donstream and ustream *irms. 4ecause

o* legal searation, the -#C cannot in*luence the day&to&day decision&making o* its integrated

donstream *irm -. #t there*ore o**ers its manager -ma comensation scheme that serves its

interests best, hile resecting the rules *or legal unbundling.9$or the comensation schemes to be

e**ective, it must be credible3 it should be a art o* a ash eHuilibrium.

ne ossibility, as considered by -ickers (19=5), $ershtman and udd (19=>) and Sklivas

(19=>), is to give manager -ma comensation wroortional to a linear combination o* ro*its and

revenue.1/Sklivas (19=>) shos that such a comensation scheme wis eHual to a roortion o* the

revenues minus costs, here the costs are eighted by a *actor a .

=he strategies Q

$% and Q

&% (and their resective inverses Qv and Q' ) are deendent on the onershi share .

$or notational convenience # ill not include the variable @ A in the derivation to *ollo. # allo *or a bidding *unction

Q% to be strictly increasing on an interval /, Qu ith 3 / 1< ) and Sklivas (19=>) considered the e**ect o* comensation schemes in the conte;t o* to

cometing *irms ho each have a manager that makes the crucial outut and ricing decisions. hey *ound that, due to

an interactive e**ect, the otimal comensation scheme has a cost eight asuch that a (!(a )!) *or 4ertrandcometition (Cournot cometition)2 the otimal comensation scheme e;aggerates (understates) art o* the costs and

makes the *irms cometing eaker (stronger). he *irms become @*at catsA (@to dogsA) in the sense o* $udenberg andirole (19=:).


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1 ( (1 ) )w i a a *= +

(here is the comensation, is the ro*it, * is the revenue, a is the linear eight, and i

denotes the roortion),

( ( ) (1 ) )i a * c a *= + ,

( )i * ac= .

$rom here on, # ill re*er to *actor a as the cost eight. Setting 1a> gives the manager the

incentive to be more concerned about costs and less about revenue. Such a manager can thus be

e;ected to be less *ocused on e;ansion and more on cost&cutting. #n contrast, setting 1a< gives

the manager the incentive to be less concerned about costs and more about revenue. Such a manager

can thus be e;ected to be more aggressive and more *ocused on e;ansion in the market. $rom this

ersective, normal ro*it ma;imi+ation is the secial case here the cost eight is set eHual to

unity3 1a= .

Proortion i is determined endogenously in the model. s the e;ected comensation *or

manager -mmust eHual his reservation age /w , roortion iis determined by

/! Q ! ( )Q= =w i * ac w . #n an auction, the costs and returns are e;ected values that are

endogenously determined by the bids. #n this case, the e;ected comensation *or manager -mis

( )! Q Q= $ $ $w i ' % u a% . he e;ected value o* the auction, Q$ $% u , corresonds to the revenue11

and the e;ected ayment, Q$ $' % a% , is the e;ected cost o* reali+ing the @revenueA.

2. Resul's

2.1 Second#price auc'ions

#t is a ell&knon result that in second&rice auctions, bidders have a eakly dominant strategy

to set their bid eHual to their value, regardless o* the number o* bidders in the auction or their

bidding strategies (e.g., see Krishna, //). here*ore, the indeendent bidders O ill bid their

values. Danager -m

e**ectively only ays roortion a o* his bid, and thus set atimes his bid eHual

to his value3 =$ $a% u . s a result, -mill thus bid Q $$ $

u% u

a= . Proosition 1 summari+es the

result.

Proposi'ion 1(+n a secondprice auction wit- n! %idders, of w-ic- n are independent and one is

integrated, t-e independent %idders %id t-eir values, Q =& & &

% u u , and t-e integrated %idder %ids

11Ie ill see shortly that Q

$' % is the robability o* manager -

minning the auction.


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Proposi'ion %(+n a secondprice auction wit- n! %idders, of w-ic- n are independent and one is

integrated, t-e $+1 sets t-e cost weig-t for t-e integrated %idder eual to ( ) Q 11

= +

nan

,for any

1n

.Proof(ee t-e ppendi'.

Proosition has to interesting imlications. $irstly, note that *or the onershi roortion

( )1

/ 13 Q 1 < < <


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onershi share in the ustream *irm and thus does not receive a share o* the auction outcomes.

he e**ects on auction outcomes are summari+ed by Proosition 6.


integrated and -as cost weig-t ( ) Q 11

= +

nan

, w-ere values are distri%uted independently and

uniformly on 56,!7, t-e independent %idders %id t-eir value, and t-e integrated %idder %ids

Q (1 )1

= +

+ $ $ $% u u

n,for any 1n .s a result, wit- increasing :

a8 9-e e' ante e'pected auction revenue is increasing in .

%8 9-e e' ante e'pected profit of t-e $+1 is increasing in .

c8

9-e strategic profit, t-e increase in profits relative to not setting a cost weig-t, is increasing in .

d8 9-e e' ante e'pected profit ofi

& is decreasing in . 9-e relative loss in profit for eac-

independent %idder is increasing in .

e8 9-e e' ante efficiency is decreasing in .

Proof(ee t-e ppendi'.

Ihen the onershi share increases, the auction revenue increases as ell (Pro. 1a). otably,

*or an auction ith to bidders (thus ith one cometing indeendent bidder), the auction revenue

is eHual to :1

+ , hich is shon belo to be di**erent *rom auction revenues in *irst&rice auctions.

lso, the total ro*it o* the -#C (the ro*it o* its donstream *irm lus its share o* the auction

revenue) increases (Pro. 1b). lso the strength o* the incentive *or - to bid more aggressively

increases.16he strength o* this incentive, hich # call the @strategic ro*itA, is the relative increase

in ro*its by setting the otimal cost eight. #t can be calculated by taking the di**erence in ro*its

beteen using a strategy o* ma;imi+ing total ro*its (donstream *irm ro*its and times auction

revenue) and o* using a strategy (hich # call the naUve strategy) o* ma;imi+ing the ro*it o* only

the donstream *irm. he ro*it o* indeendent biddersi

& decrease2 they are less likely to in,

and i* they in, they ays a higher rice (Pro. 1c). he e**iciency o* the auction decreases2 no, in

some cases, - ins ithout having the highest value (Pro. 1d).

16his is an imortant indicator *or e;ternal validity o* the model2 e;erimental evidence has shon that the strength o*

incentives is imortant *or theoretical redictions to sho in real settings (ertig and rtmann, //1) .


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1

,i*. 2 Ou'comes in second#price auc'ions wi'& one independen' idder

Pro*it loss *or indeendent bidderPercentage increase in auction revenueStrategic (e;tra) -#C ro*it as a ercentage o* @naUveA total ro*its

Loss o* e**iciency as a ercentage o* total e**iciency ,ithout o,nershiintegration.

0.2 0.4 0.6 0.8 1

10

20

30

40

50

Disrimination against t!e

independent bidder "derease in

profit#

Strategi profit $I%

&ffiieny loss

Inreased aution re'enue

$igure 6 shos the e**ect o* onershi share on auction outcomes hen the integrated bidder

cometes ith one indeendent bidder. here is a considerable e**iciency loss,1:u to


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,i*. 6 Ou'comes in second#price auc'ions wi'& 1 % 2 6 and independen' idders

a Discrimina'ion profi'

(

)

1

*

0.2 0.4 0.6 0.8 1

10

20

30

40

50

price effec'

(

)

1

*

0.2 0.4 0.6 0.8 1

5

10

15

20

25

Relative loss in ro*it *or eachcometing indeendent bidder O

#ncrease in rice (auction revenue)

d Incen'i8e for a**ressi8e iddin*

(

)

1

*

0.2 0.4 0.6 0.8 1

2

4

6

8

10

c Inefficienc/

(

)

1

*

0.2 0.4 0.6 0.8 1

1

2

3

4

5

6

7

Strategic ro*it -#C Loss in e**iciency

$igure : shos that e**ects are strong *or lo numbers and converge to +ero hen the number

o* indeendent bidders goes to in*inity. he discrimination e**ect o* integrated onershi is

remarkably strong. %rah (a) shos the loss in e;ected ro*its *or each cometing indeendent

*irm, hich can be as high as 5/V. Iith to cometing indeendent *irms, each o* them has a

decrease in ro*its o* u to 66V. !ven ith as many as three cometing indeendent *irms, each has

a decrease in ro*its o* u to 5V. %rah (c) shos the strength o* incentives *or - to bid more

aggressively, as given by the strategic ro*it as a ercentage o* the naUve ro*it. his can be as high

as u to =.6V ith one cometing bidder, u to :.>V ith to cometing bidders, and u to .=V

ith three cometing bidders. %rah (d) shos the loss in e**iciency, hich reresents a

considerable social loss.

Perentage Perentage

Perentage Perentage


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1:

2.% ,irs'#price auc'ions

2.%.1 T&e 3I- wi'& a firs' mo8er9s ad8an'a*e

$or *irst&rice auctions # restrict the analysis to the case ith one indeendent bidder O. Ihile in

second&rice auctions the imlementation o* a comensation scheme *or manager -m does not

a**ect the bidding o* an indeendent bidder O, this is not so in *irst&rice auctions. he bidding

schedule o* O is a**ected by the comensation scheme *or manager -m, an e**ect # ill call the

@interaction e**ectA. he -#C can use the interaction e**ect to strategically in*luence the bidding

schedule o* O. $or such an interaction e**ect to occur, O needs to kno the value o* the cost eight.

#n the main analysis # ill assume that O is rational and O is thus able to calculate the otimal cost

eight *or the -#C. # ill also assume that the rules on legal searation *orbid the -#C *rom

sreading *alse in*ormation about the comensation scheme. s a result the -#C can be sure that

the comensation scheme it announces is knon and believed by indeendent bidder O2 this givesthe -#C a *irst movers advantage. #t is ironic that recisely legal searation 0 meant to increase

cometition 0 is a means o* credible commitment that gives the -#C a *irst movers advantage.

4elo, # ill rela; these to assumtions.

$igure 5 deicts the timeline o* events in the auction. t time 1, the -#C imlements a

comensation scheme *or manager -mith cost eight a , and O is in*ormed o* its comensation

scheme (or deduces it by calculating the ro*it ma;imi+ing choice o* comensation scheme *or the

-#C). ote that the oner o* indeendent bidder O can only credibly instruct O to ma;imi+e ro*its

(Iilliamson (19=6).1>Danager -m and O, anticiating each others reactions, simultaneously

determine the bidding *unctions Q$ $

% u and Q& &

% u . t time to, -m and O, lugging in their

resective values, determine their bids in the auction and the highest bidder ins.

,i*. " Timeline of )e/ decisions

t1 t

-#C3 he -#C imlements a comensation

scheme ith cost eight a

he -#C, bounded by the rules o* legal

unbundling, sticks to the comensation

scheme as announced in t1

- F O3 Danager -mis in*ormed about cost

eight a . O is in*ormed about cost

eight a (or deduces it). Danager -mand

O simultaneously determine the bidding

*unctions Q$ $

% u and Q& &

% u .

Plugging in their resective values -m

and O determine their bids. he highest

bidder ins the auction.

1>See the endi; *or a numeric e;amle based on the model.


15/36

;

15

%iven the bidding strategy o* O, Q& &% u , - ins the auction hen the bid o* the indeendent

bidder, Q& &% u , is smaller than its bid $% 3

6) Q < & & $% u %

1 < & $ $u % % ' % .

he robability o* - inning the auction is thus QQ$; ' % , hich is eHual to Q$' % , as values are

dran *rom the uni*orm distribution on /,1Q. he e;ected ro*it o* - ith value reali+ation $u ,

bidding $% , is there*ore3

:) ( ) / Q = $ $ $ $ % u % w .

Likeise, the e;ected ro*it o* indeendent bidder O ith value reali+ation u , bidding &% , is

5) ( ) Q = & & & &v % u % .

he e;ected comensation *or manager -mis3

) Q Q

Q Q

= =

$

a ' % a ' %' %

u a% v % a%.

o calculate the reaction *unction o* indeendent bidder O, di**erentiate eHuation < ith resect to

% , set it eHual to +ero and solve *or W Qv % 3

=) Q Q

Q Q

= = &

v % v %v %

u % ' % %.

!Huations > and = *orm a system o* di**erential eHuations that can be solved *or Q' % and Qv % .

*ter taking inverses, this gives us the bidding *unctions o* O and -. Proosition : resents the

result.


16/36

;

1 shos the e**ect o* the onershi share on the bidding *unctions. Ihen /.6 , the

-#C sets the cost eight eHual to one, and O and - bid as in a standard symmetrical auction ith

uni*orm values 1

Q =% u u (the thick straight bidding *unction). $or /.6< - bids less

aggressively, and *or /.6 > more aggressively. O accommodates the bidding o* -.

$igure = shos the e**ect o* integration and legal searation on auction outcomes. he -#C

gains *rom legal searation hen the onershi share is smaller or larger than /.6. Ihen the

onershi share is smaller than /.6, the eaker bidding o* - and O loers the e;ected rice by u

to 1) and

Sklivas (19=>).


19/36

;

19

/.


20/36

;

/

this gives the -#C a *irst movers advantage, hich enables the -#C to take advantage o* the

interaction e**ect as shon above.

nce this assumtion is rela;ed and the -#C is alloed, or otherise able, to rovide *alse

in*ormation about the comensation scheme, the -#C cannot credibly commit to ?ust any

comensation scheme. #n the second ste in the timeline in $igure :, t, the -#C no is able to

change the comensation scheme ith a di**erent cost eight a 2 as a result the -#C has no longer a

*irst movers advantage and the auction outcomes are less *avorable *or the -#C.

# calculate the ash eHuilibrium cost eight by *irst suosing that the -#C announces a

comensation scheme ith cost eight a , and then, assuming that indeendent bidder O believes

the announcement, ma;imi+es its ro*its , Q?E$+0 a ith a (ossibly di**erent) cost eight .

ash eHuilibrium e;ists i* and only i* the -#C announces a comensation scheme ith cost eight

?Ea *or hich ( )R%DO , Q= =?E ?E $+0 a a .

$or any announced comensation scheme ith cost eight a the bidding *unction o* O is3

1 (1 ) 2 Q

(1 )

+ =

& &

& &

&

a u u% u a

a u.

Danager -mthen ma;imi+es his ro*it given the bidding *unction o* O, 2 Q& &% u a , and , hich

results in3

) 2 , Q

(1 )+ =

$ $

$ $

$

u a u % u a a u

.

he -#C then sets to ma;imi+e its comound ro*it3 R%DO ( , Q)= $+0 a .

$igure < shos numerical aro;imations1*or the otimal cost eight Q?Ea as a *unction o*

the onershi share *or *irst&rice auctions ithout *irst movers advantage (also *or *irst&rice

auctions ith a *irst movers advantage and second&rice auctions). he -#C ithout a *irst movers

advantage cannot strategically use the interaction e**ect in *irst&rice auctions and there*ore sets the

cost eight eHual to unity *or no onershi. #nterestingly, the cost eight in *irst&rice auctions

ithout *irst movers advantages is close to the cost eight in second&rice auctions, but loer and

increasingly so hen the onershi share increases.

1# used a Dathematica rogram *or aro;imation. he recise code (ith comments) can be donloaded as a

Dathematica *ile *rom htt3XXhome.cerge&ei.c+XsvkXLegallyYsearated.


21/36

I

1

,i*. $ ,irs'#price auc'ions wi'&ou' firs' mo8er9s ad8an'a*e

0.2 0.4 0.6 0.8 1

10

20

30

40

50

60

Becrease in e;ected ro*its *or indeendent buyer

#ncrease in rice aidStrategic (e;tra) -#P ro*it as a ercentage o* @naUveA total ro*its

Loss o* ,el*are as a ercentage o* total ,el*are ,ithout integration

+ain for t!e $IP

&ffiieny loss

Inreased prie

Disrimination independent

buyer "derease in profits#

$igure 9 shos the e**ects on auction outcomes. ote that a -#C wit-outa *irst movers

advantage receives a negative strategic ro*its *or / /.:< < . Legal searation o* the *irm *rom

the -#C ithout a ban on sreading *alse in*ormation about the comensation scheme becomes a

burden *or a -#C that has a relatively small onershi share o* the ustream *irm. $or higher

onershi shares, the strategic ro*it is very close to that in the *irst&rice auction ith a *irst

movers advantage.

2.2 Re8enue e=ui8alence

he revious e;osition shos that revenue eHuivalence does not generally hold *or these tyes

o* auctions. Restricting the *ocus on markets ith to bidders, o* hich one is indeendent and one

is integrated ith *ull onershi, the auction revenue is aro;imately eHual to /.: in second rice

auctions, to /.55 in *irst&rice auctions ith a *irst moverWs advantage, and to /.5 in *irst&riceauctions ithout a *irst moverWs advantage.

his should not be surrising3 one o* the su**icient assumtions *or revenue eHuivalence,

symmetry, does not hold, and the asymmetry that is introduced in this model, a cost eight, a**ects

the auction revenue di**erent *or di**erent auction *ormats. #n *irst&rice auctions indeendent

bidders accommodate the bidding o* the integrated bidder due to the interaction e**ect, but do not

do so in second&rice auctions.

ne o* the assumtions in the above model is that O is er*ectly in*ormed about the value o* the

cost eight. Rela;ing this assumtion can reinstate revenue eHuivalence3 i* indeendent bidders in

*irst&rice auctions are not in*ormed about the strategic delegation used by the -#C and thus assume


22/36

I

that the integrated bidder ma;imi+es ro*it (a cost eight eHual to unity), then indeendent bidders

do not change their bidding and as a result revenue eHuivalence beteen *irst and second&rice

auctions holds. Proosition < *ormali+es this intuition.

Proposi'ion !( -en independent %idders &i>incorrectly8 %elieve integrated %idder $ to ma'imi@e

downstream profits, and t-is %elief of independent %idders &iis known to $ and t-e $+1, t-en t-e

auction revenue is identical in firstprice and secondprice auctions.

Proof( ee t-e ppendi'.

he bidding behavior o* indeendent bidders in the auction sketched in Proosition < is not

eHuilibrium, and indeendent bidders are likely to udate their belie* and to adat their bidding

schedule to accommodate the aggressive bidding o* the integrated bidder, thus again usettingrevenue eHuivalence.

2.6 Does '&e 3I- wan' le*al unundlin*+

s the analyses in Sections 6.1 and 6. sho, the -#C is alays better o** under legal

unbundling than under onershi unbundling.

he -#C is also better o** under artial legal unbundling (o* only the ustream *irm) than under

legal unbundling (o* both the ustream and donstream *irm), e;cet in *irst&rice auctions hen

onershi share are small. #n second rice auctions the -#C earns the highest ro*it hen the

bidding *unction o* its integrated donstream *irm ma;imi+es the combined ro*its o* its

donstream and ustream *irms (see -an Koten /11), and under artial legal unbundling the -#C

can order its donstream *irm to do so. he -#C cannot order its donstream *irm to do so under

legal unbundling, but instead designs a comensation scheme that motivates the integrated bidder to

choose a bidding *unction that imer*ectly aro;imates such a ma;imi+ing bidding *unction. s a

result, the ro*it o* the -#C is loer under legal unbundling than under artial legal unbundling. $or

the same reason the -#C is better o** ith artial legal unbundling in *irst&rice auctions *or high

onershi shares. he interaction e**ect, hoever, has a small e**ect on ro*its that becomes

ositive hen the onershi share is +ero or very small. #n this case the -#C sets the cost eight

larger than one to make the integrated bidder act as a @*at catA to loer its e;ected ayment hen

it ins the auction. s a result a -#C re*ers legal unbundling hen its onershi share is smaller

than /.16 .

Betermined by numerical arocimation.


23/36

I

6

6. -onclusions

# modeled a -ertically #ntegrated Cororation (-#C) that ons both a monooly ustream *irm

and a donstream *irm in a cometitive market. s the monooly ustream *irm rovides an

essential, scarce inut, the -#C has been *orced by regulation to allocate its roducts or services by

auction. #n an earlier aer, -an Koten (/11), # shoed that a -#C could increase nonetheless its

ro*its by having its donstream *irm bid more aggressively2 hich increases the ro*its o* the

-#C, loers el*are, and loers the ro*its o* cometing donstream *irms. #n the resent aer, #

e;lored in a similar setu to hich e;tent the additional legal searation o* the donstream *irm

*rom the -#C could imrove auction outcomes. Ihen the donstream *irm is legally searated, the

-#C can no longer imlement a comensation scheme to ma;imi+e the ro*its o* the overall -#C.6

oever, the comensation scheme analy+ed in this aer mimics ma;imi+ing o* the total -#C

ro*its to a considerable degree, hile resecting the legal searation. 4y imlementing thiscomensation scheme, the -#C increases its ro*its, increases the auction revenue, decreases

e**iciency and decreases the ro*its o* indeendent donstream *irms.

Dy model suggests that onershi searation is a solution3 once the -#C is not the residual

claimant o* the auction revenue any more, it loses the incentive to have its integrated *irm bid

e;cessively aggressively. lied to the electricity market this remedy imlies outlaing -#Cs to

have their generator *irms bid *or caacity on its merchant interconnectors. nother ossible

remedy is to strictly regulate the auction revenue and revent -#Cs *rom receiving the auction

revenues o* their ustream *irm, and instead use rate&o*&return regulation. lied to the electricity

market this remedy imlies outlaing the building and oerating o* merchant interconnectors by

-#Cs that on generation *irms. lternatively, regulators might *orbid use o* the comensation

scheme. oever, this reHuires regulators to have a very good understanding o* the oerations o*

the donstream *irm2 they have to be able to determine (and, likely, to de*end in court) to hich

e;tent a comensation scheme ma;imi+es the ro*it o* the donstream *irm as oosed to the ro*it

o* the -#C.

". >ppendi?

Proposi'ion %(+n a secondprice auction wit- n! %idders, of w-ic- n are independent and one is

integrated, t-e $+1 sets t-e cost weig-t for t-e integrated %idder eual to ( ) Q 11

= +

nan

,for any

6# assume here that legal searation is e**ective. #n cases here it is likely that violations o* the restrictions imosed bylegal searation go ununished, the -#C can *reely instruct its donstream *irm to ma;imi+e the ro*its o* the -#C. #

sho in -an Koten (/11) that the Hualitative outcomes remain unchanged (the -#C ro*its, el*are and cometingdonstream *irms su**ers).


24/36

:

1n .

Proof(Asing $ for t-e integrated %idder and & for t-e independent %idders, t-e profit function for

t-e $+1 -as %een derived %y $an Koten >26!!8 as:

),

( )

, ins, u , Q Q Pr Q (1 ) Q = + $/ / $ $u an

$+0 u a $ $ a $ $ $ u a $ &m %u % u m % , ith

, Q Pr- insQ !highest bid *rom n bidders T - ins and u Q)

$$ u a $ $ m % a ,

,

nd Q Pr- has highest bidQ

$$u a $&

m % %

+

th th

Pr has (i81) highest bidQ !ndhighest bid *rom n &1 bidders T - has (i81) highest bidQ=

n

i

$ .

9-e form of euation !8 depends on t-e si@e of $u = if $u a euation !8 takes t-e following form:

1) 11,

/ Q

$

n$ $

%n n

$ u a $ $ %m % % n@ @d@ ,

1

1

+=+

n

$

n%

n,

and

16) ( ),

1

1

Q

( 1)(1 )( )Z(1 ) (1 )

( )Z Z (1 )

=

+ !

$ $

$u a

inn n i i $

$ $ $ $ $ i& i %$

m %i i @ @ %n

n% % % % % @d@ n i i %

,

( )

1

1

1 ( 1 )+

= + + n$ $n

n % n n% .

9-us su%stituting Q = $$ $u

% ua

into euation ! and simplifying gives:

1:)1

( ) 11, ( 1)

Q ( ( 1) ( 1 ) (1 )( ))) +

+= + + + +n

$

n n n

$+0 u a / $ $ $ a nv a B n u B nu a n B u .

+f >$u a , t-en manager $ wins wit- pro%a%ility one >as Q 1 DO( )= > >$

$ $ &

u% u %

a

, and as

15)1

1

,/

Q1

> = =

+$n

$ u a $

nm % n@ @d@

n,

t-e e'pected profit of t-e $+1 is t-en:

1 >= =

+$ $n

$+0 u a $ $ $ u a $ $

nu u m % u

n,

9-e e' ante e'pected profit of t-e $+1 is t-us eual to:

1>)1( ) ( ) ( )

, ,/

, Q$ $

an n n

$ $ u a $ $ u a $ a

E a du du > = + ,


25/36

5

( ) ( 1) ( ( 1)) 1 ( )( )( 1)

n a n a n n n

n n

+ + + + + +=

+ +.

Cifferentiating t-e e'pected profit of t-e $+1 to a gives t-e first order condition:

1=)( )

, Q(1 )

6

=

+ + +

n$dE a n nada n n n

.

etting t-e first order condition eual to @ero and solving for a gives:

19) ( ) Q 11

= +

nan

.


integrated and -as cost weig-t ( ) Q 11

= +

nan

, w-ere values are distri%uted independently and

uniformly on 56,!7, t-e independent %idders %id t-eir value, and t-e integrated %idder %ids

Q (1 )1

= +

+ $ $ $% u u

n,for any 1n .s a result, wit- increasing for all 1n :

a8 9-e e' ante e'pected auction revenue,

( )

( ( 1) ) Q

( )( 1)

+ +=

+ +n n nEm

n n, is increasing in .

%8 9-e e' ante e'pected profit of $,( ) ( )

( 1) Q

( )( 1)

+ + + +

=+ +

n

$

n nE

n n,is increasing in .

9-e strategic profit, t-e increase in profits relative to not setting a cost weig-t, is eual to

( )( )

( ) ( ) ( )

1( ) ( )

Q /Q /Q( : )

( 1)/Q /Q

+= + + +

++

n n n

$+0 $+0

n n

$+0

E E m nn n

nE m.

c8 9-e e'pected profit ofi

& , ( )

1 Q

( 1) ( )

+ =

+ +in

&

n

n n, is decreasing in . 9-e relative loss in

profit for eac- independent %idder,

( ) ( )

( )

Q /Q

/Q 1

=

+i i

i

n n

& &

n

& n, is increasing in .

d8 Efficiency,6

( )

< < Q

( 1) ( )

+ + + =

+ +n n n n n

n n

( ) Qn , is decreasing in .

Proof(

a8 9-e e' ante e'pected auction revenue,

( )

( ( 1) ) Q

( )( 1)

+ +=

+ +n n nEm

n n, is increasing in . 9-e e' ante

e'pected payment %y $ is eual to


26/36

,

=

+

= + / /a

n @ @$ $ v a $ v aa aa a

n

Em m d@ m d@

( )11

/ 11

1 1

+

= +

= + + + ! !

a n

@a a a

n

n nd@ d@

n n, >using euation 2 and 48

(1 )

6

+=+ +

n

n n

9-e e' ante e'pected payment %y all & is eual to

1),

( ) +

a/ 11

Q Q

=

+

= @ a

an

& & an

mEm d@ ,

( )

11

/ 1 1

( 1)(1 )( )Z

(1 ) (1 )

( )Z Z (1 )

== +

+

! @

a

ia nn n i i a@ @ @ @ @

a a a a a iia na

i i nn d d@

n i i

,

( 1 )

( 1) ( )

+ =

+ +

n n

n n.

9-us:

) ( ) ( ) ( ) Q Q Q = +

n n n

$ &Em Em Em

(1 ) ( 1 )

6 ( 1) ( )

+ + = +

+ + + +

n n n

n n n n,

( ( 1) )

( )( 1)

+ +=

+ +

n n

n n.

%8 9-e e' ante e'pected profit of t-e $+1,( )

( )

( 1) Q

( )( 1)

+ + + +=

+ +n

$+0

n nE

n n,is increasing in .

9-e relative increase in profits %y setting a cost weig-t is eual to

( )( )

( ) ( ) ( )

1( ) ( )

Q /Q /Q ( ( 1) )( 1)/Q /Q

+= + +

++

n n n

$+0 $+0

n n

$+0

E E m n nnE m

.

Asing euation D,( )

( ) ( 1) ( ( 1)) 1 ( )

, Q( )( 1)

+ + + + + +=

+ +n

$+0

n a n a n n nE a

n n, su%stituting for a

wit- Q 11

=

+a

ngives

( ) ( )

( 1) Q

( )( 1)

+ + + +=

+ +n

$+0

n nE

n n. Cifferentiating to s-ows t-at

( ) Q n$+0E is increasing.

9-e relative increase in profits %y setting a cost weig-t is eual to


27/36

>

( )( )

( ) ( ) ( )

1( ) ( )

Q /Q /Q( ( 1) )

( 1)/Q /Q

+= + +

++

n n n

$+0 $+0

n n

$+0

E E m nn

nE m.

c8 9-e e'pected profit ofi

& , ( )

1 Q

( 1) ( )

+ =

+ +i

n

&

n

n n, is decreasing in . 9-e relative loss in

profit for eac- independent %idder,

( ) ( )

( )

Q /Q

/Q 1

=

+i i

i

n n

& &

n

& n, is increasing in .

9-e e' ante e'pected payment of all independent %iddersi

& is eual to

( )

( 1 ) Q

( 1) ( )

+ =

+ +n

&

n nEm

n n,

>see calculations under a8. Asing symmetry, t-e e' ante e'pected payment of an independent %idder

i& is t-us eual to t-is num%er divided %y n:

( ) ( )1

( 1 ) Q Q

( 1) ( )

+ = =

+ +in n

& n &

n nEm Em

n n

9-e e' ante e'pected gross profit of t-e auction >e'cluding payment8, Q i

ross

&E , for an

independent %idderi

& is eual to1

/ Q Q = i i

ross

& wins & & &E 0 u u du , and

( ) 11 Q (1 ) += i i i in

& wins & & &n0 u u u as t-e pro%a%ility of an independent %idder to win t-e auction is

eual to t-e pro%a%ility t-at -is %id is -ig-er t-an t-at of t-e integrated %idder >w-ic- is t-e case

w-en1

(1 )

+

i& $nv u ), and -ig-er t-an t-at of t-e ot-er n! independent %idders. 9-us

1 Q

6

+ =

+ +iross

&

nE

n n

9-e e'pected profit of an independent %idderi

& is t-us eual to t-e e' ante e'pected gross

profit minus t-e e' ante e'pected payment:

( ) ( ) Q Q Q = i i i

n ross n

& & &E E Em ,

1 ( 1 )

6 ( 1) ( )

+ + = + + + +

n n n

n n n n,

1

( 1) ( )

+ =

+ +

n

n n.

9-e relative loss in profit for an independent %idder is t-en:

( ) ( )

( )

Q /Q

/Q 1

=

+i i

i

n n

& &

n

&

E E

E n.


28/36

=

d8 Efficiency,6

( )

< < Q

( 1) ( )

+ + + =

+ +n n n n n

n n, is decreasing in .

Efficiency is eual to t-e profit of t-e n independent %idders, t-e profit of t-e $+1, and t-e auction

revenue t-at -as not %een received %y t-e $+1:

( ) Q Q Q (1 ) Q = + + in & $+0 nE E Em .

u%stituting for Q $+0

from a8, Qm from %8, and Q i&

from c8 gives:

6 ( )

< < Q

( 1) ( )

+ + + =

+ +n n n n n

n n.

Proposi'ion 6(+n a firstprice auction wit- two %idders, of w-ic- one is independent and one is

integrated and -as cost weig-t a, w-ere values are distri%uted independently and uniformly on

56,!7, t-e %idding functions of & and $ are given %y:

9)

(1 ) Q

(1 )

+ =

$ $

$ $

$

u a u a% u

a u

1/)

1 (1 ) Q

(1 )

+ =

& &

& &

&

a u u% u

a ufor 1a and 1

Q& & &% u u= for 1a= .

9-e ma'imum %id % is eual to)1(

1

a%

+= .

Proof( 9-e conditions t-at t-e inverse %idding functions Q% and Qv % s-ould fulfill are:

238 Q Q

Q Q

= =

$

a ' % a ' %' %

u a% v % a%.,

248 Q Q

Q Q&

v % v %v %

u % ' % % = =

.

;urt-ermore, a solution s-ould fulfill t-e following additional constraint:

28 /Q/Q/ ==y' >a %idder wit- value @ero %ids @ero8.

2D8 1QQ == %y%' , w-ere % is t-e ma'imum %id 1/ a %idder wit- value ! %ids a uniue ma'imal %id8.

*ewriting 28 and 2D8 gives

2F8 Q ( Q ) Q = ' % v % a% a' %

2#8 ( Q 1) ( Q ) Q Q = +' % v % a% a' % v % a%

2"8 Q ( Q ) Q = vy % ' % % v %

368 ( Q ) ( Q ) Q Q = +v % a ' % % v % a' % a% .


29/36

9

dding up 2F8 and 2"8 gives

3!8 ( Q 1) ( Q ) ( Q ) ( Q ) + = ' % v % a% ' % % v % a a%

328 ( Q ) ( Q ) "

=

"

' % % v % a% a%

%

.

+ntegrating 328 over 6 until t-e ma'imum %id % using /Q /Q /= =' v gives

338 = )1()1( %a%a%

348 1 (1 )a% a % a%+ + = .

9-erefore t-e ma'imum %id % is given %y

381

1=

+%

a.

+ntegrating 328 over 6 until % using /Q /Q /= =' v gives

3D8 ( Q ) ( Q ) =' % % v % a% a% .

pplying 3D8 to 28 and 2D8 gives

3F8

)QQ(Q

%

%%'%'%'

= ,

3#8

Q( Q ) Q

=

v % v % a%v %

a%.

Asing !28 su%stituted into t-e condition Q Q 1= =' % v % , 3F8 and 3#8 can %e s-own to -ave t-e

solution:

3"8

Q

1

%' %

% a %

=

+

,

468

Q

1=

+

a%v %

% a %.

9aking inverses gives us t-e optimal pure %idding strategies:

9)

(1 ) Q

(1 )

+ =

$ $

$ $

$

u a u a% u

a u

1/)

1 (1 ) Q

(1 )

+ =

& &

& &

&

a u u% u

a u

for 1a and 1

Q& & &% u u= for 1a= .


30/36

6/

Cifferentiating t-e %idding functions to a gives, for /, 1> a a and / 1< increasing8 in *or /.6> > /.6< 8

Proof(+ first prove t-at t-e optimal cost weig-t, Qa , is decreasing in t-e owners-ip s-are :

Qsign 1

= # $

dad

.

9-e profit function of t-e $+1 is given %y:

( )[ ]( )

1 1

/ Q , Q Q (1 ) ( , ) ( , ) = +

$ $$+0 $ $ $ $ & & & $

' % ua ' % u % a u % a u du du .

Asing t-e a%ove functions, it can %e s-own t-at , Q $+0 a is twice continuously differentia%le for

/, 1>

a a and / 1< a a .

nd t-us Q, Q Q

sign sign 1

= = # $# $

$+0d ada

d da d .

a8

9-e e' ante e'pected auction revenue is increasing in .

9-e %idding functions are strictly decreasing in a, t-us t-e auction revenue

[ ]1 1

/ / Q , Q, , Q= $ $ & & $ & m a


32/36

6

( )

/

6

1 ( )1

Q

1

!=

$+0

aa a a rc1sc-

aw

a

( )6

Q

1 (1 ) rcCsch rcSinh 1

1 1&

=

+ + + ! ! !

a aaa a aa a

.

e8

9-e e' ante efficiency, Q is decreasing >increasing8 in *or /.6> > /.6< 8

9-e welfare as a function of a,

( )6

1 Q 1 (1 ) rcCsch rcSinh 1

1&

= + ! !

a

a a a a aa

,is ma'imi@ed at t-e cost

weig-t 1=a , w-ic- is reac-ed at /.6 and t-us Q is decreasing >increasing8 in *or /.6>

> /.6< 8.

Proposi'ion !( -en independent %idders &i>incorrectly8 %elieve integrated %idder $ to ma'imi@e

downstream profits, and t-e %elief of independent %idders &iis known %y $ and t-e $+1, t-en t-e

auction revenue is identical in firstprice and secondprice auctions.

Proof(+ndependent %idders &i%elieving integrated %idder $ to ma'imi@e downstream profits

implies &i%elieving $ to ma'imi@e a compensation sc-eme wit- a cost weig-t set eual to one.

+ndependent %idders &it-en %id as in t-e symmetrical mode:

1i i& &

n% u

n=

+, and t-e -ig-est %id is eual to

1

n%

n=

+.

9-e $+1 and $ are informed of t-e %idding functions of t-e independent %idders. iven value

$u and %id $% , t-e e'pected profit of $ will %e:

438

1

, Q ( )

n

$ $ $ $ $

n

u % % u a%n

+

= ! .

9-e first part is t-e pro%a%ility t-at $ wins t-e auction= t-is follows from

1

1i i i& $ & $ & $

n n% % u % u %

n n

+< < .

-en u a< , $ wins t-e auction w-en 1 1( 1)i i

$& $ & $

un n nu % u un n n a a+ +< < =

+.

-en u a> , $ %ids t-e -ig-est %id1

n%

n=

+and wins t-e auction wit- pro%a%ility one.

9-e $+1 -as profit function:

1 11

/ / , Q ( (1 ) ( (1 )

1) 1) 1$

a an$ $

u$+0 $ $ $ $ $a

a

u un n n@ a u du u du n@ d@ du

a n a n n

% & = + + ' ( + + + ! ! ) *!!

9-e first two integrals give t-e e'pected profit w-en $ wins t-e auction, t-e first integral w-en

$u a< , t-e second w-en $u a> . 9-e t-ird integral gives t-e e'pected payment of t-e independent

%idders. 9-is is eual to t-e e'pected -ig-est %id of n %idders conditional on $ losing t-e auction

>t-us conditional on $u

anot %eing t-e -ig-est value8. 1alculating t-e integrals gives

1

6/ , Q ( 1/ :(5 ) 9 : )$+0 a a a = + + , and ma'imi@ing t-is function for Qa gives

Q 11

an

=

+, t-e same cost weig-t as in secondprice auctions.

9-e auction revenue is eual to:

1 11

/ / , Q

1) 1) 1$

a an$ $

u$ $ $a

a

u un n n@ m a du du n@ d@ du

a n a n n

% & = + + ' ( + + + ! ! ) *!! .

9-e first two integrals give t-e e'pected payment of $, t-e first integral w-en $u a< , t-e second

w-en $u a> . 9-e t-ird integral gives t-e e'pected payment of t-e independent %idders. 1alculating

t-e integrals and su%stituting Q 11

an

=

+gives

( )

( ( 1) ) Q

( )( 1)

n n nEmn n

+ +=

+ +, w-ic- is identical to

t-e auction revenue in secondprice auctions.

E?ample( a compensa'ion sc&eme for @Aana*er ;B+

+n t-e te't it is s-own t-at owner & will not give its manager incentives different from profit

ma'imi@ing as -e -as no owners-ip s-are in t-e upstream firm running t-e auction. +n ot-er words,

owner & will always provide a compensation sc-eme wit- cost weig-t 1s= . ;or an illustration of

t-is general principle, suppose t-at %ot- t-e $+1 and owner & -ad t-e opportunity to offer t-eir

managers compensation sc-emes and commit to it. ;urt-ermore, t-e $+1 -as full owners-ip of t-eupstream firm and & -as no owners-ip. ssuming t-at t-e optimal c-oices of cost weig-ts for %ot-


34/36

6:

managers are determined simultaneously, owner & would offer cost weig-t 1.:61s , w-ic- makes

%ot- %idders %id less aggressively, and t-e $+1 would offer cost weig-t #/.6/= /.619 [a a < ,

w-ic- makes %ot- %idders %id more aggressively > # [a is t-e cost weig-t t-e $+1 would -ave

c-osen for 1s= 8. 9-e %idding functions of independent %idder & and integrated %idder $ would %e:

(1 ) 2 , Q

( )

+ =

& &

& &

&

s u a u s% u a s

a s u,

(1 ) 2 , Q

( )

+ =

$ $

$ $

$

a u s u a% u a s

s a u.24

9-e ma'imum %id would %e /.5>5% . +n t-is case, t-e profits of & would increase to

# , Q /./>1 /./ = .2

9-e result a%ove can %e generali@ed for any owners-ip s-are -olding of t-e $+1. Gwner &

offers a cost weig-t of 1.6>s w-en t-e owners-ip s-are of t-e $+1 is @ero, and increases t-e cost

weig-t w-en t-e owners-ip s-are of t-e $+1 increases up to a ma'imum of 1.:61s , w-en t-e $+1

-as a full owners-ip s-are.

Gwner & cannot, -owever, credi%ly commit to t-ese compensation sc-emes wit-out a legal

reuirement to pu%licly announce -is compensation sc-eme= -e -as t-e possi%ility to provide a

>secret8 side contract t-at sets 1s= >ma'imi@ing profits8. +ndependent %idder & t-en finds its

%idding function %y ma'imi@ing -is profits, given t-e a%ove %idding function of $= 2 , Q $ $% u a s .

-ile $ would %elieve t-at & c-ooses t-e %idding function 2 , Q & &% u a s as descri%ed a%ove, &

c-ooses instead t-e %idding function:

1 [ 1

( [ )

+

& &

&

u a u

a s u for \/.5 for ]/.1 , Q = > & &a s a s . s t-is deviation is profita%le for

owner &, -im setting 1>s cannot %e part of a ?as- euili%rium.

>c)nowled*men'

# ould like to thank Levent ^elik, Libor Bu_ek, Peter Katu_`k, an Kmenta, homas&livier

Lautier, Samuel Lee, vner Shaked, Sergey Slobodyan and to anonymous re*erees o* the

!uroean ournal o* La and !conomics *or their e;cellent comments. Secial thanks to Birk

:hese *ormulas are obtained by solving :) and a likeise eHuation *or the manager o* allied bidder O ith cost

eights.5

ther interesting auction outcomes ould be that the ro*its o* the holding comany ould *all,/ Q /.56//Holding1ompany a w

//.5


35/36

65

!ngelmann and ndreas rtmann. # am grate*ul *or *inancial suort *rom research center grant

o.LC5: o* the Dinistry o* !ducation o* the C+ech Reublic imlemented at C!R%!&!# and the

Loyola de Palacio chair at the RSCS o* the !uroean "niversity #nstitute.

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