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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.
Proposi'ion 2(+n a secondprice auction wit- n! %idders, of w-ic- n are independent and one is
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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,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.
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;
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.
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;
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=>).
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;
19
/.
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;
/
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.
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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
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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.
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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).
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:
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 > = + ,
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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
.
Proposi'ion 2(+n a secondprice auction wit- n! %idders, of w-ic- n are independent and one is
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
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,
=
+
= + / /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
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>
( )( )
( ) ( ) ( )
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.
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=
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% .
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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= .
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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
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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-
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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
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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.
!. References
4iglaiser, %., Be%raba, P. (//1). Bonstream integration by a bottleneck inut sulier hose
regulated holesale rices are above costs.*?C Journal of Economics, 6(), 6/&615.
4urkart, D. 1995. @#nitial shareholdings and overbidding in takeover contests.AJournal of ;inance
5/(5)3 1:91&1515.
Consentec (//:). nalysis o* cross&border congestion management methods *or the !" internal
electricity market. vailable at htt3XXeuroa.eu.intXcommXenergyXelectricityXublicationsX .
CR! (/1/). Beliberation o* the $rench !nergy Regulatory Commission dated 6/ Setember /1/on the alication o* article > o* Regulation (!C) o. 1=X//6 dated < une //6 and on
conditions *or access to the $rench electricity transmission grid *or ne e;emt interconnectors.
Beatriont, D. (19==). Commitment through renegotiation&roo* contracts ith third arties.
*eview of Economic tudies, 55, 6>>&=9.
Bi;it, . (//). #ncentives and rgani+ations in the Public Sector3 n #nterretative Revie. he
Journal of Human *esources, 6>(:), .
!uroean Climate $oundation (/1/). Roadma3 ractical guide to a roserous, lo&carbon
!uroe. echnical nalysis. -olume 1. vailable at htt3XX.roadma/5/.eu
!uroean Commission (//:). ote o* dg energy F transort on directives //6X5:&55 and
regulation 1=/6 in the electricity and gas internal market.
!uroean Commission (//>). Reort on !nergy Sector #nHuiry. vailable at
htt3XXec.euroa.euXcometitionXsectorsXenergyXinHuiryXinde;.html .
!uroean Commission, (//9). Birective //9X>X!C o* the !uroean Parliament and o* the
Council o* 16 uly //9 concerning common rules *or the internal market in electricity and
reealing Birective //6X5:X!C. **icial ournal o* the !uroean "nion, L11X55.
!R%!% (//9). !R%!% rinciles3 Caacity allocation and congestion management in natural gas
transmission netorks n !R%!% !valuation o* Comments Paer, Re*3 !/9&%D&/>&/6.
$ershtman, C., udd, K.L. (19=>). !Huilibrium incentives in oligooly.merican Economic *eview,
>>(5), 9>&9:/.
$udenberg, B., irole, . (19=:). he *at&cat e**ect, the uy&dog loy, and the lean and hungry
look.merican Economic *eview, >:(), 6
-
8/11/2019 VanKoten_ Legal Unbundling and Auctions in Vertically Integrated _Utility_ Markets_ POSTPRINT
36/36
ertig, R., rtmann, . (//1). !;erimental ractices in economics3 methodological
challenge *or sychologistsIe-avioral and Irain ciences, :, 6=6&:/6.
E*ler, $., Kran+, S. (//>). Legal "nbundling can be a %olden Dean beteen -ertical #ntegration
and Searation. 4onn !conomic Biscussion Paer o. 15X//>.
Kat+, D., L. (1991). %ame&laying agents3 "nobservable contracts as recommitments. *?C
Journal of Economics, (6), 6/>&6=.
Lauerta, C. //>). he costs o* moving to a er*ect orld3 $orced onershi unbundling in the
natural gas and electricity sectors. he 4rattle %rou, Ltd.
Mystein, $.., Kind, .., SGrgard, .L. (//>). Danagerial incentives and access rice regulation,
European Journal of Law and Economics, 6(), 11>&166.
Parisio, L., 4osco, 4. //=). !lectricity rices and cross&border trade3 -olume and strategy e**ects,
Energy Economics, 6/(:), 1>>5.SchEne, S. //9).uctions in t-e electricity market= %idding w-en production capacity is
constrained. Sringer&-erlag, 4erlin.
Sklivas, S. (19=>). he strategic choice o* managerial incentives. *?C Journal of Economics, 1=
(6), :5&:5=.
-an Koten, S. (/11). Derchant interconnector ro?ects by generators in the !"3 !**ects on
ro*itability and allocation o* caacity. !"# Iorking Paer (RSCS).
-an Koten, S., rtmann, . (//=). he unbundling regime *or electricity utilities in the !"3
case o* legislative and regulatory catureEnergy Economics,6/(.
-ickers, . (1995). Cometition and Regulation in -ertically Related Darkets, *eview of Economic
tudies, .
Iilliamson, .!. (19=6). Credible Commitments3 "sing ostages to Suort !;change.merican
Economic *eview, >6, 519&:/.