p
a
p
a
p
a
Figure 4 Figure 5dH
pH
dL
pL
pH
pL
p
a
p
a
Figure 1 Figure 2 Figure 3thatconfrontsalowqualit yopp onent quotingpricec. This pro tis(p H
0c)(1+
c0p H
)0a . Thereforesincethe playofthe equilibrium recommendation implies
anull pro t tob oth rms, the condition for nodeviationto H writes as (p H 0c)(1+c0p H )0a0: (7.1)
It follo wsthataseparating equilibrium existsifthe threeconditions (A),(B)
and (7.1) are met by H
.
Noteforfurtherreferencethatthe crossingof (7.1)andofa (p)o ccursexactly
for a value of p H
= 2(1 + c)=3 p 3 H
, the full information price for rm H.
Therefore the full information price mayb e used as a signal if coupled with an
advertising campaign costing a (p 3 H
). In factalso some sligh tly lower prices may
b elong to the admissible region for H
. Recalling formProp osition 2 that when
c< 1=2 the region for whic h signaling with a p ositiv eadvertising exists is
non-empt yand it implies a price in [2c;1], one can easily c heck that condition (7.1)
issatis ed for somecouples (p H
;a ) whenp 3 H
2[2c;1], namely when c<2.
The issue of existence is thereforeresolv ed.
One ma y note, to complete the discussion, that there can exist many (in
general an in nite numb er of) equilibria when the regions as described in the
preceding paragraph are non-empt y. While we do not address here the issue
of selecting among equilibria, it is in teresting to note that solely based on the
c haracterization of equilibria, one can conclude that in some cases equilibria
withoutadvertising donot exist.
Of course, lik e in the case of a monopoly, one can construct b elief systems
thatsustainonlyp o olingequilibria,but sincethefo cus hereisonseparationand
notontheissueofp o oling v ersusseparationwedonot pursueadetailedanalysis
here.
Thesystemofb eliefsin(i)-(iii)sharesafeaturethatismostgeneralingames
with twosignal senders,namely that b eliefs dep end up on what b oth playersdo,
or, inshort, b eliefs are "correlated".
It is p ossible to generate separating equilibria of this game also by using
systems with "uncorrelated" b eliefs. For instance, b eliefs of this typ e assign
probabilit y one of b eing H to any rm playing a strategy that satis es some
conditions(inparticular(A)and(B)),whatevertheotherplayerdo es. Obviously
this impliesthat the observationof a strategy couplelik e( H ; H ) impliesb elief b ( H j H
) =1. This is valid only if ! comprises the state (H,H). It is p ossible
to show that there exist systems of non correlated b eliefs sustaining separating
H
equilibria m ust) the c haracterization in Section 3 ab ov e based up on conditions
(A) and (B). To eliminate the in uence of the value taken by b ( H
j H
) up on
the result that advertising ma y b e necessary, we assume that b ( H
j H
) = 0,
so as to render as large as p ossible the set of situations in whic h a price alone
strategy ofthe typ e H
=(p;0) can work asa signal.
Assume that consumers b eliefs have the follo wing structure. (i) If they
ob-serv ethat no rm uses advertising and that prices are equal to c at b oth rms
consumers b elieve that the state is (H,H). (ii) If only one rm plays H
and if
this satis es (A) and (B) ab ov e, then they b eliev e that this rm is H and the
otherisL, unlessthe other rm also playseither H
, or(0;0)inwhic hcase they
b eliev e that state is (L,L). (iii) An y other strategy couple di eren t from those
contemplatedby (i)and (ii) inducesthe b elief that the state is(L,L).
Formally: (i) (b i ( i j j );b j ( i j j ))=(1;1)if ( i ; j )=((c;0);(c;0)); (ii) (b i ( i j j );b j ( i j j )) = (1;0) if ( i ; j ) = ( H ;x ) with x2= f H ;(0;0)g and with H
satisfying conditions (A)and (B);
(iii) (b i ( i j j );b j ( i j j ))=(0;0)otherwise.
Note that (iii) encompasses the symmetric couple ( H
; H
) so that these
b eliefsimply that condition (A) iswrittenwith b ( H
; H
)=0.
It m ust b e shown now that the equilibrium strategy prescribe that: if the
state is (L,L) then i
and j
are (0;0) at eac h rm; If the state is (H,L) they
are H = (p H ;a ) by rm H and L = (p H =2;0) by rm L, with H satisfying
condition3.2,3.3 andaconditionthatshallb ede nedb elo w; nally,if thestate
is(H,H) they are (c;0)by eac h rm.
First, if the state is (H,L) or (L,H) the strategies played m ust b e H
, and
(p H
=2;0)resp ectively. The b est deviations from equilibrium under the assumed
system ofb eiefs are H
for rm L and (p H
=2;0)for rmH. But thesedeviations
cannotb e pro tablesince H
satis esconditions(A)and (B)ab ov e. This couple
of actionsis therefore acouple of m utualb estreplies.
Second,ifthe stateis(L,L)then theplayofanullpriceandof noadvertising
byb oth rms m ust constitute a couple of b est replies: if a rm deviates to any
other strategy with a p ositiv e price it shall still b e p erceived as L, therefore it
cannot increase its pro t ab ov e zero. Therefore the couple ((0;0);(0;0)) is a
coupleof mutualb est replies.
Itremainstob ev eri edwhetherunderthestate(H,H)thecandidatethatthe
b eliefs prop ose, namely the couple((c;0);(c;0)) is a pair of m utualb est replies.
It is immediate to see that the only p ossible deviation left to either rm by the
b eliefs is the play of strategy H
instead of (c;0). That deviation generates an
Pro ofof Prop osition 1
Pro of: Supp ose that (p;a ) satis es b oth (i) and (ii). Supp ose further that
(p;0) do es not satisfy either one or b oth (i) and (ii). Since (p;a ) satis es (ii)
(1+v0p)(p0c)0a0v+c0 then, a fortiori (1+v0p)(p0c)0v+c 0.
The lowest value of a that can b e associated to p is therefore giv en by (i) and
is (1+v 0p)p 0v a +
. Then, assume = (p;a +
) . By continuity of the
function (1+v 0p)p there exists a price p 0 > p such that (1+v 0p 0 )p 0 = v.
Hence assume the strategy 0
= (p 0
;0), whic h v eri es constraint (i), is used
instead of . Constraint (ii) for 0 writes as (1+v 0 p 0 )(p 0 0 c) 0 v +c
0. Since satis es (ii), for this inequality to b e v eri ed, it is sucien t that
(1+v0p 0 )(p 0 0c)0v+c(1+v0p)(p0c)0v+c0a +
. But this writesas
(1+v0p 0 )p 0 0c(1+v0p 0 )0v 0 (1+v0p)cor(1+v0p 0 )(1+v0p), whic h is true since p 0
> p and since b oth expressions in parentheses are non-negative.
The argumen tapplies also for allstrategies (p,a) with a>v +
and it is therefore
complete. 2
Pro ofof Lemma1:
Pro of: Supp ose that at an equilibrium rm L plays an action 0
di eren tfrom L
whenthestateis(H,L).Byde nitionofaSeparating
Equilibrium rm Lisp erceiv edasL anditsopp onent asH.However,
bydeviatingtostrategy L
,ifitisstillp erceiv edasLwithprobabilit y
one it will play according to its b est reply against H
, and if it is
p erceiv edas L with probabilit yless than one, it will receiv e ahigher
demand thanif it iswith probabilit yone, and itspro t will increase,
therefore, in either case there is no strategy available to rm L that
dominates L
: 2
7. Appendix 2: Existence
The necessary conditions for the existence of a separating equilibrium are
suf- cien t to c haracterize the nature of the signal used, but are not sucien t to
guarantee existence ingeneral. Recall furthermorethat the analysis has b een so
farconcernedonlywith theactionsprescribedinstates(H,L)and(L,H) ,andthe
otheractions haveb een left unsp eci ed.
The presen tSection lls this gap and shows that existence is guaranteed, in
Journalof PoliticalEconom y , 86, pp. 485-503.
[16] Shaked,A.andJ.Sutton[1982]: "RelaxingPriceCompetitionthroughPro
d-uct Di eren tiation". Review of Economic Studies ,49, 3-13.
[17] ShapiroC.[1982]"Consumer Information,Pro duct Qualit y,and seller
Rep-utation", BellJournal of Economics, 13, pp. 20-35.
[18] ShapiroC. [1983]:"Premiumsfor HighQualit yPro ducts as Ren tsto
Repu-tation",QuarterlyJournal of Economics, 98, pp. 659-680.
[19] Sp ence,M. [1973]"JobMark etSignaling",QuarterlyJournalof Economics
87, 355-374.
[20] Tirole, J.[1989]: The Theory of Industrial Organization. Cam bridge, MA,
MIT Press.
[21] Wolinsky,A.[1983],"Prices asSignalsof Pro duct Qualit y",Review of
[1] Bagwell, K. and G. Ramey [1990], "Adv ertisingand Limit Pricing". Rand
Journalof Economics ,19, 59-71.
[2] Bagwell,K.andM.Riordan[1991],"HighandDecliningPricesSignalPro
d-uct Qualit y",AmericanEconomic Review 81, 224-239.
[3] Co op er, R.andT.Ross[1984], "Prices,Pro ductQualities andAsymmetric
Information", Review of Economic Studies 51, 197-208.
[4] Dorfman, R. and Steiner, P. [1954]: "Optimal Adv ertising and Optimal
Qualit y".AmericanEconomic Review , 44, 826-836.
[5] Fudenb erg, D. and J. Tirole [1986], "A Signal-Jamming Theory of
Preda-tion",Rand Journal of Economics 17, 366-376.
[6] Gabszewicz, J. and J-F. Thisse [1979]: " Price Competition, Qualit y, and
Income Disparities".Journal of Economic Theory,20, 340-359.
[7] Kihlstrom, R.and M.Riordan [1984],"Advertising asa Signal", Journal of
PoliticalEconom y94, 796-821.
[8] Klein B. and Leer K. [1981]:" The role of Mark et Forces in Assuring
Contractual Performance".Journal of PoliticalEconom y ,81, pp.615-641.
[9] Martin, S. [1993]: Advanced Industrial Economics. Cam bridge,MA, Blac
k-well.
[10] Matthews,S.A. and D. Fertig [1990],"Advertising Signals of Pro duct
Qual-it y", NorthwesternUniv ersity,CMSEMS D.P. 881.
[11] Milgrom,P.and J.Rob erts [1986],"PricesandAdv ertisingSignalsof Pro
d-uct Qualit y",Journal of PoliticalEconom y94, 796-821.
[12] Nelson, P. [1974],"Advertising as Information", Journal of Political
Econ-om y81, 729-754.
[13] Riordan, M. [1986]: "Monopolistic Competition with Exp erience Go o ds",
QuarterlyJournal of Economics ,90, pp.629-650.
[14] Sc hmalensee,R.:[1972]: TheEconomicsof Advertising.Amsterdam:
is quite obvious, while it is not so in the context of a monopoly. By fo cussing
on the single- rm problem some authors hav e stressed the importance of low
in tro ductory prices as a signaling p olicy (see Sc hmalensee[1978]), while others
hav eattributed more importanceto high-price p olicies as signaling devices (see
Bagwelland Riordan[1991]). The explanation we usehere do es not con ictwith
either those views of low (or of high) in tro ductory prices as signals, although
we stress the importance of advertising componentsof a signaling strategy that
allow a price p olicy to b e a signal 21
. In our example a price higher than the
fullinformation price|whenrev elationissp ontaneous the fullinformation price
itself|ma ysignalwithoutadvertising. Buttherearesituationswhereadvertising
is necessary for prices higher than, equal to, or lower than the full information
priceto separate.
The oldideathat theen tryof new rms mayb edeterredthrough advertising
nds itscounterpartin our model in the idea that signaling through advertising
allows a lower price than signaling through price alone and reduces the mark et
share for the rivals. The low qualit y rm by advertising can use a price low
enough to discourage en try of a rm with a still lower qualit y, while without
advertising the same price cannotdeter the en trants.
This typ e of advertising is most lik ely to continue over time and to vary in
a pro-cyclical fashion, as it is directed not so m uch to separate one incum b ent
from another incum b ent but to discourage, through time, the mimic king from
p otentialen trants.
21
ThesignalingroleofpricesisalsothefocusofWolinski[1983]andCo op erandRoss[1984]. Inthese works,ho wever,some consumersare informedab outpro duct qualitiesor canacquire informationatacost(i.e. thepro ductisasearchgoo d). Thequestiontherestudiedisthenthe extenttowhich equilibriumprices transmitinformation frominformed touninformed agents. Itishighprices thatha vereceivedthemostattentionin thoseworks.
cyclical b ehaviorof demand. Forinstanceassume that the mass of consumers is
M t
wherethesubscripttdenotesadate. Ifadvertisingisusedasanen trybarrier,
then it p ersists; howeverit m ust also varyaccording todemand conditions: the
no-jamming constraintprev enting a op to en terand imitate rm L b ecomes:
p L 2 (p H 0p L 0 v 2 )M t a L : (4.3) As M t
variesalong the cyclesovariesthe minim umamoun tof advertisingof
rm L.
As a conclusion weget that advertising varies pro-cyclically.
5. Concluding remarks onadvertising, signaling, andprice
policy
When advertising is used as an en try barrier, since in that case it is clear that
aprice-alone strategy can always b e mimic kedbyan en trantof lowerqualit y,it
arisesasanaturalequilibriumb ehavior. Whenitisjustusedbyahighqualit yto
separatefroma low qualit yitsrelativ e meritsov era price-alonestrategy should
b e in tuitively explained as they seem to apply for the duop oly and not for the
monopoly case.
Note rst that to obtain separation when one rm is of high qualit y and the
other is of low qualit y the former m ust discourage imitation by visibly wasting
some resources. This can b e done by an abnormal increase (for the case of a
decreaseinpriceseecommentsb elo w)inprice,orbyaddingthe xedcostsof an
advertisingcampaign. A highprice,howeverispainfulintermsoflost customers
that switc h to the rival supplier. This e ect is larger the more elastic is the
rm's demand to the price di erence. For high enough prices if qualit y do es
not command a high premium the high qualit yis out of the mark et and cannot
separate. The qualit ypremium for rm H inour model is higher (in p ercen tage
terms)the loweristhe parameterv. Ahighv inducesalowp ercen tagedi erence
inutility(u H 0u L )=u L =(m0p H +p L )=(v0p L
). Thisaccounts inpart for the
dicult ytoobtainseparation through a highprice and noadvertising when v is
high. By using advertising and an appropriate price together, the high qualit y
rm ma y succeed in discouraging imitation without raising its price to o m uch
ab ov ethat of the rival.
Second, the price of the low qualit y rm at a separating equilibrium is a
decreasing functionof the price of the highqualit y rm (in monopolythis is not
so). Thismeansthatthe lowerthe pricethatisused bythe latterforseparation,
the lower the margins that it can enjoy by imitating the low qualit y rm. This
mak es it easier for the high qualit y to b e discouraged from mimic king the low
qualit y. Also in this resp ect the use of advertising, since itallows areduction in
f L L His m 3 =p H 0p L
0(0: 5)v. The totaldemand addressed tothe two rms Land
0is thereforeequal tom 3
.
Assume then that at state (L,H,0) rm L m ust deter the op with a
(sepa-rating) strategy L = (p L ;a L
). A necessary condition for this strategy to deter
the y er-by-the-nightisthat if this en tersand playsexactly L
it mak esa loss.
The no-jamming constraint prev entinga op fromen tering and imitate rm
L is: p L 2 (p H 0p L 0 v 2 )0a L 0: (4.1)
The R.H.S. in the inequality ab ov eisjusti ed by the factthat the full
infor-mationpriceand pro t of a op iszero. The L.H.S.issimply the pro t of a op
that enters and imitates a rm of typ e L that is playing (p L ;a L ) against a rm H that isplaying (p H ;a H ). If a L
= 0 the y er-by-the-night always nds it pro table to en ter so that
advertising isnecessary for rm L tok eepthe op out 20
. Obviously,anecessary
conditionforthelowqualit y rm toseparatefromthe opthroughadvertisingis
thatbysodoingitmak esapro t higherthanifitaccommodatesthe en tryofthe
y er-by-the-night. The rm L pro t after accommodation is p L 2 (p H 0p L 0 v 2 ).
Andthe price p L
that maximizesthis pro t is equal top `
(1=2)(p H
0v=2). A
deviationfromthe en tryprev entingprice p L thatb elongs to L =(p L ;a L ),top `
en tailsapro tequalto(1=4)(p H
0 v=2) 2
. Thereforeaconditionthat L =(p L ;a L )
m ustsatisfy is that
p L (p H 0p L )0a L >(1=4)(p H 0v=2) 2 : (4.2)
Finally, the b ehavior of rm H m ust assure that rm L do es not want to
imitate rm H inaduop oly,i.e. that p L (p H 0p L )0a H >p L (p H 0p L )0a L (this
againis the no-jamming condition).
The lesson from this second example is that the theory here exposed can
ac-count for (i) low quality rms advertising together with high quality rms, (2)
persistence of both rms advertising over time.
Note that the existence region for high-price and no advertising for rm H
shrinks further if the low qualit y rm advertises. In fact the L.H.S. of all
con-ditions (A) and (B) is lowered by the xed amoun t a L
, so that the incentive
constrainta z
(p) isshifted upward,and therange ofv-valuesthat are largerthan
the ro ot z c shrinks accordingly asa L is increased. 20
Whenthestateis(L,L,0)thetwo rmsoftyp eLcan detertheentryofthethird rmby
usingaprice-advertisingcouple(p LL
;a LL
)satisfyingtheno-jammingconditionp LL 1 3 0 a LL 0 ;
which ensures that entry is not pro table. The two typ e L rms mak e nonnegativ epro ts
providedp LL 1 2 0a LL
0. Clearly, there are man y such couples (p LL ;a LL ), one exampleis (p LL ;a LL )=(v ; v 3
p eriod. Similarly, the rep etition of promotion campaigns on television by some
brands ma y hav e the same function. Furthermore, as it shall b e shown b elo w
p ersistence can o ccur when renownbrandsma yb e inducedto advertiseinorder
todeter the en tryof other rms.
4. Advertising as an Entry Barrier
Assume there is a third rm in addition to the twopreviously considered. This
rm isa pro ducer oflowestqualit y, inthe sense that it can b e one of twotyp es:
L or0, but not of typ e H. Ifa buyer purc hasesthe go o d 0 atprice p 0 she gets a utilit y u 0 =0 p 0
. Tosimplify matters assume that a op can nev erb e mistak en
forahighqualit ypro duct, butitisindistinguishablefromalowqualit ypro duct,
anassumption that could b e relaxed ina more complete v ersionof this game.
To k eep with the approach of short term in teraction, we assume that the
en try, price, and advertising decisions are all sim ultaneously taken. If we had
assumedrep eat purc hase,and a m ulti-p eriod framew ork,itwouldb e p ossible to
modifythe examplehere inorder toconsiderthe b ehaviorof incum b entsagainst
p otentialen trants.
In this game it is common knowledge that there can b e such a pro ducer,
called a " yer-by-the-night", in the sense that ev erybo dy knows that if three
rms are on the mark et one could b e a op and m ust lea ve the mark et after
havingdeceiv edconsumers once. Weshall concen trateonthe asymmetric states
(H,L,0) and those obtained p erm utingthe order of the en tries. Since qualit y H
cannotbyhyp othesisb eimitated bythe op,inthesestatesthe opm ustimitate
the low qualit yif itwantsto en ter. Then if the state (H,L,0) realizes rm L has
toprev entthe op from en tering 19
.
Ifthe typ e0 rmen tersand replicates the strategyof rm Lthen consumers
cannot distinguish whic h rm is L and whic h is the op. Firm H, by contrast
ma yseparatefrom rm L using a strategy that can b e describedanalogously to
whathasb een doneab ov esoastoprev ent rmLfromimitating|forbrevitywe
donot re-state the conditions (A) and (B) for this game.
Note that if the op en ters and imitates rm L, then this rm and the op
are b oth b eliev ed to b e ops with probabilit y 0.5 and will share the demand
addressed to the corresp onding expected qualit y as it shall b e brie y shown.
The consumers know that there is atmost one op, hence their expected utilit y
from buying from one of the two rms that uses the strategy L = (p L ;a L ) is 19
Undertheassumptionthata highqualit ycannotb emistak enwith a op, whenthestate is (H,H,0) the yer{by-the-night cannot enter. If the state is (L,L,0) , under revelation one wouldobserveadv ertisingfromb othlo wquality rms,asitisbrie yexplainedinthefollo wing footnote. Finally, ifthe state is (L,L,L)all rmspla y the Bertrandequilibrium with a price equaltomarginalcost(here zero)andnoadv ertising.
leftpart ofFigure 4,whic hhas b een drawnfora value ofv >2,and of c=0: 25:
thecurv ea (p)isrecognized asstarting fromtheorigin, andA (p)starts fromthe
p oint c, where a y
(p H
) = 0. The two constraints there cross at the p oint where
p H
=2c, and at the p oint wherep H
=1. It can b e shown that for c<1=2 these
crossingso ccurinthe same wayasdepicted inthatgraph 17
,i.e. one has thatfor
p H
intherange[2c;1]theinequalit yA (p)>aholds,whileoutsidethatrangethe
opp ositeinequalit yholds(the righthandgraphin Figure4 hasb een drawnfor a
value of c=0,the valid regionshrinks insize as cis increased formzero to0.5).
It follo ws that in general,for c<1=2, the region to whic ha separating strategy
H
m ustb elong isformed by(i)anon-empt yregionwhereadvertising isstrictly
p ositiv e; (ii) a (p ossibly empt y) region consisting of all p oints on the abscissa
lyinginthe in terval[ v;z(c)]. This prov esthe rst partof the Prop osition.
(Toprov ethe part of the prop osition regarding the case c>1=2 consider Figure
5, whic h has b een drawn under the hyp othesis that c = 0: 7. It is apparent
from Figure 5 that if v > 2, then a separating equilibrium if it exists is giv en
bythe p oint of tangency of A (p H
) and a (p H
). The same situation arises for all
values of c 0: 5, b ecause for these values one can easily c heck that A (p H
) has
a unique maximum at the p oint where p H = 2c, and that at p H = 2c one has a (p H )=A (p H
), sothat the equilibrium H
isunique in these cases 18
). 2
We will nally note that a price couple equal to the full information prices
forthe high and lowqualit ymayb e used ata separating equilibrium if the high
qualit y rm accompanies the full information price byan adequate expenditure
inadvertising. Forinstance, forc=0: 25one has that p 3 H
=5=6 and a=a s
(5=6)
ma yconstitute aseparating strategy H
for H.
The importantfeatureof the resultssofarobtained isthat they,in thesame
lineasforthe monopolycase,establishacharacterizationofequilibria,preceding
acomplete sp eci cation ofb eliefs.
Existence isdiscussed inApp endix 2.
3.4. Persistence
Asitisclear, the plausibilit ythat advertisingm ustb e usedina one-shotset-up,
impliesthatitcanb eusedalsoinsituationswhererep eatpurc haseisnotpresen t.
For instance in the case of the restaurants quoted in the In tro duction. The
luxurious setting of one of two restaurants can b e in terpreted as an ostentation
17
Inparticular,p H
=2 c isthep oin twherea s ;a y ;a z ;allcross; p H
=1 isalw aysone ofthe ro otsof theequationa
s =a
z
,and itisthelargest ro otforc<1 = 2. 18
Whenc = 1 then 2 c = 2 and the p oin t of tangency of the twoconstraints implies that p
H
=2. For c >1 thetwoconstraintsdo nottouch an ymore sinceA(p H
)<0 for c >1,so thattheseparatingequilibriawithadv ertisingdonotexistforthesevaluesofc.
of Figure4 b elo w)and it is de nedby A (p H )=(p H 0c) 10 p H 2 =a y (p H ); (3.10) for p H <2c, andby A (p H )=(p H 0c) 10 p H 2 0 1 2 p H 2 0c =a z (p H ); (3.11) for p H >2c. Notethat a z =a y at p H =2c sothat A (p H )is continuous 15 . Furthermore2c is also a maximum of A (p H ) if p H
> 0: 5. While for c< 0: 5 the maximumis at
the rightof p H
=2c and it coincides with the maximumof a z
(p H
).
The in terplay of the curv es a (p H
) and A (p H
) determines the regions in the
space of (p H
;a ) couples to whic h the separating strategy H
; in state (H,L) or
(L,H),mustnecessarily b elong if a separating equilibrium of the game exists.
Note, to start,that if v <2 strategies in volving azero amoun tof advertising
and that satisfy the constraint derived by condition (A) always exist. If and
onlyifA (p H
) in tersectsthehorizontalaxistothe rightof v 16
, however,thereare
price-alone strategies that also satisfy constraint(B).
For the purp oses of the presen t Section|namely to demonstrate that the
p ossibilit yofadvertisingenlargesthesetofparameterrangesforwhic hseparation
ma y o ccur ov er and ab ov e the range for whic h separation ma y obtain through
prices only|it is sucient to show that, when v > minfz(c);2g, there exist
ranges for the cost parameter c for whic h a strategy H
with strictly p ositiv e
advertising satis esnecessary conditions (A)and (B).
Prop osition 3. For c < 1 and v > minfz(c);2g the only non-trivial separating
equilibriathatma yexistin volveastrictlyp ositiv elev elofadvertisinginthestates
(L,H) and (H,L). Furthermore, for c <1/2 the high qualit y rm has a strictly
p ositiv epro t, while for c 1/2 its pro tsare null but itsmark etshare p ositiv e.
14
Thepro tto rmHiftheequilibrium strategiesarepla yedis
(p0c)d H (p H ;p H = 2)0a=(p0c)(10p H = 2)0a:
ThenconditionBwritesas
(p H 0c) 10 p H 2 0amax 1 2 p H 2 0c ;0 : (3.9)
Therigh thand termiszeroifp H
<2 c, that iswhen rmH wouldmak enegativ epro ts if itdeviatedtothepriceofitsrival,butjustneedstomak enon-negativ epro ts.
15
The functionA coincides with the Min[ a z
;a y
] o ver the relevant range and so it can b e moreeasilyretained.
16
Theconditionisthat thelargestro otofa z (p H ),denotedz(c)= 1 4 (3+2 c+ p 904 c+c 2 ) islargerthanv .(Notethatforallc>0,z(c)>c andthatthero otsofa
y
separation.
In fact if v >2 the only prices that can signal rm H in the state (H,L) are
higher than 2, but then this rm receiv es zero demand as stated in Subsection
3.1 ab ov e, and the equilibrium. The fact that a high value of v destroys the
equilibriawhere price-alone strategies are used can b e in terpreted economically.
Welea vethis discussion howeverfor the concluding Section.
It is now p ossible to ask whether with v >2 advertising can separate where
price-alonestrategiescannot. Letusturnnowforthispurp osetotheimplications
of condition (B).
Note that when rm L playsaccording toits b est reply, ^ p L =p H =2; then the
demand to rm H underfull information is giv enby
d H (p H ; ^ p L )=10p H =2: (3.8) sothat H ( H j L ;1)= (10p H =2)p H :
Notetostart thatthe demandto rmH (andto rmL)instate (H,L)if Hplays
the same strategy as rm L, should ingeneral b e determinedby the b eliefs held
by consumers when the couple ( L
; L
) is observed. However, in the case here
analyzedthe matterissimpli ed byLemma1: sinceL playsaccordingtoitsfull
information b est resp onse to p H
, it is nev erthe case that p L
> v. If b oth rms
playp L
, therefore, allconsumers buy ev enif they think that the state is (L,L),
sothat the mark etis en tirelycovered foranyb elief b ( L
j L
). Therefore,again,
b eliefs are irrelevant here, and the tie is broken as it is customary by assuming
that demand is split inequal parts 13
.
Condition(B)describesafunction,A (p H
),thatde nesthemaximalamoun ts
of advertising consistent with separation. This function lo oks generically as a
quasi-concav e function with a kink at the p oint where p H
= 2c, (see discussion
13
InamodelwhereD L
(p)hasnoverticalsections,butitisdo wnwardslopingwhereveritis p ositiv evalued,thentheassumptionthatb (
L ;
L
)=0wouldpla ytherolethattheassumption b (
H ;
H
)=0pla ysforcondition(A).Thecalculationswouldonlyb ecomelessstraightforward whilethemain conclusionswouldnotb ealtered.
termisthenequaltoD b
1 H
2
0a,wherebrepresen tstheb eliefsheldbyconsumers.
Thenfor p H
>v the condition writes as
(1+ v0p H b ) p H 2 0a p H 2 2 (3.7)
Conditions (3.6) and (3.7) when com bined de ne a continuous function a (p H
),
whic hisconcaveshap edandithasakinkincorresp ondenceofp H
=v,asdepicted
inFigure 3. The graphof the functionto the right of v is shifted, withits piv ot
inthe p oint with co ordinates (v;a (v)),in the rightdirection asb increases from
0to 1. Forb= 0it coincides with the horizontal axis 12 , in fact,p b =v for b= 0 and p b >v for b >0. The function a (p H
) delimits the lower b ound for a in a separating strategy
H
foranygiv en levelof p H
.
Third, and nally, note that the range of prices for whic h a high price and
no advertising strategy can separate is the in terval of prices at the right of the
in tersectionofthe curv ea (p H
) with the priceaxis. Since this in tersectionmo ves
rightwardasb ( H
j H
)isincreased,therangeofpricesthatcanseparatewithout
advertisingislargertheloweristhevalueofb ( H
j H
). Togetthedesiredresult,
thereforeweshallsetb ( H
j H
)=0soasto"considerthelessfav orablecasefor
the necessit yof advertising".
Assumption 2: b ( H
j H
)=0:
Notethat under this assumption the function a (p H
) dep ends onthe value of
b ( H
j H
) only if v < 2, in whic h case it lo ok as in the right graph depicted
inFigure 3, in the opp osite case in fact there is nokink and a (p H )= (p H =2)0 (p H =2) 2
,as depicted in Figure4 b elo w.
A rstconditionforaprice-alonestrategytoworkasasignalisthattheprice
is higherthan v (and in particular higher than p b
if violating Assumption 2 one
had b > 0). Notice inciden tally that such a price may b e higher than the full
information price, in particular it must b e higher than that price if v > p 3 H
=
2(1+c)=3.
Simply lo oking at Figure 3 it is clear that if v is larger than 2 then a
price-alone strategy implies p H
> 2 and therefore it yields zero demand to rm H.
Thenwe can state
12 Formally,leta s (p H )= p H 2 0 p H 2 2 ,forp H <v ,andleta b (p H )=p H 0 b +v 2 b 1 +p 2 H 0 2+b 4 b 1 forp H 2[ v ;p b ],wherep b =(2b+2 v )= (2+b )isthehighestro otofa b (p H
). Then,recallingthat d H =0 forp H 2, a(p H )=a s (p H ) if p H <v ; a(p H )=a b (p H ); if p H 2[ v ;p b ] ; anda(p H )=0ifp>p b .
alone strategies it can b e obtained with a p ositiv elevel of advertising
expendi-tures.
To b egin with, letde nea strategy fora rmas afunction that describesits
c hoiceof action for eac h giv enstate of nature| rms mo vesim ultaneously after
thestate is c hosenbyNature. Anaction isacouple (p;a ) constituted byaprice
anda lev elof xedcost advertising,a , with a0. First,itis useful tostate the
follo wingresult.
Lemma 1: Independen tly of the consumers' system of b eliefs, at a separating
equilibrium of the game rm L inthe state (H,L)plays L =( ^ p L ;0).
Pro of: seeApp endix 1.
Obviouslythis resultgreatly simpli es the analysis. Thestrategy playedby rm
L instate (L,H) is, inthe duop oly example here considered, ^ p L =p H =2 and zero
advertising,or, inour notation, L = p H 2 ;0 .
Let usanalyze the implications of condition (A)for our duop oly example.
If rm L imitatesthe price and advertising usedby rmH then consumers
willformb eliefsb ( H
j H
). It isthen crucialtodeterminethe roleof b ( H
j H
)
for the c haracterization of the separating strategies and to c ho ose the value for
itthat do es not in terferewith the results.
First, giv en b ( H
j H
), then the consumer's utility from buying when b oth
rms use the same strategy is giv enby b ( H j H )u H +(10 b ( H j H ))u L ; that
is,shortening the notation, b (v+m0p)+(10b )(v0p). This implies that the
consumer indi eren tb et weenbuying and not buying is m b = (p0v)=b. So that total demand is D b =1+v=b0p=b if p>v and it isD b =1if p<v 11 .
Second, going back to condition A (no-jamming), for a couple of price and
advertising (p H
;a ), used by rm H , if p H
< v , then all consumers buy one
unit, and demand to eac h rm is 1/2, so that if it plays H rm L has pro t L ( H ; H ;b ( H j H ))= p H 2 0a . Ifitplays ^ p L (p H )= p H 2
(andzeroadvertising)
itmak es pro t L ( L j H ;0)= p H 2 2 . In the case p H
<v,then the valueof p H and of a that satisfy condition A m ustsatisfy
p H 2 0a p H 2 2 ; (3.6)
Note that for p H
> v condition A do es not write as in (3.6) ab ov e, b ecause
demandisnot inelastictopriceasnot allconsumersnecessarilybuy. The L.H.S.
11
NotethatthedemandD b
corresponds todemandD H
ofSection2,whenb=1,andtoD L whenb=0. Whileitselasticpart rotatesdo wnwardasb isdecreasedform1 tozero.
H H
the signal sent by rm H. But it do es not necessarily imply that L is p erceiv ed
as H by consumers: whether on or out the equilibrium path, in fact, observing
H
at b oth rms ma ynot lead to the b elief that with probabilit yone the state
is(H ;H).
These twoprop erties lead, taken in turn, totwo necessary conditions on the
equilibrium strategies. For k;j 2 fH ;Lg , let j ( j ; k ;b ( j j k
)) denote the pay o to rm of typ e
j when (i) playing strategy j
against strategy k
playedby its rival of typ e k,
and (ii) giv enthe inducedb elief on itstyp e b ( j
j k
).
Necessary condition A, whic hma yb e called "no-jamming condition" 9 writes as: (A) L ( H ; H ;b ( H j H )) L ( L j H ;0):
Necessary condition (B) writes as
(B) H ( L ; L ;b ( L j L ) H ( H j L ;1):
Recall again that the analysis is, for the time b eing, concerned with the
prop-erties of the strategies played when the state is (L,H) or (H,L) in a separating
equilibrium. These twoconditions are necessary, forany giv enb elief system
im-plying particular values of b ( H j H ) and b ( L j L ). If it is p ossible to show
thatthe c hoiceof these twovaluesis irrelevantforthe follo wingresults then the
last in uence of b eliefs on the analysis of necessary conditions (A) and (B) is
remo ved 10
.
3.3. Necessary conditions and signaling
The plan of the argumen tin this subsection is the follo wing:
1) We show that condition (A) is most favorable to price-alone strategies when
b ( H j H )=0. 2)Weassumeb ( H j H
)=0andshowthatwithprice-alonestrategiesseparation
cannotalwaysobtain.
9
The term signal jamming is used by Fudenb erg and Tirole 1986, in a context where an informedpla yerma ypreventanotheruninformedpla yerfrom observingasignal.
10
Notethat since H
and L
are byde nition part of a separating equilibrium theyreveal thestate(H,L) or (L,H) andthere is nochoicebut 0 or 1,as it applies,for theR.H.Sin the inequalitiesin (A)and (B).
of the two represen tations is self eviden t. For our conv enience we adopt the
second.
A t rstsightthetaskofde ningb eliefsasafunctionfromcouplesofstrategies
( i
; j
)(four-dimensionalv ectors)tocouplesofprobabilities(b i ( i ; j );b j ( i ; j ))
isformidable. Luckilyitisp ossible toobtainresults thatare b elief-independent,
in the sense that they apply to any system of b eliefs that sustain a separating
equilibrium. Thisexemptsusfromthetaskofjustifyingthec hoiceofaparticular
structure of b eliefs forthe resultsthat shall b eobtained inthe presen tSection.
Let us transform the notation sligh tly so that b i
( i
j j
) denotes the
proba-bilit yassigned to the ev ent that rm i is H when this rm plays i
against the
playof j
by rm j. The notation mak esitclear that rmsare symmetricinthe
sense that for any , one has b i
( j ) = b j
( j ), i.e. that rms are assigned
the same b elief when they play iden ticalstrategies 7
. Even if this is an obvious
prop ert ywe state it formally for convenience:
Prop ert y1: Ifthe rmsadoptidenticalstrategiesthentheconsumersbeliefsassign
to either rm an identical probability of being of high quality.
A(fully)separatingequilibriumisonewhere: (i)b eliefsassignauniquev ector
(b i ( i j j );b j ( i j j
)) toeac h strategy pro le;(ii) the rms playpure strategies
thatleadtoadi eren tactionpro leineac hstate; (iii)b eliefsareconsistentwith
the rms' strategies 8
. Let us pro ceed to the analysis of the strategies ( H
; L
),
that m ustb e playedat a separating equilibrium when the realized state is(H,L)
or (L,H)| the strategies that are played at the other states of Nature do not
a ect the c haracteristicsof ( H
; L
) that are discussedhere.
(A) First, it must b e a prop ert y of any separating equilibrium of the game
that when the state is (L,H) or (H,L) the rm of typ e L must not nd it
convenient to deviate, from the action L
that the equilibrium prescribes,
tothe use ofthe action H
that is prescribed forthe typ e-H rm.
(B) Second, itm ust b e aprop ert y of anyseparating equilibrium that when the
stateis (L,H) or(H,L)the rm of typ eH has no incen tiveto deviate from
the equilibrium prescription H
and use the strategy L
that is prescribed
to rm L.
7
A more stringentsymmetry requirementis that b i ( 0 j 00 )= b j ( 0 j 00 ). Although this restrictionisquitenaturalitisnotnecessaryfortheanalysisherep erformed,aditistherefore notused.
8
Notethatp oin t(i)in thede nitionexcludes partiallyseparating equilibria,i.e. equilibria wheresomebut notallstatesarep o oled. Wearenotin terestedin partialseparationhere.
and it is p
L
=v otherwise. A Nash equilibrium in prices under full information,
with b oth rms enjoying a p ositiv emark etshare 5
, and p ositiv epro ts o ccurs if
the tworeaction functions cross at the p oint (p 3 L ;p 3 H )giv enby (p 3 L ;p 3 H )= 2(1+c) 3 ; (1+c) 3 ! : (3.5)
Whenthecrossingofthetworeactionfunctionso ccursatthisp ointb oth rms
enjoyap ositiv emark etshare(seeFigure2foranexample). Thisisp ossibleifand
onlyif cand v are inthesetS de nedbyS =f(c;v)jc2[0;2];v (1+c)=3g 6
.
It ishenceforth assumed:
Assumption 1 : (c;v)2S.
3.2. Necessary Conditions
Toanalyzetheduop oly caseweshall useamethodologythatparallelsascloseas
p ossible the one traditionally used for the monopoly. First the necessary
condi-tions for separation shall b e determined, then a c haracterization of the
separat-ingequilibriais derived,and nally (in anApp endix) theexistence ofseparating
equilibriais demonstrated.
Unlik e in the monopoly case the consumers observe two couples of
price-advertising strategies, one for eac h rm. There are four states of Nature: (L,L)
designs the state where b oth rm are of typ e L, (L,H) and (H,L) design the
states where one rm is H and the other is L, (H,H) designs the state where
b oth are of typ e H. Let ! denote the set of states that are admissible, here let
therefore b e ! = f(L;L);(L;H);(H ;L);(H ;H)g . A tthe rst stage of the game
Nature c ho osesa state and onlythe two rms observe Nature'smo ve,theythen
sim ultaneouslyc ho ose, at the second stage, their strategies ( i
; j
) : Finally, at
thethird stage, consumers formb eliefs and purc hasefromone or theother rm.
Thereareatleasttwoequivalentwaysofrepresen tingb eliefs. The rstassigns
toanystrategypro le( i
; j
)playedbythetwo rms,iandj,afourdimensional
v ector of probabilities, one for eac h state. The second assigns to eac h strategy
pro le an ordered couple (b i ( i ; j );b j ( j ; i
)) that represen ts the probabilities
5
Weare notin terested to equilibria where only one rmsurvives, for this reason also we ha venotin tro duced xedcostsinthecostfunctions. Notethatintheexampleheretreatedthe lo wqualit y rm at equilibrium alw aysenjoys a p ositiv emark etshare, whilethe high qualit y rmcouldb eoutofthemark etifitscostisto ohigh. Itisthissituationthat weruleout.
6
Thepricep 3 L
isan equilibriumpriceifandonly ifp 3 L (1+c ) 3 v . Thepriceof rmHis higherthanc ifc< 2(1+ c ) 3
, i.e. ifc<2. Furthermore, sincethemarketdemand to rmH at prices (p 3 L ;p 3 H
)is equal to (10((1+c)= 3)), theconditionc <2 also guaran teesthat this b e p ositiv e. Whencethede nition oftheset S inthetext.
3.1. The structure of competition under full information
Beforethe studyof the signaling game describedin theIn tro duction ab ov e, itis
necessarytobrie ypresen tthefullinformationresultsofcompetitioninduop oly.
Assume that the cost conditions are the same as for the monopoly case, again
withoutlossofgeneralit y,assumethatc L
=0. Letthebuyer'sutilityb edescribed
bytheexpressions(2.1)and(2.2)ab ov e. Theconsumerthatisindi eren tb et ween
buyingqualit yHorLhastasteparameterm (p H ;p L )=p H 0 p L ;if0<p H 0 p L <1.
Thenitiseasytoshowthatthedemandtothehighqualit y rmisthecontinuous
functiond H (p H ;p L ) describedby d H (p H ;p L )=minf10p H +min[ p L ;v] ;1g; if p H <1+min[ p L ;v] (3.1) d H (p H ;p L )=0 otherwise.
Notehere thatfor anyvalue of p L , d H (p H ;p L )=0 for p H 2.
Similarly,demand to rm of typ eL is giv enby
d L (p H ;p L )=minfp H 0p L ;1g; if p L <p H ; (3.2) and d L (p H ;p L )=0 otherwise.
The twodemand functionsare depicted inFigure 1.
The reaction function for rm H is describedby the function
^ p H =(1=2)(1+p L +c); if max[c01;0]p L v; (3.3)
if bycontrast p>v , then rm L has zero demand and rm H reaction function
consistsof its monopoly price, that is
^ p H =(1=2)(1+v +c); if p L >v:
Finally,if rm Lquotesapricelowerthan c01then rm Hcannotquoteaprice
equalto (1=2)(1+p L
+c) asthisis lowerthanits marginalcost, thereforewe set ^ p H =c for c01p L .
Similarly,the reaction functionfor rm L is
^ p L = p H 2 ; if p H 2 <v; (3.4)
monopolist has no incentive to deviate from the play of to the play of (v;0)
if the qualit y is high. Note that, as Milgrom and Rob erts[1986] show, although
man y other deviations are p ossible from the equilibrium prescription, the two
deviationsherestatedare generallyregardedascrucial. Infactitisgenerallythe
casethatone can ndasystem ofb eliefsthat supp ortsthe playof instate(H)
and of (v;0)instate (L)if satis esthe two conditions (i)and (ii).
The c haracterization of is usually the fo cus of the analysis, since it c
har-acterizes the typ e of signal used. In general is not uniquely iden ti ed by the
constraints, while these rather iden tify a set of regions in the space of couples
(p;a ) to whic h m ustb elong. In this resp ect the follo wingresult indicates that
the use of advertising is not essentialfor separation.
Proposition 1: Undermonopolyifthereexistsastrategy =(p;a ) witha>0,
thatsatis es constraints(i) and(ii), then there also existsa strategy 0
=(p 0
;0)
satisfying the same constraints.
Pro of: See the App endix.
Note that Prop osition-1 can b e in terpreted as follo ws: the existence of a
separatingequilibrium,undermonopolyandinaone-shotgame,do esnotimpinge
onthe p ossibilit yof advertising;in other terms,the p ossibilit y toadvertisedo es
not enlarge the sp ectrum of circumstances under whic h separation ma y o ccur.
This however do es not mean that advertising can b e excluded on some game
theoretic ground b ecause to do that one needs use of an equilibrium selection
criterion. This isdone in Milgromand Rob erts[1986] who showthat advertising
resists the application of standard re nements criteria onlyif rep eat purc haseis
assumed, and we donot restate the argumen t here.
There isaneconomic reason, however,whyadvertising isnot necessary: itis
more costly to signal through advertising than through price. The pro of of this
statemen t is simple: de ne a (p) = (1+v 0p)p 0v. For any giv en price this
function giv es the minimal amoun t of advertising that is necessary to separate.
Then, maximize the pro t of the high qualit ymonopolist with resp ect to price
and advertising under the constraint that a max [0;a (p)]. This is equivalent
to maximizewith resp ect to p the function 5( p)=(1+v 0p)p0a (p) overthe
in terval p in [0;p a
] where p a
is the highest ro ot of 0 = (1+v 0p)p0v. Since
a (p) is monotone decreasing in p, and since 5 0
(p) > 0 the pro t so written is
increasing inprice, sothat a maximumobtains atp a
with a (p a
)=0.
Sayingitdi eren tly,consideragainthe separationconstraint(i)ab ov e. Since
advertising adds to the costs of a high qualit y monopoly as m uch as it adds to
thoseof alowqualit yitisrelativ elyeasier toimitatethan ap olicyof highprice:
the latter is more costly in terms of lost pro t (unit margin times demand) for
amonopoly of lowqualit y,who pro duces ata lowmarginal cost, than for one of
H
taste parameter, ranging in the unit in terval [0;1], uniformly distributed over
this range so that the consumers p opulation has unit mass. If a consumer do es
not buy her utility is zero. The consumer that is indi eren tb et ween buying or
not ahighqualit y pro ducthas taste parameterm =p H
0v. The demandto the
monopolist of high qualit yunder p erfectinformation is then
D H (p H )=min[1+v 0p H ;1] if 1+v p H , and D H =0 if 1+v p H .
If the go o d is of low quality, then utilit y is assumed to b e in variant with m
and tob e giv enby u L =v0p L : (2.2)
Thereforedemand tothe monopolist of low qualit y under p erfectinformation is
D L =1 if v p L , and D L =0if v <p H .
The p erfect information prices are p m H = maxf(1+v+c)=2;vg and p m L = v
for the high and the low qualit yresp ectively. The case where (1+v+c)=2 v
is of no in terest since then the monopolist has no incen tive to separate when
her qualit y is H. Eliminating this case, then, the full information pro ts are
resp ectivelygiv enby m H =[(1+v0c)=2] 2 and m L =v.
Under imperfect information, assume that consumers know that the
monop-olistma yb e ofone ofthe twoqualities,sothatthere areonlytwop ossiblestates
ofNature, denoted by (H)and (L). Let denote acouple (p;a ) of price and
ad-v ertisingused bythemonopolist. Foranyobservationof the consumers forma
b eliefab out the pro duct qualit y. More preciselya b eliefis de ned asa function
b ()indicatingthe probabilit ythatthe pro duct isofhigh qualit y. Then, giv ena
particular priceand advertising com binationc hosenbythe rm, the consumer's
expected utilit yis u ()=b ()(v+m0p)+(10b ())(v0p),with u ()=u H
if
b ()=1and u ()=u L
if b ()=0.
A separating equilibrium, lo osely sp eaking, is constituted by strategies and
b eliefs with the prop ert y that , say, is playedif the state is H, and L
, say,is
playedifthestateisL,andtheb eliefsaresuchthatnodeviationfromthese
strat-egyprescriptionispro table. Itiswellknownthat applicationofthe elimination
ofdominatedstrategiesimpliesthatataseparatingequilibrium L
=(p m L
;0),and
weshallnotrep eat theargumen there(see Milgromand Rob erts1986). This
im-pliesthat thereare twonecessaryconditionsforseparation,theyare resp ectiv ely:
(i ) (1+v0p)p0av; (2.3)
and
(ii ) (1+v0p)(p0c)0a v 0c: (2.4)
Condition (i)states that astrategy can b e part ofaseparating equilibrium
advertising. In terestingly,this typ eofadvertisingdo es notserv etoseparatefrom
existing rms,but fromp otentialen trants,and thereforewhere observed itmay
b eerroneously ascrib edtootherreasons notdep ending onimperfectinformation
ab outqualit y. Thistyp eofadvertisingp ersistsovertimeaslongasthe threatby
lowerqualit y rms p ersists, anditvariesinthe samedirection asdemand varies,
namelyit variespro-cyclically.
Ourexplanationoftheen trybarrierattributeofadvertisingisnotbasedup on
the e ects on consumers' tastes, as advertising is here purely dissipativ e. It is
in teresting to note that in an article on limit pricing and advertising Bagwell
and Ramey [1988] used price-adv ertisingcouples as informativ estrategies by an
incum b enttosignalits costofpro duction toanen trant. Theyfound thatpurely
dissipativ eadvertising couldnot b e usedas an en trybarrier.
Othermodels (ofrep eat-purchase)thatare relatedtothe studyofexperience
go o ds are the reputationmodels lik eKleinand Leer [1981]andShapiro [1983],
based on the importance of qualit y premia for the inducemen t to a monopolist
to in tro duce a high qualit y instead of a low one (see also Riordan [1986]). In
this resp ect our analysis also has some consequences, inspite of the assumption
we mak ethat the typ es of the rms are c hosenby Nature. Where rms cannot
rely on rep eat purc hase, in fact, a high qualitycan b e in tro duced only if it can
separatefromthe lowqualities.
2. Monop oly in the Absence of Repeat-Purchase
Themainimplicationsoftheanalysiscanb ederiv edviaasimpleexample,already
usedforthe monopolycasebyBagwelland Riordan[1991],and hererearranged,
whereneeded, toin tro ducea v ertically di eren tiatedduop oly 4
.
Consider amark etwhere amonopolistsells ago o d that can b e of qualit yH
or L. Unit pro duction costs are c for the high qualit y and 0 for the low qualit y.
There are no xedcosts of pro duction, although the monopolist can v oluntarily
add a discretionary amoun t of xed cost, a; in the form of wasteful advertising
campaigns. Eachconsumerbuyseitheroneunitornone. Ifthego o d isofqualit y
H the consumer's utilit yafter purc hase is
u H =v+m0p H (2.1) 4
Although several examples exist (see Gabszewicz and Thisse[1979] seminal pap er, and Shak edand Sutton [1981]) we do not ha ve yet a generaltheory of verticaldi erentiation in oligoplyundercompleteinformation. Theauthorsha veworkedoutasetofnecessaryconditions foraduop olytob ede ned asverticallydi erentiated,andha vecheckedthatthemain charac-teroftheanalysiscanb epreservedinthatmoregeneralset-up. Theexp osition,ho wever,then b ecomes mingled to conceptualissues p ertainingto thefull information generalizationofthe verticaldi erentiationmodelsthatdonotaddan yusefulinsigh tswhilethedi erenceb etween ourexplanationofadv ertisingandthetraditionalone b ecomesunclear.
uninformed party, here the consumers, holds ab out the other rm's typ e aswell
asof itsown typ e.
Thisfeatureof b eliefsdo es notdep endonthe numb erofinformedparties|it
is eviden tthat in the job mark etgame of Sp ence [1973]there are man yworkers
but the b eliefs of the emplo yer on the typ e of worker Smith do not take in to
account what worker Jones has sp en t on education 3
. It dep ends rather on the
prop ert y that the pay o (here the pro ts) of an informed play er dep ends up on
what the other playerdo es (e.g. itspricing b ehavior), and on the fact that this
reciprocal dep endence is common knowledge to allplayers.
The pap erpro ceeds asfollo ws. First, inSection2,the problem withone rm
only is in tro duced and the notation established. The main reason for Section
2 rests not up on its novelty but on the need to brie y clarify why in the
ab-senceof rep eat purc hasethe monopolycase is insucien ttoexplain anyformof
advertising,and to pavethe wayfor the remaining Sections.
Section 3, then, constitutes the core of the pap er. Two rms compete, eac h
b eing of one amongtwop ossibletyp es, eac h rm knows itstyp e and that of the
competitor whileconsumers donot observethe realizedstateof Nature butonly
the strategies played by the rms. On the basis of this observation consumers
formtheirb eliefs. Thepurp oseoftheSectionisthatofderivingac haracterization
of separating equilibria that do es not dep end on the b elief system adopted by
consumers. As a method, the approach consists of writing down two necessary
conditionsthatthe strategiesplayedbythetwo rmsm ustsatisfyinthestatesof
Naturewhentheirqualitiesdi er: thesesimply saythatneither rmmust ndit
pro tabletomimicexactlytheb ehaviorof therivalwhentheirtyp esdi er. Only
usingthese twoconditions it isshown that there are cases in whic haseparating
equilibrium, if it exists, must in volve the use of advertising bythe high qualit y
rm if the qualit ytyp es di er. The rst task ofthe presen tresearc his therefore
accomplished inSection 3, since an explanation is providedfor advertising that
do es not impinge onrep eat purc hase.
The issueof existenceofseparating equilibriaissolvedinApp endix2,whic h,
however, do es not dev elop a complete typ ology of p ossible b elief systems since
thisisirrelevantforourresultsanditwouldleadusastrayfromthenon-technical
issues that motivatethe analysis.
In Section 4, the idea that en try ma y b e deterred through advertising is
examined using the results of Section 3. The Section presen ts an extension of
the basic model obtained in tro ducing the p ossibilit y that the duop oly mark et
structure b e contestable by a rm whic h can also b e of two typ es: low and
"very low", and whic h can mimic the b ehavior of a low qualit y. A true
low-3
Similarly,iftheindustryisp erfectlycompetitiv ea rmcannota ectwithitsb ehaviorthe b eliefsthatconsumers holdab outthetyp esoftheother rms. KhilstromandRiordan[1984] modelthereforedo esnotsharethisfeature.
brands of long-established reputation also sp end considerable sums on
advertis-ing. This phenomenon cannot b e explained by Nelsonian theories, unless one
admits a constant in ow of new consumers at eac h p eriod who are unaware of
the qualit y of the brand b eing advertisedand who en ter a rep eat purc hase
pro-cess. Another way out would b e to assume that consumers do not have p erfect
recall|orthatthec haracteristicsofthepro ductsonthemark etc hangefastwhile
purc haseshapp eninfrequen tly 2
. Itseemsdiculttoaccepttheideahoweverthat
themagnitudeofthisin owb elargeenoughtojustifythe largestreamov ertime
of advertisingexpenditures that one observes. Similarly,this typ eof advertising
isnotencompassedbytheexplanationinKihlstromand Riordansince,although
they do not assume rep eat purc hase, rms need to advertise only in the in
tro-ductoryphase.
Third,theempiricalliterature(aswellassomenon-signaltheoriesof
advertis-ing lik eDorfman and Steiner[1954])had long since notedthe relativ e constancy
of the advertising-sales ratio of rms over time (see for instance Sc hmalensee
[1972]). This means inparticular that advertising varies pro-cyclically.
Fourth,invariousmark etswhere rmsofhigherqualit ycompeteagainstrivals
oflowerqualit y,advertising bylowqualit y rmsisconspicuous andsometimesit
compares tothat of the high qualit y rms.
The explanation provided in the presen t pap er encompasses all these four
typ es of advertising and it therefore enlarges the quota of advertising
expendi-tures that can b e attributed to a signaling e ort by rms. Furthermore, quite
surprisingly, the explanation we provide con rms an old idea, namely that high
advertising expenditures can b e used as a strategic en try barrier. It is worth
emphasizing that the en tryprev enting attribute of advertising is derivedin the
presen t pap er without recurring to ad hoc assumptions ab out the in uence of
advertising onconsumers' tastes.
Themodelb elo wabandonsthe repeatpurchase(whic hhowevercouldb e
rein-tro duced at no cost) and the one- rm assumptions. It explicitly considers the
problem of nding separating instrumen tsfor the case where two rms compete
onthe samemark et. Noneofthesetwo rmshas anestablishedreputationbutit
canb e ofhigh orof lowqualit y;thereforethe consumers are confrontedwith the
problemof in terpretingthe price-adv ertisingstrategies of b oth rmsatthe same
time. In terestingsituations ma yarise that donot app ear in the monopoly case.
For instance, a rm ma y try and exploit the consumers imperfect information
by copying the strategy adopted by its rival. This typ e of mimic king b ehavior
is rather di eren tfrom the one to whic hthe signaling literature in economics is
used: in our case, in fact, it is quite obvious that if two rms send the same
signal(whether along oroutside the equilibrium path) then theconsumers must
attribute them the same probabilit y of b eing of a giv en typ e. In other words
2
The 1
explanation of advertising by Nelson [1974] is well known. In a context
whereconsumers rep eatedlypurc haseanexperiencego o d|namely oneofa
qual-it ythatcanb elearnedonlyafterpurc hase|apparentlywastefuladvertising
cam-paignsinduce rational consumers torealize that the advertisedbrands sell a
su-p erior pro duct. Consumers would not re-purc hase the go o d after a rst trial if
it were not of go o d qualit y, and the in tro ductory advertising costs could not b e
reco veredin subsequentp eriods.
Nelson argumen ts|thatapply toanyformofwastefulexpensesby rms and
notjusttoadvertising|restonrepeatpurchase. Alongthoselinessev eralauthors
hav edev elop ed rigorous models to scrutinize the validity of Nelsonian theories
(see among others Milgrom and Rob erts [1986], Sc hmalensee [1982]; see also
Martin[1994]forarecen tsurvey). The limitationintheNelsoniantheoryisthat
it can account only for in tro ductory advertising whic h is terminated after the
pro ductb ecomesknown. Moreover,mostofthe literature considersthe strategic
in teraction among one rm and the p opulation of consumers. Kihlstrom and
Riordan[1984]represen tanexceptionsincetheyconsiderap erfectlycompetitive
industry with free en try, where rms are price-tak ers. They obtain the result
that advertising equilibria can arise also when the in teraction among rms and
consumers is not rep eated, provided the high qualit y rms hav e lower variable
costs than their lowqualit yrivals.
There seems to lac k a uni ed theory whic h can explain sev eral phenomena
relatedto advertising.
First, advertising or other wastefuland observable selling expenses are
com-mon in mark etswhere consumption has a transient nature. Think for instance
tothe ownersofrestaurantsthatcrowdsometouristicareas (thisexampleisalso
inTirole [1989]), who in vestsometimes considerable sums inluxurious settings,
silv er cutlery, numb er of waiters, and the lik e, although they do not expect to
receiv e the same customers rep eatedly. One ma y observe that some restaurants
will sp end money on these items and others will not. However, a theory based
onrep eat purc hase cannotassign an informativ erole tothese expenditures.
1
C-D.Fluet,D epartementdesSciencesEconomiques,Univ ersityofQueb ecatMon treal,CP 8888Succ.A,Mon treal-Queb ec-(Canada),H3C3P8. PaoloG.Garella,Dipartimen todiScienze Economic he,Strada Maggiore 45, 40123 Bologna (Italy), e-mailgarella@boph01.cineca.it.We wish to thank participan ts in workshops at Univ ersitat Autonoma de Barcelona, I.G.I.E.R. (Milano), and Johns Hopkins Univ ersity (Baltimore). F. Forges provided commen ts on an earlierversionbut do esnotsharean yresponsibilityon theremainingerrors. A suggestionby JacquesRobertwasparticularlyusefulat anearlierstage ofthepap er. The nancialsupp ort fromtheQueb ecFundFCARisgratefullyakno wledged.
Claude D. Fluet
University of Queb ec atMontreal
and Paolo G. Garel la Universitadi Bologna Septemb er1995 JELClassi cation : L13, L41 Abstract
The presen tarticle providesa uni edexplanation for sev eralphenomena related
to advertising by rms. (i) Adv ertising without rep eat purc hase of the pro
d-uct, (ii) advertising from established brands, or p ost-intro ductory, (iii) sim
ul-taneous advertising from low and high qualit y rms, (iv) its p ersistence and
pro-cyclicalit y. The explanation is originalb ecause it rests up on oligop olistic
in-teraction. The analysis hinges up on two fundamental results. The rst is that
advertising allows separation when a signal via prices only do es not. The
sec-ondisthatpurelydissipativ eadvertisingcanb eused tostrategically deteren try.
Hence, alink isestablished b et weenen trydeterrence and signaling.
Keywords: Adv ertising,signaling,en trydeterrence,imperfectinformation,
