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On perfect competition : definitions, usages and foundations

242 pages
Au sommaire de ce numéro : On perfect competition : definitions, usages and foundations / Appropriation in a competitive theory of value / Price takers vs. great numbers : a critique of the Edgeworth-Walras convergence à la Debreu-Scarf / Negishi on Edgeworth on Jevon's law of indifference, Walra's equilibrium, and the role of large numbers : a critical assessment / Edgeworth on competition : a note on Franco Donzelli / Edgeworth on competition : a reply to Antoine Rebeyrol / On price-making contracts and economic theory : rethinking Bertrand and Edgeworth / Price taking as an asymptotic limit of strategic behavior / Competition : the ways to perfection / The perfection competition paradigm : evolving from its ambiguities. (Numéro en anglais).
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Histoire de la pensée et théories
History of T hought and Theories

On perfect competition:
definitions, usages and foundations

De la concurrence parfaite :
définitions, usages et fondements

Publié avec le soutien du CNRS, de l’université de Paris Ouest
et de l’Institut d’études politiques de Lille



On perfect competition:
definitions, usages and foundations
De la concurrence parfaite :
définitions, usages et fondements


5-7, rue de l'École-Polytechnique, 75005 Paris
ISBN : 978-2-336-00256-9
EAN : 9782336002569

Nathalie BERTA
Ludovic A. JULIEN
Fabrice TRICOU

Joseph M. OSTROY







On perfectcompetition:
definitions,usagesand foundations.........7

Appropriation in a competitive

Pricetakers vs. greatnumbers:
a critique ofthe Edgeworth-Walras
convergence à la Debreu-Scarf...............77

Negishi on Edgeworth on Jevon’slawof
indifference, Walra’sequilibrium, andthe
role of large numbers:
a critical assessment............................. 109

Edgeworth on competition:
a note on Franco Donzelli ................... 155

Edgeworth on competition:
areply to Antoine Rebeyrol....................163

On price-making contractsand
Bertrand and Edgeworth .........................171

LeonidasPC. KOUTSOUGERAS ricetaking asan asymptotic limit
ofstrategic behavior............................ 189



Competition:theways to perfection....05

e perfection competition paradigm:
evolving from itsambiguities.................19

Nathalie BERTA
Ludovic A. JULIEN
Fabrice TRICOU

Joseph M. OSTROY







De la concurrence parfaite :

Appropriation et théorie concurrentielle
de lavaleur............................................5

Price takingversusgrand nombre d’agents:
une critique de la convergence
entre WalrasetEdgeworth.....................77

Une critique de l’objection de Negishi à
Edgeworth : loi d’indifférence
de Jevons, équilibre de Walras
etgrand nombre d’agents.................... 109

Edgeworth à proposde la concurrence :
une notesurFranco Donzelli............... 155

Edgeworth à proposde la concurrence :
uneréponse à Antoine Rebeyrol ............163

Contratetprice making:unréexamen
de Bertrand etd’Edgeworth ..................171

LeonidasC. KOUTSOUGERAS Leprice takingcomme limite asymptotique
de comportements stratégiques............ 189



Concurrence : leschemins
de la perfection....................................05

de la concurrence parfaite .......................19

On perfect competition: definitions, usages and foundations


1 3
Nathalie Berta , Ludovic A. Julien , Fabrice Tricou

1. Introducon

Accordingto Stigler, expressingsome commonsense,“competition isa
rivalrybetween individuals…and itarises whenever two ormore parties
strive for somethingthatall cannotobtain”[Stigler1987: 531]. Market
competition isindeed arivalry, among producerson oneside and among
consumersonthe other, butalso among producersand consumersfor the
exchange gains theymust share. In other words, competition can more
widelyinduce distribution conflicts. Inthislatter sense,two isolatedtraders
negotiating in an Edgeworthian contextcan besaidto be in competition.
Stressingthestruggle inthesharing of exchange gains, Makowski and
Ostroy[001], [01], inthisissue,relate competitivevaluationto
individual appropriation. Increasingreturnsnotablygenerate exchange gains
comparableto a collective goodwhose appropriation is subject to a costly
andthusinefficientnegotiation among agents.

Surprisingly,the established benchmark of competition,theso-called
perfectcompetition, neutralizes thesestrategic behaviorsand conflictual
interactions,resulting inthe elimination ofthese distribution conflicts.
As shown byMakowski and Ostroy, perfectcompetition (associatedwith
constant returns) dissolves these conflictsof appropriationsince every
individual can be paid accordingto hismarginal contribution. Inthe perfectly
competitive framework, competition isa pacified interaction grounded on a

1. Universityof ReimsChampagne-Ardenne. E-mail: nathalie.berta@univ-reims.fr

. Universityof Burgondy. E-mail: ludovic.julien@u-paris10.fr
3. Universityof ParisOuestNanterre la Défense. E-mail: fabrice.tricou@u-paris10.fr
4. See Edgeworth [1881].

5. Howcanthe benchmark of competition preludestrategic behaviorsand distribution conflicts?Some
advancethe heuristic necessityof asimplified model prior to complexmodelsof competition. Others
detect the persistence of a Walrasianutopia (a projectof justice) ordenouncethe ideological denial of
distribution issues.


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

strictorganization;itisnota conflicting interaction operated by resourceful
opportunistic individuals.

Exposed byMakowski and Ostroy,thisdivergence between passive
“market takers”and creative marketmakers sharpens thewell-known
difference between gentle pricetakersandstrategic price makers thatattempt
to exploit theirmarketpowers. In other words, Makowski and Ostroydeepen
the gap between perfectcompetition (or the Walrasianrule) and imperfect
competition (or the Cournotianrevival).

More generally,these linksbetween perfectand imperfectcompetitions
are not straightforward, both competitionsbeingrelated intworeversalways.
Firstly, perfectcompetitionremains the benchmark fromwhichtheoriesof
imperfectcompetition are built: inthisfirst way,the definition of perfect
competition is taken forgranted—mainly the lawof one price andthe price
taking behavior—and each model of imperfectcompetitionthentries to
amendsome assumption(s)usuallyassociatedwith it. isis theway—
from perfect to imperfectcompetition—adopted in applied orindustrial
economics(section3). Secondlyand conversely, asperfectcompetition
ratherpostulates whatitis supposedto explain, gametheoretic imperfect
competition isalsousedto provide foundations to perfectcompetition,
to derive competitive behaviorsfromstrategic behaviors. Inthat second
way, from imperfectcompetitionto perfectcompetition,the definition of
perfectcompetition isno moreused asanunquestionedstarting pointbut
as the limitcase of imperfectcompetition. From perfectcompetition as the
standard definition of competition, oneswitches to perfectcompetition asa
degenerate case of competition (section 4).

Before developingthesetwo kindsofrelations,we consider(without
being exhaustive)some notionsof competition developed inthe historyof
economics, includingthe marginalistnotion of competition (section).

2. The general noon of compeon

Asa phenomenon ofrivalry, competition maybe comparedto arace between
conflicting individualsand also be connectedwith Darwinianselection, a
process thatdisplays thesurvival ofthe fittest(andthe elimination ofthe
others). Inthisline ofthought, competition isqualified asan efficient
mode ofselection,the“bestones”beingthe former winnersandthe present
survivors. Unleashed competition may thusappearasaself-defeating
process:whenthe mostefficientcompetitorhasprevailed, a monopolyarises


On perfect competition: definitions, usages and foundations

and competitionvanishes. To ensuretherobustnessof competition, many
industrial economists recommend a public interventionto protectandto
organizethe competitive interaction:some“rulesofthe game” should be
defined and enforcedto eliminate abusesof dominantposition (anti-trust
laws) andto ensurethe independence of behaviors(anti-collusion laws) in
markets. Austrian economistslike Kirzner[1979] defend an oppositeview.
For them, dominantfirms willstaydominantaslong as theymaintaintheir
competitive advantage. Competition isa neverendingrace andtemporary
winnerscan’t stopstruggling. So monopolymaybe legitimized, beyondthe
justification given bySchumpeter[194] intermsof innovation, aslong as
theydon’tbuild barriers to entry. ForHayek [1973], competition policy
shouldwisely staymodestand notdisrupt the precious “spontaneousorder.”
Andthe market system notonlydisplayscompetition: itemergedthrough a
historical competitive processas the mosteffectivesystem (and asasystem
of individual freedom). So Austrian economistsgeneralizethe principle of
competition and praise itforits virtues. eyalsounderline itsoperation
asa dynamicalprocesswhile classical and neoclassical economists tendto
emphasizetheeffectsof competition.

eviewson competition bySmith [1776], Ricardo [1817] and Marx
[1867] are prettyclose, even iftheymaydisagree on other topics. Inthe
classical framework, competition isessentiallyconnectedtothe logic of
capital and itsgeneral effectsare balancing, butalsounbalancing. Firstly,
each capitalistcompares therate ofreturn he getsin hiscurrentallocation
totherateshewould getin alternative activities. Capitalsare moved from
lowprofitability sectors to high profitabilityones. So production decreasesin
the former sectors,where pricesand profitsareraised (as the commodityis
scarcer);andsupplyincreasesinthe latterones,where pricesand profitsare
reduced (as the commodityismore abundant). Such a competitive process,
called gravitation, isequilibrating andtends to make allratesofreturn
equal. e leveling oftheratesof profitamongsectorsis thusexplained
byfree competition, a mechanismthatdeterminesnotonly the formation

6. Accordingtothe Austrianschool,“free competition”means “free entryon markets”above all.
7. See Mc Nulty[1987].
8. See Duménil and Lévy[1990],who also mentionthat the classical field of competition
isnothomogeneous: nonreproducibleresources(whose appropriation generates rents) are distinguished from
reproducible commodities(for whichthetheoryof production price applies).
9. See Eatwell [1987] and Semmler[1987].


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

of pricesbutalsothe distributSecondlion of income. y, manyclassical
economistspredicted a longrun decrease ofthe generalrate of profit: Ricardo
feared a gloomyfuture and Marxannounced a global crisisforcapitalism.
Competition playsa majorpartinthis systemictrend, pushing capitalists to
keep on investing in order tosurvivethe competitiverace. ForMarx,this
processleads to arise inthe organic composition of capital and eventually to
a fall ofthe generalrate of profit.

Marginalisteconomistschangedthe economic conceptual framework,
shifting from a conception ofsocietymade ofsocio-economic groups(or
evenstruggling classes)to a conception ofsocietymade of homogeneous
individuals. Andtosolvethe general problem of economic coordination,
neoclassical political economists such asWalras relied on competition.
Marketcompetition isnot simplerivalryand opens the possibilityof a general
settlement, aunanimousagreementon asituationthatcan be determined
intwo logicalsteps. First,to putJevons’lawof indifference in Mill’s terms:
“there cannotbetwo pricesinthesame market,”becausethe poorlypaid
supplierandthe heavilycharged demander wouldwant to changetheirdeals
and could do it(simply recontractingtogether). Second,to put the lawof
supplyand demand in Mill’s terms:“Demand andsupply…will be made
equal. Ifunequal atanymoment, competition equalizes them.”ere cannot
be a disequilibrium price onthe market, becausetherationed demanders/
suppliers would consent to a price change allthesuppliers/demanders would
agreewith. So, marketcoordination is successful iftransactionsare all done
at thesame price,the price equatingsupplyand demand,which determines

3. From perfect compeon to imperfect compeon:

Stigler[1957]recalledtheway the informal notion of perfectcompetition
emerged inrelationwiththe developmentof imperfectcompetition inthe
1930’s. More precisely, heshowed how these features today usuallyassociated
to perfectcompetitionwere adopted afterWorld WarII. ese features

10. See Arena [1979], pages133 to 137.
11. Andtheydistinguished perfectcompetition foritsjust virtues(Walras) orforitsefficientproperties
1. e notion ofrecontracting isdueto Edgeworth [1881].
13. Orjust some ofthem, depending onthe prevailingrationingscheme.


On perfect competition: definitions, usages and foundations

coverlargethemes: large numberof agents(alsorelatedtothe absence of
collusion orcoalition), perfectinformation, free entryand homogeneityof
commodities(sometimesalso associatedwith divisibility).

ese intuitive featuresorconditionsareusedto justify whatcompetition
asa processis supposedto achieve: first,the homogenization of price
embodied inthe‘lawof one price’andsecond,the absence ofstrategic
behaviorembodied inthe pricetaking behavior. Indeed, perfectinformation
is supposedto guaranteethat the price is unique,while homogeneityis
supposedto ensurethat thisprice is the only signalrequired forindividual
choices. Besides,the large numberof agentsis usedto justify the pricetaking
behavior,whilethe large numberof agentsisjustified byfree entry. is
definition of perfectcompetition ismainly used in applied orindustrial
economics. Modelsof imperfectcompetition arethen built uponthe
amendmentof atleastone ofthese features. esetheories—dealingwith
monopoly, duopoly, information asymmetry, productdifferentiation and
so on—then constitute a non-unified myriad of partial equilibrium models
displayingsome kind ofstrategic behaviorandraisingsomesocialwelfare

Debreu[1959] brokewiththese previousintuitive featuresof perfect
competition—large number, free entryandso on—, providingthe formal
andrigorousdefinitionthathad became canonical in general equilibrium
theory: each good isassociatedwith asingle price expressed in anuméraire
and eachrational agent(eithera producerora consumer) isa quantitymaker
who behavesasa price-taker.

Debreuand morewidely the axiomatization of general equilibrium
hadthe advantageto precisethe assumptionsformally required byperfect
competition. Andthese precisionsbrought two consequences. First, itclearly
set the conditions required for the existence andthe Paretian optimalityof
the general equilibrium andthus strictlydrew the normativescope ofthe
competitive framework:“General competitive equilibrium above allteaches
the extent towhich asocial allocation ofresourcescan be achieved by

14. ese featuresare notnormalized. Stigler[1957] doesnotevoke
homogeneitybutintroducesmobilityof factors. atis whyone can also find five featuresinthe literature. In contrast, Roberts[1987] does
notevoke mobilitybuthomogeneityand divisibility, and alsothe absence of externalityand increasing
returns. eway these featuresfluctuate among authors revealslooserelations withthe general
equilibrium framework.

15. One mustaddtothe definition of perfectcompetitionthe condition of“universalityof
markets”[Arrow, 1969] foritavoids the presence of externalitiesand morewidelyof all missing markets.


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

independentprivate decisionscoordinatedthrough market.”[Arrow197:

Second, axiomatization provided a clarification ofthestatusof
competitivetraits. Indeed,therelation betweenthese intuitive featuresand
‘Arrow-Debreu’sformal definition is sometimesambiguous. Assumptions
of homogeneityand divisibilityare perfectlyembodied inthetheory,
tosuch a point that theymay seemredundant:thestrictdefinition of
goods—asphysically specified, dated and localized commodities—includes
homogeneity sincetwo commodities whichwould notbe perfectlyidentical
would necessarilyconstitutetwo differentcommodities;andthe definition
ofthe commodity space asIRn also allows to avoid indivisibility.“Strikingly
however, free entryand large numberplayno explicit role inthis theory: all
thetheorems would hold iftherewere butasingle potential buyerandseller
of anycommodity.”[Roberts1987: 838] First,the numberof agentsisfixed
in ArrowDebreu’sframework; second, again from a formal pointofview,
the large numberassumption isnotnecessary, even if itis usuallyclosely
relatedto perfectcompetition. eway the pricetaking behaviorcan be
based onthe large numberof agentsisasubjectof intense discussions since
Edgeworth [1881]’sconjecture and Debreu-Scarf [1963]’sproof.

So perfectcompetition—embodied inthe lawof one price andthe price
taking behavior—can beseen asa frameworkthat “canreallyprevail onlyat
equilibrium”[Arrow1959: 41] foritis ratherpostulatedthan endogenously
setand doesnotallowany satisfactory theoryof price and equilibrium
formation. Despitethesewell-known critics(about thesetting ofthe price
and beyond about thestabilityofthetâtonnement), perfectcompetition
remains the benchmark fromwhich neoclassical imperfectcompetitive
theoriesare built, probablybecause of its strong normative contentand its
unifiedtheoretical framework.

Imperfectcompetition has since experienced arebirth: one doesnot start
fromthe given perfectcompetition assumptions,tryingto amendthem;
butconverselyone grounds these assumptions thanks to a gametheoretic
rationale. In particular, imperfectcompetition is usedto found competitive
behaviorsfromstrategic behaviors, in order to endogenizethe previous
postulated competitive framework.

16. As stressed inthe famousquotation from Arrow,“each individual participantis supposedtotake price
asgiven and determine hischoicesas to purchasesandsalesaccordingly. ere isno one leftover whose
job itis to make a decision on price.”[Arrow1959: 43]


On perfect competition: definitions, usages and foundations

4. From imperfect to perfect compeon: foundaons

ree differentlinesofresearchwere developed in a general equilibrium
frameworkto give arational foundationto perfectcompetition, or rather to
competitive equilibrium. In addition,theyallsharethe common perspective
to provide gametheoretic foundationsforperfectcompetition by the
construction of a gamewhose equilibrium coincides withthe competitive
equilibrium inspecific conditions(typicallyforlarge economies). Without
being exhaustive, let’s sketchthesethree linesofresearch.

e Edgeworthian linestudies therelation betweenthe core andthe
competitive allocations[Hildenbrand, 1974]. e core providesa foundation
ofthe competitive equilibrium. Two kindsof approachesmaybe invoked:
the asymptotic approach andthe atomlessapproach. Both approaches
are based on cooperative gametheory. e asymptotic approachwas
performedthroughreplication procedure forfinite economiesbyDebreu
and Scarf [1963]. eynotably show, providedthat the initial endowments
areuniformlybounded,that the core of an economy replicated an infinite
numberoftimesconverges towardthesetof competitive equilibria. e
otherone is the atomlessapproach,wherethesetof agentsisindexed by
a continuumwith an atomlessmeasurespace. Aumann [1964] considers
a market with a continuum oftraders. Accordingto him:“oughwriters
on economic equilibrium havetraditionallyassumed perfectcompetition,
theyhave, paradoxically, adopted a mathematical modelthatdoesnotfit
thisassumption. Indeed,the influence of an individual participanton
the economycannotbe mathematicallynegligible, aslong as there are
onlyfinitelymanyparticipants.us a mathematical model appropriate
to the intuition notion of perfect competition must contain infinitelymany
participants. Wesubmit that the mostnatural model for thispurpose
containsa continuum of participants,similar tothe continuum of points
on a line or the continuum of particlesin a fluid.”[Aumann 1964:39] In
thisEdgeworthian perspective,the price-taking andthe coalitionalstrategic

17. e“no-surplus”characterization of perfectcompetition
intermsof“valuationwithoutappropriation”[Ostroy1980;Makowski and Ostroy,001] can beseen asan alternativeway to found perfect
18. Khan [010]reviews several methodsformodelling perfectcompetition intermsof core equivalence
and existencetheorems. eseminaltheoreticalreference isEdgeworth [1881].

19. Shitovitz[1973] assumesan economyinwhich atomsface an atomless sector. He notablyobtains the
counterintuitiveresult that when atomshavethesame endowmentsand preferences the core coincides
withthe competitive allocations.


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

behaviorscan be identifiedunderindividual negligibility. e cooperative
approach hasbeen criticized by the non cooperative one, especiallybecause
itdid notexplainthe formation of coalitions,which notablyquestionshow
a core allocation is reached.

esecond line ofresearch introducesnon cooperative behaviors
underCournotian competition [Mas-Colell, 198]. e allocationsare
implementedthrough interrelated markets, and competitive behaviorsin
marketscan be obtained from an environmentinwhichstrategic interactions
occur. Twoways were followed. e firstone is thestrategic marketgames
whichwere developedto circumvent the auctioneer[Shubik, 1973;Shapley
and Shubik, 1977;Dubeyand Shubik, 1978;Postlewaite and Roberts, 1976;
Postlewaite and Schmeidler, 1978;Sahi and Yao, 1989;Amiretal., 1991]
among others. Someresultsof convergence intermsof limit theorems
are obtained. esecondway, opened byGabszewiczand Vial [197] in
an exchange economy with production, and pursued byCodognato and
Gabszewicz[1991], [1993], d’Aspremont, DosSantosFerreira and
GérardVaret[1997] forpure exchange economies, features theworking andthe
consequencesof marketpowerin interrelated markets.
DifferentCournotWalrasequilibrium conceptscan be modelled, each depending ontheway
strategic behaviorisintroduced [Gabszewiczand Michel, 1997]. Inthese
Nashian perspectives,the Cournot-Walrasequilibria can coincidewiththe
competitive equilibrium inthe case of large economies[Lahmandi-Ayed,
001]. Morerecently,the Cournot-Walrasequilibrium concepthasbeen
developedwithinthestrategic marketgamesapproach in marketeconomies
with a continuum oftraders[Busetto etal.,008; 011]to endogeneizethe
type of behavioraseithercompetitive or strategic.

ethird line is recentandthrowsa differentlightonthestrategic
foundationsof perfectcompetition, in bringingtogethermatching and
bargaining games[Gale,000]. Conversely tothetwo preceding linesof
research,these dynamic modelsaim at specifyingthe economic institutions
withinwhich agentsinteract. Rubinstein and Wolinsky[1985] consideraset

0. eseminalreference isCournot[1838].
1. Onthispoint,see and Postlewaite-Schmeidler[1978]whoshow that the price-taking behaviormay
be a dominant strategy.

. Anotherapproach, based on conjecturalvariations,takesinto account the perceptionsbyagentsof
theirmarketenvironmentand concerns the agent’sbeliefsabout therivals’ responses to change in his
ownstrategy[Bowley, 194]. e degree of marketpowermaybe parameterized byconjecturalvariations
[Dixit, 1986]. Itcan also beshownthat the competitive equilibrium isa locallyconsistentconjectural
equilibrium [Julien,010],sustainingthe ideathatperfectcompetition isonlydefined in equilibrium.


On perfect competition: definitions, usages and foundations

oftradersflowingthroughthe marketover time andsearching at random for
trading opportunities. Whentheymeet,thetermsoftradesare determined
bybargaining. Itcan beshownthat the dynamic matching andthe bargaining
implement the competitive equilibrium [Gale, 1986]. Some extensionsare
given byMcLennan and Sonnenschein [1991]. ese finite game models
generate limits theorems, but theyare essentiallyassessed on period length
ordiscountfactorand notonthe numberoftraders. Sothe coincidence
between perfectand imperfectcompetitionsdoesnothere depend onthe
(large)size ofthe economy, contrary tothe basic idea developed inthe
Edgeworthian and Cournotian perspectives.

5.Contribuon highlights

Compeon, appropriaon and valuaon

Neo-classical economicsessentiallyenvisions the pricesystem as “the barometer
ofvaluation”involving pricetakingreactive agents. In“Appropriation fora
competitivetheoryofvalue,”L. Makowski and J.M. Ostroycontrast this
view withthe alternative conception ofthe pricesystem as “the meansof
appropriation”moved byprice making opportunistic agents. ere isactually
nostrictmutual exclusion betweenvaluation and appropriation, buteach
paradigm or theory tendsfavoronetheme andto downgradethe otherone.
On oneside, from Walras to Debreu, neo-classical economicsfocused on
valuation, appropriation being eitheran independentconcern orasecondary
issue. Inthisline, appropriation isa propertyofvaluation:“Appropriation
is thestandard by whichthe efficiencyofvaluation ismeasured.”Onthe
other side, intheview studied and developed byMakowski and Ostroy,
appropriation ispromoted as the main question and as the driving force
ofvaluation. Inthatline,“appropriation isa generic description of an
individual’sefforts to extractgainsfrom others,” so distribution leads(and
isnotabsorbed by) price determination. e dualitybetweenvaluation and
appropriation proposed byMakowski and Ostroyisfruitful and innovative,
asitallows themto develop a modifiedversion of mainstream economics
onthe basisof a newlight thrown onthe historyof economicthought.
Under thisperspective, five different themescan berevisited:rentasan
appropriation phenomenon in classical political economy; the primacyof
valuation in neoclassical political economy; valuation and appropriation
in planned ormarketeconomicsystems;property rightsas the bound for


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

appropriation in institutional economicsand finally, of course, incentive and
appropriation in newmicroeconomics.

The Edgeworth-Walras convergence

A. Álvarez’spaperisentitled“Pricetakingvsgreatnumbers: A critique ofthe
Edgeworth-Walrasconvergenceà laDebreuScarf.”islimit theorem is used
to give foundations tothe Walrasian equilibrium, arguingthatEdgeworth’s
theoryofrecontractisasuitableway toreach competitive allocations. Itis
seen asa generalization of Edgeworth’sconjecturewhichsets thatWalrasian
equilibrium isa limitcase of Edgeworthian equilibriumwhenthe number
of agentsisinfinite. e paperchallenges this usual interpretation ofthe
Edgeworth-Walrasconvergence. First, it shows that the Walrasian framework
avoidsquestions thatareunavoidable in an Edgeworthian framework:the
pricetaking assumptionrestson institutional assumptions—thenuméraire,
the presence ofthe auctioneerand of brokers—which alltry to neutralize
strategic behaviors,to avoid price manipulation. Second, it shows that the
strategic behaviorsbehind Edgeworth’sconception ofrecontracting are
misleading inthe cooperative game framework of DebreuScarf andthat
the core isnota goodrepresentation of Edgeworth’s ‘finalsettlements’. e
assimilation ofthe‘finalsettlements’andthe coalitionsofthe gametheoryis
based on awell-known but veryparticularexample—thereplica economy—
of Edgeworth’s writingsand involvesawrong interpretation of Edgeworth’s
notionsof coalition, combination orcooperative association.

F. Donzelli’s “critical assessment”about “Negishi on Edgeworth on Jevons’s
Lawof indifference, Walras’equilibrium, andtherole of large numbers”also
deals withthe Edgeworth-Walrasconvergencewith an infinite numberof
agentsand focusesonthe Edgeworthian conceptof coalition. However,the
pointofviewadopted byF. Donzelli isdifferent: he questions the objection
addressed byNegishi [198]totheso called Edgeworth’sconjecture. First,
the paper setsaunifiedreformulation—withthe contemporary toolsof
microeconomics—of Walrasian and Edgeworthian equilibria, clarifyingthen
thestatusof Jevons’s ‘lawof indifference’and ofthe large numberassumption
forboth authors. Second,using his reformulation of Edgeworth’sprocessof
recontract, F. Donzelli addressesobjections to Negishi’s result. e latterhas
shown,usingsome open coalitions that the arbitrage mechanisms supporting
the lawof one price are at work as soonthere aretwo agents: in other words,
reaching Walrasian equilibriawould not requirethe assumption of a large
numberof agents. F. Donzelli’spapercriticizes thisposition,stressingthat


On perfect competition: definitions, usages and foundations

Negishiusesassumptions which are notcompatiblewith Edgeworth’s
recontracting. ese interpretationsof Edgeworth’s recontracting and
coalitionsandtherole of arbitrage mechanismshavethen beenthesubject
of a discussionwith A. Rebeyrol inthisissue.

Cournot,Bertrand and Edgeworth

e article of L. Koutsougeras, entitled“Price Taking as the Asymptotic
Limitof Strategic Behavior,”providesa generalization ofthe ideathatNash
equilibriatendto competitive equilibria as the numberof agentsincreases
withoutlimit. e authordevelopsan asymptotic approachto explainthe
emergence of pricetaking behaviorinthe framework ofstrategic market
games. isframework enables to dealwith price formation andtrade process
inthe line of Dubey-Shubik [1978], Peck-Shell [1989] and Sahi-Yao [1989]
among others. He notablyprovidesa criterion—arate of convergence—
to measurethe individual behavior’sdeparture from pricetaking,usingthe
wedge betweenthe pricevector’shyperplane andthesupporting hyperplane of
the indifferencesurface in equilibrium. Itis shownthat,underassumptions
onthe distribution oftraders’characteristics,this wedge (the gap indicator)
becomesarbitrarily small foralltradersas the numberof agents tends toward
infinity. So,strategic behaviorisapproximately thesame aspricetaking in an
economy with a large numberof agents. e approximation becomesfiner
whenthe numberoftradersincreases.

In hisarticle, entitled“On price-making contractsand economictheory:
rethinking Bertrand and Edgeworth,”R. Routledge outlinesan alternative
approachto contractformationwhich combinesBertrand’s[1883] insight
regarding price competitionwith Edgeworth’s[1881] notion ofrecontracting.
Inthe firstpartofthe paper,the authorcriticizes the inabilityofthe
standard models(relatedtothe Bertrand paradox)to provide a convincing
price-making foundation forcompetitive equilibrium. He providesaricher
approachto contractformationwhich maygive a more credible foundation
forperfectcompetition. e mainresultis thata price-making analog of
the Debreu-Scarf [1963] approach can be providedtoshow that, in large
markets, price-making contractsare‘close’ tothe competitive equilibrium.

3. e marginalrate ofsubstitution in casetheutilityfunction is twice differentiable.


Nathalie Berta, Ludovic A. Julien, Fabrice Tricou

Walrasian allocationsare contained inthe Edgeworth core and price-taking
equilibria are contained inthe Bertrand core. Hence, as thesetof market
tradersbecomeslarge,the onlyprices whichremain inthe Bertrand core
are competitive prices. erefore a newprice-making foundation for the
competitive equilibrium emergesfromthe Bertrand core.

Final synthec notes

In hisanalytical note,“Competition:theways to perfection,”R. DosSantos
Ferreira distinguishes two (times two)typesof foundationsforperfect
competition. e first way to perfection is the absence of marketpower
found in large economies. is “smallsize”argumentcan be found in a
noncooperative contextà la Cournotorin a cooperative contextà la Edgeworth.
Beyondthe monopolycase, Cournot seescompetition asa non-cooperative
game between producers. Whenthe numberof competitorsgoes up,the
marketpowerof eachregularlygoesdown.“Indefinite competition”is the
limitcasewherethe marketprice hasbecome insensitiveto each producer’s
action andtends to equalthe marginal cost. Edgeworth developsasimilar
idea in a differentcontext,when heseespure exchange asa cooperative game
between contractors. Whenthe numberoftradersgoes up,the bargaining
powerof eachregularlygoesdown. In a large economy,theshrunk core
isnothing morethanthesetof Walrasian allocations. esecondway to
perfection isa given normal conduct, eitherpeaceful oraggressive. at
“standard of behavior”argumentcan be found in Walras(among others) for
the quietmode orin Bertrand for the hostile mode. Pricetaking behavior
maybeseen asa norm of conduct voluntarilyobserved by the marketagents,
whatever their sizes. Under this vision,the presence of pricetakershas to be
completed by the intervention ofsome marketmaker(s):sometâtonnement
operatorsin Walrasand a“marketparticipant”forDebreu. Bertrand
advancesanothernorm of conductforproducers: priceundercutting.
Such an“aggressive”pricesetting mayleadto a market result similar tothe
“peaceful”perfectlycompetitive equilibrium, as soon as there are only two
producers. So, perfectcompetition ishere grasped asan outcomethatcan be
obtainedthrough opposite conducts.

Tostarthisepistemological and ethical comment,“e perfectcompetition
paradigm: evolving from itsambiguities,”M. Dardistates that thisparadigm


On perfect competition: definitions, usages and foundations

isnotareference for theworking of competition, buta benchmark for the
alleged outcome of competition: equilibrium. isentailsissuesabout the
epistemologicalstatusofthe paradigm,which isintensified by the numerous
interpretationsofthe normative meaning at stake. euniversal construction
ofthe competitive equilibrium isfascinating, asitjoinsindividual pursuitof
happinessand efficient social order;but twoshortcomingsmaybe identified.
First,there are persisting epistemological ambiguities. e assumed
competitiveresult relieson a peculiarkind of marketorganization,the
tâtonnement,which displaysneither robust stabilitynorempirical accuracy.
Debreuaccepted perfectcompetitionto bereducedto an algebraicstructure
isolated from facts, farfrom both Walras’sidealism and Pareto’spositivism.
Recently, manyformsof competitive outcomeshave beenstudiedthanks to
complexdynamicsapproachesand gametheorymodels,which challenge
the perfectcompetition paradigm as the onlybenchmark. Second,there
are deeperethical ambiguities, about thereduction ofsocial happiness to
itsindividual andtradable components. Behindthe questioning of Pareto
optimality, individual preferencesare challenged as the onlybasisfor social
good:with Sen, democraticvaluesare broughtback onthe economic field
and economics takesback its shape of political economy, embedded in ethics
and political philosophy.


eworkshopFoundations, definitions and usages of perfect competitiontook
place at the Universityof ParisOuestNanterre la Défense on January13
and 14 ,011. We are gratefultotheresearch centerEconomiX (UMR
CNRS735),the departmentof economicsofthe Universityof ParisOuest
Nanterre la Défense (thanks to C. Bidard), andthe Region Île-de-France
forfinancial and organizationalsupports. We also acknowledge A. Béraud,
G. CodognatDe Vo, M roey, B. Ingrao and A. Rubinstein for their report
activities, and also N. Yannelisforhisparticipation intheroundtable.


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