Bargaining versus price competition in markets with quality uncertainty

Tilburg University

Bargaining versus price competition in markets with quality uncertainty

Bester, H.

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1993

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Bester, H. (1993). Bargaining versus price competition in markets with quality uncertainty. (Reprint Series).

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CBM

R

8823

1993

137

o~Resw.~h lilllllllllll~l~l~l~~lnllll~llllllilll

Bargaining versus Price

Competition in Markets with

Quality Uncertainty

by

Helmut Bester

Reprinted from The American

Economic Review,

Vol. 83, No. 1, March 1993

Reprint Series

~ 5~

_,~Q

CENTER FOR ECONOMIC RESEARCH

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ISSN 0924-7874

Bargaining versus Price

Competition in Markets with

Quality Uncertainty

by

Helmut Bester

Reprinted from The American

Economic Review,

Vol. 83, No. 1, March 1993

K.U.B.

BIBLIOTHEEK :

TILBURG

Bargaining versus Price Competition in Markets

with Quality Uncertainty

fIr flr.l.ti)uT Besrrti~

7-his paper fixuscs trn thc cndugcr.uus dctcrmination of trading rulcs. In muny markets, as for cxample in lhe retail husi-ness, prices are simply posted by scllcrs, and the buyer has little direct in(luence on how much he has to pay. In other markets prices arc the outcomc of hilatcral ncgotiations, so that both thc scller and thc buyer takc an active part in setting the price. Examples includc not only the bazaar of a less dcvel-oped nation, bul also the markets for used cars, real estate, antiques, and ínputs for manufacturing firms. This papcr providcs a theoretical explanation of which pricing in-stitution is likely to emerge in a markct where buyers are imperfectly informed about the quality of goods ur services. 1 compare the performance characteristics of postcd-offer pricing with negotiated pricing and find that each arrangement has specific merits. ~'hese determine the equilibrium pricing policy as the outcome of compctilive interactions between the market partici-pants.

The kcy insight of my analysis is that the price-determination aspects of market orga-nization can also afíect yuality. Suppose the buyer has to visit a firm to determine its choice of product quality and that hc cxpc-riences switching costs when moving from une seller to anothcr. The incentive to pro-vidc quality in the posted-price regimc is that the consumer may walk away to an-other store if the quality is too low. Switch-ing COSIS may Undermine IhÍS incentive be-cause they creatc a lock-in eficct. A scller whu has a locked-in customer may rcduce his cost by choosing a lower quality. This

'Center (or Ecorwmic Rexearch. Tilburg Universily.

P.O. 13ux Q0153, 5(xx) LE Tilburg. The Netherlands. I thank Dilip Monkherite, Larry Samuekon, Jonalhan Thc~ma~. Gric van Uamme. and lw~i referees (or thcir comments

argumcnt is oftcn uscd tu adwK:tlc sclf-cnfurccd hans tin pricc advcrtising for providers of pro(cssional scrviccs such as docton and lawyers.' While posted-pricing promotes er crnre price competition, it may Icad to a dctcrioration in product quality.

ln contrast with posted pricing, bargain-ing determines the price of the good ajtrr thc buycr has arrived at a storc and learned its qualily. Hcre lhc incen[ive lo provide yuality is gencratcd by lhc fact that thc scllcr gcts some fraction of the total sur-plus. He will seck to maximize Ihis surplus by selectíng the scxially cfficicnt quality. As a result, thc ncgotiatcd-pricc markct ducs not exhibit the moral-hazard problem that characterizes the posted-price market. However, the locked-in consumer tinds him-sclf in a situation of partial hilateral monopoly with the scller. This allows the seller to exploit his customer, and the har-gaining may result in a relatively high price. The different impact of switching costs on price and quality in the posted- and the ncgotiated-price markets determincs the competítivencss of these trading rules.2

"f-hcre is a considerable literature study-ing the formation of prices in decentralized markcts where peirs of agents bargain over thc gains from trade.' 'fhis literature takes

~Yuk-Shec Chan anJ Hayne Leland (19N2) and William Rogeruro (198R) ezamine thi~ argumenl.

' For a comparison o( pnsred and nego[iated pricing in a IaMtratory experiment, sec James Hong and Charles Plnlt 1198?).

~This includes work hy Peter Diamond and Eric M;ukin f1Q7y1. Ariel Ruhinstein and Asher Wolinskv ( 1985), Unuglas Gale (14K6a.b). and myself (19HR). A dilTerent cunlexl ic considered in my 19ti9 paper. wbere I replace rhe price-sening stage o! the standard spalial eompetilinn modcl with a F:vgaining gamc. Furthcr references and a aetailed discussion of bargaining in e markel setting are (ound in the moaograpb by Martin Osborne and Ruhinstein (I~Nq.

1 Y)l.. Rr NO. I RIi.S7'Flt: li,-tRr;.41NING I'IíR.SC~.S PItICI: COM1f!'li'I'!77ON 2T)

lhc Irading rulc as exogcnously givcn; thc sellers arc prohibited from competing with each other hy pusting prices. -I~he uptimal sclling sUategy vf a monopvlistic scllcr is studicd hy John Riley and Richard Zcck-hauscr (19R3) and hy Drcw fudcnbcrg cl al. l 1987). 'I~hcir analysis is cunccrncd with thc yucstion of whether a fixcd postcd pricc yiclds a higher payofi for the seller than a haggling strategy. Bcginning with thc work of William Vickrey (19(iU, the choice of sclling mechanisms is an important topic alsv in the auction literature.' It turns out that posting a fixed price is the optimal strategy for a monopolistic seller of a single good when he faces a single potential buyer. Similarly, with many buyers, posted pricing is optimal for the monopvlist when he pro-duccs the good tmdcr constant rcturns to scalc and can freely vary thc amount olfered for salc (see Millon Harris and Arthur F2a-viv, 1981a,b). Paul Milgrom (19R7) cmbcds the auction model in a noncooperative-bargaining modcl in which thc owner of thc good always has the right tv resell thc itcm lo other traders. He finds that conducting an auction allows a weak bargainer to benc-fit from Ihe presence of stronger bargainers, sv that typically the sale will be by auction rather than by priva[e olfer. Thc following features distinguish my model (rom this lit-cralure: there are many producers operat-ing uncler constant rcturm to scalc; thcsc producers can compc[c hy advcrtising priccs; huyers are imperlectly infonned about pruduc[ yuality: and buycrs facc switching costs and cannot negotiate with several sell-crs at the same time.

To address the problcm, 1 study a simplc model that allows one to derive an eyuilib-rium solution both for negotiated and posted pricing. It is presented in Section l. Sections 11 and 111 investigate the equilibrium out-comc undcr both trading rules. Bascd on this analysis, I endogenizc the determina-tion vf tracling rulcs in Sccdetermina-tion IV, whcrc I

'Stc I'nston McAfcc and John McMillaa (1987) and Paul Milgrum t 1987) for a sun~iy.

show that Cor each parame[er constcllation there is a unique equilibrium pricing mech-anism. Concluding remarks are contained in

Scction V.

1. The M11oJcl

Considcr a markct with N 1 2 identical firms. Each firm produces a singlc gcxid at conslant rcturns to scale. Before the markct opens, each firm decides once-and-for-all on lhe quality q e(qt„ q~) of its oulput, where qt, ~ 4~. The cost vf producing one unil of quality q is c(q) with c(qh) ~ c(q~). In the model all consumers arc identical. ~~hey do not interact slrategically with each other. This together with thc assumption of conslant returns to scale allows one to con-sidcr each buyer in isolation independenlly of thc total number of consumcrs. Each consumer purchases at most one unit of the good. His utility from purchasing quality q at the price p is given hy q- p. Alterna-tively, hc may not purchase the good frum any of Ihe N firms and rnnsume some 'but-side good'" instcad. The price and the qual-ity uf the outside gvod are exogenously fixed so that the consumer enjvys the net bencfit r frvm buying it.

The buycr docs not directly observe lhc firms' choice of yuality. He Icarns the qual-ity q sold at a parlicular storc only by visit-ing Ihc storc. Thcrc is a cosl lo visitvisit-ing a storc. Switching from onc of thc N scllcrs to anothcr or to consuming the outside gvod takes one time unit. As the buycr discounls (uturc bcncfits by the discount faclor 11 ~ S c I, this creates a swilching cosL We will view S as a mcasurc of thcsc costs and investigate its impact on the formation of prices in this market. This is dvnc undcr thc fullowing assumplion:

Íl) 9h-c(qn)~r'~q~-c~qe)~0.

2xn

rnr: ,t,~fran~a.v I;cuNn,tllc arvtrn~

et~tac )I I9vt

surplus from producing thc luw-yuality goocl is takcn to bc too low tu competc with the uutsidc gcxtd. This implics th:u undcr im-pcrfcct informatiun lhc htrycr will ncvcr visit a storc that hc suspccls to olier yualiry q,.. Accordingly. 1 can con(inc thc analysis tu situatiuns whcrc thc srllcrs lind cluxning yuatity qt, to he uptimal.

It. The Ncgotiated-t'rice hlarket

In the negotiated-price market the con-sumer has the option of purchasing the out-side good or visiting one of the N stures tu bargain aboui the pricc uf [he goud. Upon entering a sture, he observes the quality q actually chosen by the seller and su the price negotiations proceed under symmelric information. The "disagrecmcnt puint" in this bilatcral bargaining siluatiun represcnts the payofís of the buyer and thc seller. respectivcly, if no sale lakes place and thc buyer quils; it will he dcnoted :ts (d.(I). Of cuursc, the buyer's payolf d depcnds upun his switching cost and lhe net henefit that he expects from hargaining with anolher scllcr or simply frum cunsuming thc outsidc goud. Accordingly, in cquilihrium, d will be dctermined cndogenously. The seller's profit trom nat making a sale is zero. He kceps a constant inventory of the good so that after each sale he incurs the cost c(q) of produc-ing one unit. Suppose the gcneralizcd Nash bargaining solution is the outcome of the bargaining.5 Then the price upon which the parties agree isR

(~)

~Plq.~)-argmaxr,[q-p-cl]`.

X[n-~(q)J'-"

`Tbe generalized Nash solution is studied by John

Harsanyi and Reinhard Selten (197Z). An

axiomatiza-tion of this soluaxiomatiza-tion is given by fhud Kalai (1977) and Alvin Roth U9791. Kenneth Hinmore et al. lI9R(,)

derive the generalized Nash bargaining sotution as the nonccxiperative equilihrium nf an extensive game in which the parties alternate in making o(Ters and rnun-teroffers.

"Of courxe. an agrecment will hc reachcJ unly if lhe surplus q-r~q)-d i~ nonncgutivc Tbi. cundition is

always fulfilled in the eyuitibrium delined bclow.

with ll G a C I. This solution splits lhc

sur-plus su that thc huycr reccivcs thc fraction rr. 'I"he paramcter cr may thereforc he inter-prclcd as cxpressing lhc huycr's " h:ug:tining puwcr"; by varying a from zero tu unity. une can ohtain any pricc that is irtdiviclually raliunal hulh litr thc huycr and thc sdlcr. Much of my :utalysis will focus vn thc juint impact uf thc hargaining paramclcr rr and Ihc fric;tion paramctcr fi on lhc markct out-comc.

In thc event of breakdown in thc ncgutia-tions, the huyer can either switch to anolher bargaining partner or he can purchase the outsidc guud. As the surplus q~ - c(q~ ) is less than t~, the huyer will not go tu one of the N stores unless he is cunvinced that he will tind quality qh.~ In thc cyuilibrium ol thc negotiatcd-price markct the buycr cx-pccls high qualily, and hc anlicipatcs lhal thc hargaining will result in sumc pricc p. Given these expectations and the delay cost uf switching, his cxpcctcd ulitity frum dis-:tgrcemcnt is

(3) cl( P) -max[fit..

rs(q~,- n)1.

tn cquilibrium thc consumcr's pricc-qualily expectations have to be consistent with the market outcome.

Ucfirritiurt: (~ is a rrc~olirrtcd-pricc

cquilih-riton if (i) 9j, - p~ t~ and ~i ? c(yt, ): (ii) 1r - W(qt,. rl ) and cf d( p); and (iii) j~

-..

c(c;i~)- ~..ar.rri- ctqr r.

The first of these conditions ensures that

both the sellers and the buyers are willing to participate in thc markct. If (i) fails to hold, then nune of the N sellers is activc, and the consumcr purchascs thc outsidc good. By ( ii), the equilihrium price p is determined by the bargaining sulution, tak-ing inlo account that the buyer's threat puint

I'r~l. .et n'c~. I ItF..~77 R: R.4RG:UNlNG 1'I:R.~[r.5' I'R1CI' ['lrAfl'I[777'InN 2ftl

b

II

IV

a

Picuae I. Nrt(a~nnren Pe~('wc Is nN Fo(~n uu(n~~i iN RrowNS II ,~NU IV: P(i~rnu

Puu mc Is nN Gotm.~nHn~~i rv Rr(:I(~Nti 1 nNU 1!

in the price negotiation is d( ~i). Finally, liii) guarantces that each single seller finds il in his own interest to select yuality y~,. In equilihrium, the buyer is inditferent amung all stores so that the sellers share thc

mar-kct cyually. ~1-o state thc main result of this

scction, 1 define the function

r - a~qn - c(9n)~

(4) Sn(a)- _(l-a)r'

Liy assumption ( I), fi~( ~) is decreasing, S~((l)- l. -cnd S,~(a)? O for all a 5 r~

(qi, - c(q~,)]. In Figure I the tunction

S-S~(a) reprcsents thc borderline betwcen thc hvo rcgions I f 11I and tI f tV.

PROPOSITION I: There is a

negnliaied-price equifibr'iunt if and only if s~ r~(a). If

S ~ S1(a), the negoriarect-price equilihrium is

trnique ~rirh

n (I-a)(I-S)qntac'(qn)

l~- I-(I-a)S

PROOF:

~~hc gcncraiízcd Nash bargaining solution is defined by the necessary and suflicient

first-order condition

(5)

N(d.d)-(I-cr)(q-~)fac(q)-Accordingly,

W(q.d)-c(q) -( I -a)~q-c(q)-d]

so that by assumption (U equilibrium condi-tion (iii) is satisfied for any p satisfying conditian (ii). By the first inequality of con-dition (i), one must have d( ji) - S(qn - p). Therefore, solving (ii) for p yields the uniyue solution stated in thc proposition. "I'his solution always satisfics thc second in-eyuality in (i); the first incquality in (i) is idcntical to a(q~, - cn]~[I -(1 - a)S]? r. By the definition of S~, this is eyuivatent to fi ~ S~(a).

1'he inequality S? S~(a) is satistied in regions 11 and IV of Figure L For these parameter constellations, Ihe consumer pur-chases the high-quality good at the price p. As ~~ exceeds c(qn), the presence of market frictions enables the sellers to earn positive profits. These are higher, the lower are S and a. lnterestingly, p approaches c(qn) both in the limit when S-~ I and in the limit when a-~ 1. 1'he first of these proper-ties justifics viewing the perfectly competi-tivc outcomc as the limiting point of a mar-ket with negligihle switching costs.

282 THIi AAIERIC.4N F.CONOAIlC REVIF.N' AIARCII 1993

markcl becomcs idcntical to the simplest 111. "fhe Pnsted-Price Market

scarch modcl with iclcntical huycrs and scll ~ crs. When a- 0 thc seller has all the bargaining powcr and ctfcctivcly makcs a take-it-or-leave-it ulfer lo his customers. Proposition I shows that in this case j~ - qri li.c., cach scller would charge the con-sumer's rescrvalion price). ~~his observation is thc wcll-known "monopoly pricc paradox" of Diamond (1971): cvcn with arbitrarily small scarch costs and a large numbcr of firms, in market eyuilibrium the price is the monopoly price. If the buyer has to pay a cost for entering the market or can opt for some outside good, this paradox predicts total market failure." In regions 1l and IV this unsatisfactory outcome is avoided be-cause cr is large enough to guarantee the buyer a sutlicient share of the gains from [rade.

lmportantly, the proof of Propositíon 1 reveals that the negotiated-príce market in-volves no prohlem of mor.tl hazard; that is, the incentive constrainl (iii) is never bind-ing. This perhaps surprising obscrvation has a simple intuition: the bargaining outcome guarantees the scller a fraction ( I- cr) of the hargaining surplus. As a result, he is always better off by producing qh because this quality yields a higher surplus than does q~. Chcxising quality qh is a dominant strat-egy for the seller in the negotiated-price market.y This fact distinguishes this market from the posled-price market, which 1 turn to in the next section, where prices are set

hejore the consumer becumes aware of

qual-ities.tl'

"In the Iiteraturc, the typical way to avoid the Uiamund result has been to assume that snme con-sumers are well informed alxiut prices (see Steven

Selop and Stigliti, 1977; ftal Varian, 19K0; Uale Stahl, 19ri9).

vThis conclucion is robust against altine

transfnrma-tinns of the sellcr's and buycr's utilities. The reason is that the generalixd Nash bargaining solution satisfies

the axiom of independence of utility rescalings.

tnThc relati~mship betwecn cr ruur and er lxisr pricing in a mrxlcl without qualilativc unccrtaíniy is explored by Gadc U9a}t1.

In Ihe posted-price market, the scllers act as Bcrtrand compctilors by posting prices. Advcrtising price information enables the scllcr to guarantec his custumers a price before they visit his store. In contrast we assume that communication of quality infor-matiun is infcasihlc. 'I~his assumption is rcl-evant in markets where yuality is cithcr tcxt costly lo communicatc or is not veriliablc to third parties. If a court finds it hard to determine whether a seller actually provides "high" quality, then buyers must distrust quality advertisements because they cannot bc enforced.

The buyer obscrves the sellers' price quo-tations and compares their attractiveness with the outside-option utility r. After en-tering a store and learning its quality he can either make a purchase at the posted price or switch to another seller. By assumption ( I), he will not go to a store if he anticipates finding quality q~.'t ln the posted-price equilibrium the buyer expects qh in each store, and so all sellers post the same price p'. As all stores appear identical to the buyer, he visits one of them at random. To confirm his expectations, competition must induce the suppliers to offer quality qh.12 As q is not directly observable, each single seller has an incentive to select qh at the posted price n` only if the buyer would quit after observing quality q~. Given his expcctations about qualities at other stores, the buyer will ccrtainly do so if q~ - p' ~ d( p~ ). In fact, we will assume that the buyer refuses to purchase low quality unless he is not actually worse ofTby departing.t' This means

'~Of course. the buyer presumes thal no scller of-fers the gond al a price below ccnt.

til assume that each seller selects yh when he is indilfcrent belween q~, and q~.

l'Ol.. 8.7 N'O. 1 (iliSTfR: IIARG~UNINC~ tTR.SU.S PRfCL COMPf:TITION 2R3

that each single seller will choose quality q~, if and only if the equilibrium price p' satis-tics the restriction p' ? rr( p' ), where

(6) ~(p')-qr-d(p`).

Whilc p~` ?~rr(Ir`) cnsures thc provisiun of high quality, a key factor in the determi-nation of p` is that priccs arc a signal oF

quality. Should sonic scllcr dcvíatc from p"

by posting p G p`, then the buyers will use the obscrved price to draw inferences about this scllcr's quality. If they interprct p as a signal of quality qr, thcy will not be a[-tracted even though p ~ p'. The opposite happens if p is regarded as a signal of

quality q,,. As in other signaling games. such

an indeterminacy of out-of-eyuilibrium be-liefs may lead to a multiplicity of equilib-rium prices p~`. To avoid this prohlcm, 1 will restrict the buycrs' bcliefs tu satisfy the "in-tuitivc criterion" proposcd by ln-Koo Cho and Uavid Krcps ( 19R7). Supposc some sellcr wants to undercut his competitors by some price p slightly bclow p' and, at the same time, wishes to convince the consumer [hat he ofters high quality. Then one may reasonably assume that this selVer succeeds if he would not gain by posting p and sclecting quality qr, even if his otfer attracts the entire market. This prerequisite is ful-lillcd if low quality dcters the customer from paying p for thc good, that is, if p? rr( p' ). Summing up. in the posted-price equilib-rium p~ only prices p? rr( P~` ) arc consid-crcd as a signal of high quali[y.

Ucfrrritiorl: p` is a po.ucd-price cquilibrium

if (i) yh - p~ ~ r~ and p` ? c(qh); ( ii) p` ?

rr( p~` ) ; and ( iii) there is no p?~r( p~`) such

that p c p~ and p c(qh) ~[ p' -c(qh)I~N.

The first of these conditions is the same

as in the definition of the negotiated-price equilihrium. Requirement ( ii) represents the sellcrs' inccntive-compatihility constraint to provide high quality. Condition ( iii) pre-cludes any of the sellers gaining by unilater-ally posting sume price p below ps that signals high quality. Here we assume that if

all sellers post the same price p`, each

sture has the same chance of atlracting

con-sumers so that its market share equals l ~N.

The equilibrium outcome depends on the

level of switching costs. Let

(7)

Su-l-(qn-9e)rl'-'l~hcn, SI, c I bccausc qh ~ qr.

PROPOSITION 2: 7llere is a posted-price

equilihriuni if aud ouly if S? Se. IJ S ~ Sn,

the postednrice equilibrilun is latique with

p' - ma~c[c(qh),(qr - Sqn)~(1- S)].

PROOF:

By the first inequality in equilibrium

con-dition (i), one has -rr( p`) - 9r - S(qn - p~ )~ As p~` ? c(qh) and N? 2, condition (iii) is satistied if and only if p` minimizes p sub-jcct to p Z c(qh) and p z~r( p` )- For S?

[4t - c(q~,)]~[qh - c(qh)j, only the first

con-straint is binding and so one has p' - c(qh). Otherwise, only the second constraint is binding so that p~ rr( p` ), that is, p~`

-(qr - Sqh)~( l- S). lf p` - c(qn), the firsl

inequality in (i) is always satisfied. For p~ ~ c(yh) this inequality becomes qh p'

-(qh - qr)~(1 - S)? u which, by definition of

fiu, is identical to S 2 Se.

1'he posted-price equilibrium may fail to exist for low values of S if Sri 1 0, that is, if

(8) qh-qlGU.

This condition implies that the consumer prefers buying the outside good to purchas-ing quality qh at a price p~ qr. It limits thc use of prices as signals of quality in the posted-price market. Even though the buyer may reasonably be convinced that prices above qr indicate high quality, because he would always quit a low-quality store with

p~ qr, he cannot be attracted by such a

ZRJ ritt:,t,tll:Itl['-1N li('ONUM1t!(' ItFI'llai' M1LIR(71 l~rl?

going to a high-qualily seller becomes smaller.t~

Regions 1 and 11 of Figurc I dcxribc thc area where a posted-price equilibrium cx-ists. For values of S hclow fit; thc lock-in elíect hecomes too strong and Icacts tu :t dctcrioration of prucluct quality. As a con-sequencc, thc inslitutiun uf puslcd-olirr pricing prccludcs thc scllcrs from hcing ac-live in the markcl and resuh~ in consun?p-tion of the outside g(xrd in rcgions lll and IV.

For S close enough to unity, thc posted price p~ equals c(qh). For lower values of S, however, one observes that price exceeds marginal costs. ~~he inerease in the pricc above the cost of producing high quality gives the firms an incentive not to otíer low quality. This is a familiar fcaturc of scarch modcls in which priccs signal procluct qual-ity (see Ashcr Wulinsky, I9R3; Rogcrson, 1988). A similar mechanism appcars :llso in expcricncc gtxrd tnarkcts with rcpcal ptn-chases, in which quality is Icarned after thc goud is bought. In thc Bcnjamin Klein and Kcith B. L,eHler (19HU model, consumers pay a quality premium which prcvcnts the sellcr from culting quality. Michael Riordan (I9R6) assumes that firms make price and quality decisions which cannot be altered over the relevant period. A high price then signals a high quality since consumers would refuse a .cecond purchase of low quality at a high price. In my model, the consumer learns about quality before buying the good and so he necer purchases luw quality at a high price.

The negotiated-price market is clcarly more efiicient than the posted-price regime in region IV of Figure I. Here the N firms remain inactive in the posted-price market, whereas negotiated pricing results in pro-duction of the high-quality good with posi-tive payofís both for the sellers and thc buyers. In contrast, the posted-price market

~aThe same argument shows lhat the eyuilihrium quality musl unravel lo q; whcn yu:dily is a arntinuouc

ehoice variable within some intcrval Iq~.~h,L T,t aw,id lotal market taiture in this situalion, unc has lo asume

lhat some consumers are well infonned ahout quality.

appears to be supcrior in rcgiun I, whcrc thc huycr rcfrains from enlcring ncgotia-tiuns hccausc his hargaining puwer is too luw. "I hc kcy insight from Nropusitions I and 2 is tha[ thc Iwo categorics uf trading inslitutions involve a tradc-u(f. I'ricc har-gaining avoids thc mural-hazard prohlcm in thc lirms' sclcction uf qualitics; yct, as lhc pricc is dclcrmincd er pn.~r aflcr thc huycr h:lv choscn lhc scllcr, il may nut guaranlcc lhc huycr a sullicicnt fraclion of thc surplus tu make bargaining attractivic ex ante. Es

anre pricing, as in the posted-pricc market,

docs not suH-er from this drawback; but, whcn the price is fixed e.t- arrte, the lock-in ctícct may havc a ncgative impact on thc scllcr's incentivc lo producc high quality. The relative imporlance of thcse consiclera-tions dcpends on the parameters fi and n. l'hc fulluwing scction will dcmunstralc that thc trade-otí bctwccn thc twu pricing insti-tutions can cxplain which will cmcrgc as an cctuilibrium lrading rttlc in a givcn cnvirun-mcnt.

IV. Thc Stability or Competilion

This section is dcvoled to analyzing which pricing mechanism is stable against compe-tition. A parlicular trading rule can survivc only if no tradcr can gain by deviating and using anothcr Irading rulc. Applying lhis idea to the negotiated-price markcl mcans that no scllcr should hc ablc to prolit from posting a price e.r orue in a situation whcrc all thc othcr scllcrs rcly on er pu.ct pricing. l'hal is. it nwst be impussiblc to attract profitably the demand of all cunsumen hy undcrcutting the negotiated-price equilib-rium p and posting p G j~. The rcason why such an atlempt may fail is that prices he-luw j~ may be viewed as an indication of low quality. Using thc same restrictiuns on hc-liefs as in Section [ll. I will assume that lhc posted otícr p convinces the consumer of quality yh only if p ~~rr( ji), whcrc ~rr(. ) is defined by (6).

DeJinitior?: Thc negoliatcd-price equilib-rium p is srahle against pricc compctition if thcre is no p G p such that (i) p? rr( ji) and

VC)L. R3 A'O. I iiE.ti77:R: R~1Rl:AlNING l~7iRSl1,S 1'RI('F ('OAIPFTI"1'ION

lio)r if and n)rh~ ij a z a` and S 5 Sc-(a).

Flci~ar. 2. Nrcc,rlnir.u Peu.IN~~ Is Si'nin r iN Rrc.u,N. II nun IV; Pusrru 1'luc.wu ls S~rnu,.r

IN RI.,'~I(,N~ I nNll Ilx

zR5

PROOF:

As j) 7 c(qr,) and N? 2, thcrc is ahvays a p G~) satisfying (ii) in the definition of sta-bility. As qr, -~) ? t~, condition (i) is idcnti-cal lu p~ r!, - ~S(rrr, - n). '1'hcrcli)rc, j) is stable if and only if therc is no p G jr satis-fying (i). 'I'his means onc must havc j~ 5

qr - S(q~, - j)). Using j) from Proposilion 1,

this condition is eyuivalent to

a

In uthcr words, the institution of ncgoti-ated pricing cannot be eroded by price-posting if any otfer below j) is either vicwed as a low-quali[y signal or fails to increase the seller's prolit even when he scrves thc whole market. To determinc the range of parametcr values for which this is true, 1 define thc function

(~~)

a(9i,-c~(9i,))-(9i,-9r) S~(a)- a(qn-r(rln))-(I -a)(qi,-9i)

Note that for

a` -(4)~-9r')I~d)1-9i }9n-c(rla)-t'~

onc has

S:1(a')-Srr-Sc(a~).

Moreover, S~da) ~ t) fur all a e(a', ll. In Figure 2 the function S- S~.(a) is depicted fur a e(a~, I); it divides the former region ll of Figure I into the regions 1l~ and II. PROPOSITION 3: Tlrr neguliul~~~l-pricr equilibrirun f~ is s,r,nh r,b~)i,r.~r ~)i~~

rr,),rl)e,i-(10) S~a(qh-c(9n)~-(I-a)(Qn-qt)~ ~ a(Nn - c(9i,)Í-(9r, - 9r).

As S ~ I, this inequality cannot hold if thc

Icft-hand side is negative. Accordingly, by thc dcfinition of Sc-(a), ( 1O) holds if and only if a )(Rn - 9r)r(r!n - c(qi,)} qh - 9~ ) - ir and S 5 Sr-(a). Note that Sr.(a) is strictly incrcasing for a 1 á and that Ss(a`)- Sc-(cr~). Accordingly, by Proposition 1 there is no negotiated-price equilibrium p for a e ( á, a~` ) and fi ~ Sc-(a). "1'his means that condition ( IO) applics if and only if a? a` and fi 5 fic.(a).

Pmposition 3 statcs that ncgotiated

pric-ing cannot bc sustained as a Nash cquilib-rium in thc firms' choicc of pricing policics for paramctcr cunstcllations in rcgions I and II' of [~igurc 2. Ncgotiatcd pricing con-stitutes a stable equilibrium only in regions

II and 1V. At first sight it may appcar

paradoxical that for S G Sc(1) the scllcrs will rely on price bargaining when the buycr's bargaining power is rathcr high. This is so, however, because competition forces scllers to adopt a trading rulc that is advan-tageous for the buyer.

im-286 THE AMLRICAN f.CONOhfIC RLl'IFW' hfARCH l99i

provements in the communication and transportation technology reduce the buyer's scarch cost. Swilching costs in combinalion with impcrfect quality information prrnidc a role for negotiated pricing in regions II and

IV. l'his may explain wliy thcre is relatively

líttle haggling in markets whcre the cun-sumer is well informed about product

qual-ity as, for example, in thc market for

nlass-produced brand goods. Also, bargaining is observed less frequently in the market for new automobiles than in the used-car mar-ket, where quality uncertainty is more im-portant. Other examples for negotiated pricing are the markets for antiques and real estate, where the buyer has to inspect quality before making a purchase.

To complete the analysis, I now

investi-gate the stability of posted pricing. 1 assume that posting p` legally commits the seller only in the sense that he cannot ask his customers to pay more than p`. However, this does not constrain the parties not lo revise jointly the terms of the transaction. If in the course of bargaining they hoth reach an agreement, then this replaces the posted price. Accordingly, [he buyer accepts lhe seller's posted offer p' only if he does not see a chance to pay less after bargaining.

Defenition: The posted-price equilibrium p'

is stable against hargaining if, given

d-d( p` ), it is the case that cp( qn, d)? p".

Given that the buyer cannot induce a price reduction by bargaining, he has to pay p' after switching to another store. Therefore, his threat point in a stable posted-price equilibrium is d( p' ), as defined by (3). PROPOSITION 4: The posred-price

equilib-rium p' is stable against bargaining ij and a~ly if either a 5 a' or a~ a` artd S z

Sc( a ).

PROOF:

Using ( 5), p' is stable if and only if

(ll) p'S[(l-a)(1-S)qn

-Fac(9n)[,[1-(I-a)S].

By Proposition 2 this condition always holds

if _{ó?[q~ - c(qn))r[qn - c(qn)] because}

then p~-c(qn). For Se(5~;,[qi -c(qn)]~

[qn - c(qn))), onc has p` -(qt - Sqn)~

( I- S), so lhat ( 1 I) is identical tu

(l2) S[a(Cln-c(qn))-(I-a)(9n-4~)~ ~ a(qn - c(~7n))-~~In - q~).

As 0 G S c 1, (12) always holds if the

left-hand side is negative, that is, if

a 5[qn - 4~],[qn -c(9n) t qn -9r~ -á.

For a 1 á, (12) is equivalent to S ~ Sc(a). By Proposition 2, p' exists if and only if S~ Sy. As Su ~ Sc(a) for a E(ir,a'), any pY is stable if a 5 a~. For a E[a', 1), one has S„ 5 Sc.(a) c [q~ - c(qn)]r[qn - c(qn)), so that over this range (I I) holds if and only if S ? Sc.(a).

Propositions 3 and 4 demonstrate that, whenever the N sellers are active in the market, a unique stable pricing institution emerges. As the stahility crilerion elimi-nates posted pricing in region II of Figure 2, our model predicts that Bertrand competi-tion will prevail in regions I and II~ and negotiated pricing will prevail in regions II and IV. Using Propositions 1 and 2, it is easily established that p' ~ p in region II' whereas p c p' in region IÍ. The endoge-nous determination of trading rules thus maximizes the consumer's equilihrium util-ity. ]n region ll' the sellers are trapped in a prisoner's dilemma type of situatíon. They all end up with lower profits because the negotiated price p makes undercutting profitable. In contrast, in region Il the sig-naling effect associated with posted pricing results in a price level p' that makes bar-gaining more efticient for coping with the moral-hazard problem.

V. Conclusion

sum-I r)t.. .Cr n(t t rrF.c77-tt: H.urc,tf.vthc: I F.rr.cU.1I'RIr'li fY)M1!1'h77"flr)N ?w~

m;fry, pustcd pricing imv,lvcs nwral hazard, whcrcas ncgc~tiatcd pricing is nut vcry cc,m-pctitivc. 1 havc shown that in nty nunlcl this lraclc-ulf hclwccn Ihc Iwu lracling inslitu-ticros uniyucly dctcrmincs thc cquilihrium pricing pl,liry. ~('hc cyuilihrium tracling mcchanism has thc intcresling propcrty tII:It it cnsures thc cc,nsumcr thc highcsl pussihlc ulilily Icvcl.

Mv muclcl sU'csses lhc rulc I,f quality unccrlainly for the dctcrmination ul pricing rulcs. Of coursc, this Icavcs out a numhcr of other considcratiuns that may bc impl,rtant. For inslancc, I h:IVC :fssumcd that bargaining proceeds undcr symmctric infurmation su that ncgotiations arc cosl-less. Asvmmctric-infurmatian bargaining modcls can gcncratc c:osts in thc lorm of dclay in :tgrecment." This may favor posted pricing. In gcncral. howcvcr, it is not clear a priuri which is thc most c(licicnl pricing inslitution whcn infurmation and inccntivc pruhlcros arc invc,lvccl.

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Reprint Series, CentER, Tilburg University, The Netherlands:

No. 1 G. Marini and F. van der Ploeg, Monetary, and fiscal policy in an optimising model with capital accumulation and finite lives, 71te Economic Journal, vol. 98, no. 392,

1988, PP. 772 - 786.

No. 2 F. van der Ploeg, International policy coordination in interdependent monetary economies, lournal of lnternational Economics, vol. 25, 1988, pp. 1- 23.

No. 3 A.P. Barten, The history of Dutch macroeconomic modelling (1936-1986), in W. Driehuis, M.M.G. Fase and H. den Hartog (eds.), Challenges for Macroecortomic

Modelling, Contributions to Economic Analysis 178, Amstetdam: North-Hollaod,

1988, PP. 39 - 88.

. No. 4 F. van der Ploeg, Disposable íncome, unemployment, inflation and state spending in a dynamic political-economic model, Public Choice, vol. 60, 1989, pp. 2l1 - 239. No. 5 Th. ten Raa and F. van der Ploeg, A statistical approach to the problem of negatives

in input-output analysis, Econontic Modelling, vol. 6, no. 1, 1989, pp. 2- 19.

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Journal of Economic Theory, vol. 47, no. 1, 1989, pp. 206 - 217.

No. 7 C. Mulder and F. van der Ploeg, Trade unions, investment and employment in a

small open economy: a Dutch perspective, inl. Muysken and C. de Neubourg (eds.),

Unentployment in Europe, London: The Macmillan Press Ltd, 1989, pp. 200 - 229.

No. 8 Th. van de Klundert and F. van der Ploeg, Wage rigidity and capital mobility in an optimizing model of a small open economy, De Economist, vol. l37, nr. 1, 1989, pp.

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No. 10 F. van der Ploeg and A.J. de Zeeuw, Conflict over arms accumulation in market and

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Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 91 - 119.

No. il 1. Driffill, Macroeconomic policy games with incomplete information: some eztensions, in F. van der Ploeg and A.J. de Zeeuw (eds.), Dynamic Policy Games in

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Publishers B.V. (North-Holland), 1989, pp. 289 - 322.

No. 12 F. van der Plceg, Towards monetary integration in Europe, in P. De Grauwe et al.,

De Europese Monetaire lntegrarie.~ vier visies, Wetenschappelijke Raad voor het

No. !3 R.J.M. Alessie and A. Kapteyn, Consumption, savings and demography, in A. Wenig, K. F. Zimmermann (eds.), Demographic Change and Economic Developtnent, BerlinlHeidelberg: Springer-Verlag, 1989, pp. 272 - 305.

No. 14 A. Hoque, J. R. Magnus and B. Pesaran, The exact multi-period mean-square forecast error for the first-order autoregressive model, Journal of Econometrics, vol. 39, no. 3, 1988, pp. 327 - 346.

No. t5 R. Alessie, A. Kapteyn and B. Melenberg, The effects of liquidity constraints on consumption: estimation from household panel data, European Economic Review, vol. 33, no. 213, 1989, pp. 547 - 555.

No. 16 A. Holly and J.R. Magnus, A note on instrumental variables and trtaximum likeli-hood estimation procedures, Annales d'Économie et de Statisrique, no. 10, April-June, 1988, pp. 121 - 138.

No. 17 P. ten Hacken, A. Kapteyn and I. Woittiez, Unemployment benefits and the labor tnarket, a microlmacro approach, in B.A. Gustafsson and N. Anders Klevmarken (eds.), The Polirica[Economy ofSocial Security, Contributions to Economic Analysis 179, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 143 - 164.

No. 18 T. Wansbeek and A. Kapteyn, Estimation of the error-components model with incomplete panels, Journal af Econometrics, vol. 41, no. 3, 1989, pp. 341 - 361. No. 19 A. Kapteyn, P. Kooreman and R. Willemse, Some methodological issues in the

implementation of subjective poverty deftnitions, The Journal of Human Resources, vol. 23, no. 2, 1988, pp. 222 - 242.

No. 20 Th. van de Klundert and F. van der Ploeg, Fiscal policy and finíte lives in interdependent economies with real and nominal wage rigidity, Oxford Econornic

Papers, vol. 41, no. 3, 1989, pp. 459 - 489.

No. 21

J.R. Magnus and B. Pesaran, The exact multi-period mean-square forecast error for

the first-order autoregressive model with an intercept, Journalof Econometrics, vol.

42, no. 2, 1989, pp. 157 - 179.

No. 22 F. van der Plceg, Two essays on political economy: (í) The political economy of overvaluation, Tht Economic lournal, vol. 99, tto. 397, 1989, pp. 850 - 855; (ii) Election outcomes and the stockmarket, EuropeanJoutna! ofPolitical Economy,vol. 5, no. 1, 1989, pp. 21 - 30.

No.23 I.R. Magnus and A.D. Woodlartd, On the maximum likelihood estimation of multivariate regression models containing serially correlated error components,

Jn[ernationalEconomic Review, vol. 29, no. 4, 1988, pp. 707 - 725.

No. 24

A.J.J. Talman and Y. Yamamoto, A simplicial algorithm for stationary point

problems on polytopes, Mathematies of Operations Research, vol. 14, no. 3, 1989,

pp. 383 - 399.

No. 26 A. P. Barten and L.1. Bettendorf, Price formation of fish: An application of an inverse demand system, European Economic Review, vol. 33, no. 8, 1989, pp. 1509 - 1525. No. 27 G. Noldeke and E. van Damme, Signalling in a dynamic labour market, Review oj

Economic Studies, vol. 57 (1), tro. 189, 1990, pp. l- 23.

No. 28 P. Kop lansen and Th. ten Raa, The choice of model in the construction of

input-output coefficients matrices, Irtternationa! Economic Review, vol. 31, no. l,

1990, PP. 213 - 227.

No. 29 F. van der Ploeg and A.l. de Zeeuw, Perfect equilibrium in a model of competitive

atms aeeumulation, Internatiotta! Economie Review, vol. 3l, no. l, 1990, pp. 131

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No. 30 J.R. Magnus and A.D. Woodland, Separability and aggregation, Economica, vol. 57,

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No. 31 F. van der Plceg, International interdependence and policy coordination in economies

with real and nominal wage rigidity, Greek Economic Review, vol. I0, no. 1, lune 1988, pp. 1 - 48.

No. 32 E. van Damme, Signaling and forward induction in a market entry context.

Operations Researdt Proceedings 1989, Berlin-Heidelberg: Springer-Verlag, 1990,

pp. 45 - 59.

No. 33 A.P. Banen, Toward a levels version of the Rotterdam and related demand systems,

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No. 34 F. van der Ploeg, International coordination of monetary policies under alternative exchange-rate regimes, in F. van der Ploeg (ed.), Advanced Lectures irt Quantitative

Ecorton:ics, London-Orlando: Academic Press Ltd., 1990, pp. 91 - 121.

No. 35 Th. van de Klundert, On socioeconomic causes of 'wai[ unemployment', European

Economic Review, vol. 34, no. 5, 1990, pp. 1011 - 1022.

No. 36 R.J.M. Alessie, A. Kapteyn, J.B. van Lochem and T.J. Wansbeek, Individual effects in utility consistent models of demand, in J. Hartog, G. Ridder and J. Theeuwes (eds.), Panel Data and labor Market S[udies, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1990, pp. 253 - 278.

No. 37 F. van der Ploeg, Capital accumulation, inflation and long-run contlict in

internationat objectives, Ozford Econotnic Papers, vol. 42, no. 3, 1990, pp. 501

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No. 38 Th. Nijman and F. Palm, Parameter identification in ARMA Processes in the presence of regular but incomplete sampling, Journa! of Tme Series Analysis, vot.

11, no. 3, 1990, pp. 239 - 248.

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No. 41

A. van Soest, I. Woittiez and A. Kapteyq, Labor supply, income tazes, and hours

restrictions in the Netherlands, Journalof Human Resources, vol. 25, no. 3, 1990,

pp. 517 - 558.

No. 42 Th.C.M.I. van de Klundert and A.B.T.M. van Schaik, Unemployment persistence and loss of productive capacity: a Keynesian approach, Journa! ofMacro- economics, vol. 12, no. 3, 1990, pp. 363 - 380.

No. 43

Th. Nijman and M. Verbeek, Estimation of time-dependent parameters in linear

models using cross-sections, panels, or both, Journal of Econometrics, vol. 46, no.

3, 1990, pp. 333 - 346.

' No. 44 E. van Datnme, R. Selten and E. Winter, Alternating bid bargaining with a smallest money unit, Cames and Econontic Behavior, vol. 2, no. 2, 1990, pp. 188 - 201. No. 45 C. Dang, The D,-triangulation of R" for simplicial algorithrtu for computing solutions

of nonlinear equations, Marhematics ojOperations Research, vol. 16, no. l, 1991, pp. 148 - 161.

No. 46 Th. Nijman and F. Palm, Predictive accuracy gain from disaggregate sampling in AR1MA models, Journal ojBusiness 6c Economic Starisrics, vol. 8, no. 4, 1990, pp. 405 - 415.

No. 47 J.R. Magnus, On certain moments relating to ratios of quadratic fotmc in normal variables: further results, Sankhya: The Indian Journal af Statistics, vol. 52, series

B, Part. 1, 1990, pp. 1- 13.

No. 48 M.F.1. Steel, A Bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches, Journal of Econometrics, vol. 48, no. 1l2, 1991, pp. 83 - 117.

No. 49 F. van der Ploeg and C. Withagen, Pollution control and the ratnsey problem,

Environmental and Resource Economics, vol. 1, no. 2, 1991, pp. 215 - 236.

No. 50 F. van der Plceg, Money and capital in interdependent economies with overlapping

generations, Economica, vol. 58, no. 230, 1991, pp. 233 - 256.

No. 51 A. Kapteyn and A. de Zeeuw, Changing incentives for economic research in the Netherlands, European Economic Review, vol. 35, no. 2l3, 1991, pp. 603 - 611. No. 52 C.G. de Vries, On the relation between GARCH and stable processes, Journal of

Econometrics, vol. 48, no. 3, 1991, pp. 313 - 324.

No. 53 R. Alessie and A. Kapteyn, Habit formation, interdependent preferences and demographic effects in the almost ideal demand system, The Economic Journal, vol. 101, no. 406, 1991, pp. 404 - 419.

No. 54 W. van Grcenendaal and A. de Zeeuw, Control, coordination and conflict on

international commodity markets, Economic Modelling, vol. 8, no. 1, 1991, pp. 90

No. 55 F. van der Ploeg and A.J. Markink, Dynamic policy in linear models with rational expectations of future events: A computer package, Computer Science in Economics artd Management, vol. 4, no. 3, 1991, pp. l75 - 199.

No. 56 H.A. Keuzenkamp and F. van der Plceg, Savings, investment, government finance, and the current account: The Dutch experience, in G. Alogoskoufis, L. Papademos and R. Portes (eds.), External Constraints on Macroeconomic Policy: The European Experience, Cambridge: Cambridge University Press, 1991, pp. 2l9 - 263. No. 57 Th. Nijman, M. Verbeek and A. van Soest, The efficiency of rotating-panel designs

in an analysis-of-variance model, Journal of Econometrics, vol. 49, no. 3, 1991, pp. 373 - 399.

No. 58 M.F.J. Steel and J.-F. Richard, Bayesian multivariate exogeneity analysis - an application to a UK money demand equation, ]ournal of Econometrics, vol. 49, no.

1~2, 199 t, pp. 239 - 274.

No. 59 Th. Nijman and F. Palm, Generalized least squares estimation of linear models containing rational future cxpectations, International Economic Review, vol. 32, no. 2, 1991, pp. 383 - 389.

No. 60 E. van Datrtme, Equilibrium selection in 2 x 2 games, Revista Espanola de Economia, vol. 8, no. 1, 1991, pp. 37 - 52.

No. 61 E. Bennett and E. van Damme, Demand cotnmitment bargaining: the case of apex games, in R. Selten (ed.), Game Equilibrium Models lIt - Strategic Bargaining,

Berlin: Springer-Verlag, 1991, pp. 118 - 140.

No. 62 W. Guth and E. van Damme, Gorby games - a game theoretic analysis of disarmament campaigns and the defense efficiency - hypothesis -, in R. Avenhaus, H. Karkar and M. Rudnianski (eds.), Defense Decision Making - Analytical Support and Crísis Management, Berlin: Springer-Verlag, 1991, pp. 215 - 240.

No. 63 A. Roell, Dual-capacity trading and the quality of the market, Journal of l:tnancial

Intennediation, vol. 1, no. 2, 1990, pp. LOS - 124.

No. 64 Y. Dai, G. van der Laan, A.J.J. Talman and Y. Yamamoto, A simplicial algorithm

for the nonlinear stationary point problem on an unbounded polyhedron, Siam Journal

of Optirnization, vol. 1, no. 2, 1991, pp. i5l - 165.

No.65 M. McAleer and C.R. McKenzie, Keynesian and new classical models of unemployment revisited, The Economic Journal, vol. LO1, no. 406, 1991, pp. 359 ' - 381.

No. 66 A.1.J. Talman, General equilibrium programming, Nieuw Archief voor Wiskunde, vol.

8, no. 3, 1990, pp. 387 - 397.

No. 67 J.R. Magnus and B. Pesaran, The biaz of forecasts from a first-order autoregression,

No. 68 F. van der Ploeg, Macroeconomic policy coordination issues during the various phases of economíc and monetary integration in Europe, European Economy - The

Economiu of EMU, Commission of the European Communities, special edition no.

l, 1991, pp. l36 - 164. ,

No. 69 H. Keuunkamp, A precursor to Muth: Tinbergen's 1932 model of rational expectations, l)te Economic Journal, vol. IOI, no. 408, 1991, pp. 1245 - 1253.

No. 70 L. Zou, The target-incentive system vs. the price-incentive system under adverse

selection and the ratchet effec[, Journal of Public Economics, vol. 46, no. 1, 1991, PP- 51 - 89.

No. 7I E. Bomhoff, Between price refonn and privatization: Eastem Europe in transition,

Finanzmarkt und Portfolio Management, vol. 5, no. 3, 199I, pp. 241 - 251.

' No. 72 E. Bomhoff, Stability of velocity in the major industrial counlries: a Kalman filter

approach, International Monetary Fund Staff Papers, vol. 38, no. 3, 1991, pp. 626

- 642.

No. 73 E. Bomhoff, Curcency convertibility: when and how? A contribution to the Bulgarian debate, Kredit uttd Kapital, vol. 24, no. 3, 1991, pp. 412 - 431.

No. 74 H. Keuunkamp and F. van der Plceg, Perceived constraints for Dutch unemployment policy, in C. de Neubourg (ed.), The Art of Full Employment - Unemployment Policy

in Open Economies, Contributions to Economic Analysis 203, Amsterdam: Elsevier

Science Publishers B.V. (North-Holland), 1991, pp. 7- 37.

No. 75 H. Peters and E. van Damme, Characterizing the Nash and Raiffa bargaining solutions by disagreement point axions, Mathematics of t7perations Research, vol. 16, no. 3, 1991, pp. 447 - 461.

No. 76 P.J. Deschamps, On the estimated variances of regression coefficients in misspecified error components models, Econometric 7ieeory, vol. 7, no. 3, 1991, pp. 369 - 384. No. 77 A. de Zeeuw, Note on 'Nash and Stackelberg solutions in a differential game model of capitalism', Journal of Economic Dynamics and Control, vol. 16, no. I, 1992, pp.

139 - 145.

No. 78 ].R. Magnus, On the fundamental bordered matrix of linear estimation, in F. van der Plceg (ed.), Advanced Lecrures in Quanritarive Economics, London-Orlando:

Academic Press Ltd., 1990, pp. 583 - 604.

No. 79 F. van der Plceg and A. de Zeeuw, A differential game of intemational pollution control, Systems and Conrrol Letters, vol. 17, no. 6, 199t, pp. 409 - 414. No. 80 Th. Nijman and M. Verbeek, The optimal choice of controls and pre-ezperimen-tal

observations, Journal of Econometrics, vol. Sl, no. 112, 1992, pp. 183 - 189. No. 81 M. Verbeek and Th. Nijtnan, Can whort data be treated as genuine panel data?,

No. 82 E. van Damme and W. Giith, Equilibrium selection in the Spence signaling game, in R. Selten (ed.), Game Equilibréum Models 11- Metltods, Morals, and Markets, Berlin: Springer-Verlag, 1991, pp. 263 - 288.

No. 83 R.P. Gilles and P.H.M. Ruys, Charactérization of economic agents in arbitrary communication structures, Nieuw Archief voor ~skunde, vol. 8, no. 3, 1990, pp. 325 - 345.

No. 84 A. de Zeeuw and F. van der Ploeg, Difference games and policy evaluation: a conceptual framework, O.tford Economic Papers, vol. 43, no. 4, 1991, pp. 612 -636.

No. 85 E. van Damme, Fair division under asytnmetric information, in R. Selten (ed.),

Rational Interactian - Essays in Honor of John C. Harsanyi, Berlin~Heidelberg:

Springer-Verlag, l992, pp. 121 - 144.

No. 86 F. de Jong, A. Kemna and T. Kloek, A contribution to event study methodology with an application to the Dutch stoek market, Journal of Banking and Finance, vol. l6,

no. 1, 1992, pp. I1 - 36.

No. 87 A.P. Barten, The estimation of mixed demand systems, in R. Bewley and T. Van

Hoa (eds.), Catrributions to Consumer Detnand and Econometrics, Essays in Honour

ojHeitri Theil, Basingstoke: The Macmillan Press Ltd., 1992, pp. 31 - 57.

No. 88 T. Wansbeek and A. Kapteyn, Simple estimators for dynamic panel data models with

errors in variables, in R. Bewley and T. Van Hoa (eds.), Contributions to Cortsumer

Demand and Econornetrics, Essays in Honour of Henri Theil, Basingstoke: The

Macmillan Press Ltd., 1992, pp. 238 - 251.

No. 89 S. Chib, J. Osiewalski and M. Steel, Posterior inference on the degrees of freedom

parameter in multivariate-t regression models, Economics Letters, vol. 37, no. 4,

1991, pp. 391 - 397.

No. 90 H. Peters and P. Wakker, Independence of irrelevant altematives and revealed group preferences, Econometrica, vol. 59, no. 6, 1991, pp. 1787 - 1801.

No. 91 G. Alogoskoufis and F. van der Ploeg, On budgetary policies, growth, and external deficits in an interdependent world, Journal of the lapanese and Inrernational

Eco~tomies, vol. 5, no. 4, 1991, pp. 305 - 324.

No. 92 R.P. Gilles, G. Owen and R. van den Brink, Games with permission sttvctures: The conjunctive approach, International Journal ojGame Theory, vol. 20, no. 3, 1992, PP. 277 - 293.

No. 93 J.A.M. Potters, I.J. Curiel and S.H. Tijs, Traveling salesman games, Mathematical

Programming, vol. 53, no. 2, 1992, pp. 199 - 211.

No. 94 A.P. Jurg, M.J.M. Jansen, ].A.M. Potters and S.H. Tijs, A symmetrization for finite two-person games, Zeitschrift frlr Operatiorrs Research - Methods and Models of

No. 95 A. van den Nouweland, P. Borm and S. Tijs, Allocation rvles for hypergraph communication situatioac, International Journa! of Came Theory, vol. 20, no. 3,

1992, pp. 255 - 268.

No. 96 E.l. Bomhoff, Monetary reform in Eastern Europe, European Economic Review, vol. 36, no. 213, 1992, pp. 454 - 458.

No. 97 F. van der Ploeg and A. de Zeeuw, International aspects of pollution control,

Environmenral mid Resource Economics, vol. 2, no. 2, 1992, pp. 1 l7 - 139.

No. 98 P.E.M. Borm and S.H. Tijs, Strategic claim games corresponding to an NTU-game,

Games and Economic Behavior, vol. 4, no. 1, 1992, pp. 58 - 7l.

No. 99 A. van Soest and P. Kooreman, Coherency of the indirect translog demand system with binding nonnegativity constraints, Journal oj Econometrics, vol. 44, no. 3,

1990, pp. 391 - 400.

No. 100 Th. ten Raa and E.N. Wolff, Secondary products and the measurement of productivity growth, Regionaf Science and Uróan Economics, vol. 21, no. 4, 1991, pp. 581 - 6I5.

No. 101 P. Kooreman and A. Kapteyn, On the empirical implementation of some game theoretic models of household labor supply, 7he Journal of Human Resources, vol. 25, no. 4, 1990, pp. 584 - 598.

No. 102 H. Bester, Bertrand equilibrium in a differentiated duopoly, International Economic

Review, vol. 33, no. 2, 1992, pp. 433 - 448.

No. l03 1.A.M. Potters and S.H. Tijs, The nucleolus of a matrix game and other nucleoli,

Mathematics of Operations Research, vol. 17, no. 1, 1992, pp. 164 - 174.

No. 104 A. Kapteyn, P. Kooreman and A. van Soest, Quantity rationing and concavity in a flexible household labor supply model, Review of Economics and Statistics, vol. 72, no. 1, L990, pp. 55 - 62.

No. 105

A. Kapteyn and P. Kooreman, Household labor supply: What kind of data can tell

us how many decision makers there are?, European Economic Review, vol. 36, no.

213, 1992, pp. 365 - 371.

No. 106 Th. van de Klundert and S. Smulders, Reconstructing growth theory: A survey, De

Economist, vol. 140, no. 2, 1992, pp. 177 - 203.

No. I07 N. Rankin. Imperfect competition, expectations and the multiple effects of monetary growth, The Economic Journal, voi. 102, no. 413, 1492, pp. 743 - 753.

No. 108 1. Greenberg, On the sensitivity of von Neumann and Morgenstern abstract stabie sets: The stable and the individual stable bargaining set, International Journal of

Game Theory, vol. 21, no. I, 1992, pp. 41 - 55.

No. Il0 M. Verbeek and Th. Nijman, Testing for selectivity bias in panel data models,

International Econornic Review, vol. 33, no. 3, 1992, pp. 68l - 703.

No. 1 I 1 Th. Nijman and M. Verbeek, Nonresponse in panel data: The impact on estimates of

a life cycle consumption function, Journal of Applied Econometrics, vol. 7, no. 3,

1992, pp. 243 - 257.

No. (12 I. Bomze and E. van Damme, A dynamical characterization of evolutionarily stable states, Anrtals of Operatiorts Research, vol. 37, 1992, pp. 229 - 244.

No. I13 P.l. Deschamps, Expectations and intertemporal separability in an empirical model of consumption and investment under uncertainty, Empirical Ecortornics, vol. 17, no. 3, 1992, pp. 4l9 - 450.

No. 114 K. Kamiya and D. Talman, Simplicial algorithm for computing a core element in a ' balanced game, Journaf of the Operations Research, vol. 34, no. 2, 1991, pp. 222

-228.

No. 1IS G.W. imbens, An efficient method of moments estimator for discrete choice models with choice-based sampling, Econometrica, vol. 60, no. 5, 1992, pp. 1187 -1214. No. 116 P. Borm, On perfectness concepts for bimatrix games, OR Spektrurn, vol. 14, no.

1, 1992, pp. 33 - 42.

No. 117 A.P. ]urg, I. Garcia Jurado and P.E.M. Borm, On modifications of the concepts of perfect and proper equilibria, OR Spektrum, vol. 14, no. 2, 1992, pp. 85 - 90. No. l 18 P. Borm, H. Keiding, R.P. McLean, S. Oortwijn and S. Tijs, The compromise value

for NTU-games, lnternational Journal of Game Theory, vol. 21, no. 2, 1992, pp. 175 - 189.

No. 119 M. Maschler, J.A.M. Potters and S.H. Tijs, The general nucleolus and the reduced game property, lnternationalJournalof Game Theory, vol. 21, no. 1, 1992, pp. 85

-106.

No. 120 K. Wárneryd, Communication, correlation and symmetry in bargaining, Economics

Letters, vol. 39, no. 3, 1992, pp. 295 - 300.

No. I21 M.R. Baye, D. Kovenock and C.G. de Vries, It takes two to tango: equilibria in a model of sales, Games and Economic Behavior, vol. 4, no. 4, 1992, pp. 493 - 510. No. 122 M. Verbeek, Pseudo panel data, in L. Mátyás and P. Sevestre (eds.), The

Econontetrics of Pattel Data, Dordrecht: Kluwer Academic Publishers, 1992, pp. 303

- 315.

No. 125 1.1. Sijben, Monetary policy in a game-theoretic fratnework, Jahrbiicher fur

Nationa(óknnornie und Statisrik, vol. 210, no. 314, 1992, pp. 233 - 253.

No. l26 H.A.A. Verbon and M.1.M. Verhoeven, Decision making on pension scltemes under rational expectations, Jonrna! of Econornics, vol. 56, no. l, 1992, pp. 71 - 97. No. l27 L. Zou, Ownership structure and efficiency: An incentive mechanism approach,

Journal of Conrparative Economics, vol. 16, no. 3, 1993, pp. 399 - 431.

No. 128 C. Fersttttnan and A. de Zeeuw, Capital accumulation and entry deterrence: A clarifying note, in G. Feichtinger (ed.), Dynarnic Econornic MOdels and Optinral

Control, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1992, pp.

281 - 296.

No. 129 L. Bovenberg and C. Petersen, Public debt and pension policy, Fiscal Studies, vol. 13, no. 3, 1992, pp. 1- 14.

No. 130 R. Gradus and A. de Zeeuw, An employment game between government and firtns,

Optinral Control Applicntions á Metlrods, vol. 13, no. 1, 1992, pp. 55 - 71.

No. 131 Th. Nijman and R. Beetsma, Empirical tests of a simple pricing moclel for sugar futures, Anrrales d'Écaronue et de Staristique, no. 24, 1991, pp. l2l - 131. No. 132 F. Groot, C. Withagen and A. de Zeeuw, Note on the open-loop Von Stackelberg

equilibrium in the Cartel versus Fringe model, Tlre Economic Jounral, vol. 102, no. 415, 1992, pp. 1478 - 1484.

No. 133 S. Eijffinger and N. Gruijters, On the effectiveness of daily intervention by the Deutsche Bundesbank and the Federal Reserve System in the US dollar - deutsche mark exchange market, in BaltenspergerlSinn (eds), Exchartge-Rate Regimes aud

Currency Uniwes, Basingstoke: The Macmillan Press Ltd., 1992, pp. 13l - 156.

No. 134 M. R. Baye, D. Kovenock and C. G. de Vries, It takes two to tango: equilibria in a model of sales, Games and Econanic Behavior, vol 4, 1992, pp. 493 - 5(0. No. l35 A. K. Bera and S. Lee, [nformation matrix test, parameter heterogeneity and ARCH:

a synthesis, Revietv of Ecot:ornic Studies, 60, 1993, pp. 229 - 240.

No. 136 H. G. Blcemen and A. Kapteyn, The joint estimation of a non-linear labour supply function and a wage equation using simulated response probabilities, Anna[es

d'Écarontie et de Statistique, No. 29, 1993, pp. l75 - 205.

No. 137 H. Bester, Bargaining versus price competition in markets with quality uncertainty,

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