5/6/99 Game Theory as a Tool for Market Design By Alvin E. Roth Harvard University, Department ...

13 Pages·1999·0.05 MB·English

5/6/99
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nyi Bv.hlEtAoR
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noitartsinimdA
Introduction:
srod tn,a aels ,vsttssl ieu rroy gkb.ueveder degehnlaeenat aMrnenoagras ipmlseaerdtnE
s r,,, esysd ,.yel rnld nwgttoalengad cetav iiluttekaltsjearrlosegiauvaddmgneneilir
d. e neoett gk tlr co eiasnoasesavstti rtirlalessshiahadiiTdrr uoaeytemlahatntgneceR
y r e sseshot sslem ct e aeuialaeiif,hthhaeughmwottrttc drtonaef“nepboomcpeoleved
.s n eo”hi etttetmaenaarkihgerftpaeomd
yllasui tg p nmet iecnmy hneo dnto rrlug cs efati ttsfcssfaeef ieohkkietdWradhcamtamrp
. ly it raei ,o t llnf see hpiorehdstmb s otiiiiinatFr hwssgeirtlnira aoscacpeisd tetcraahrtp
s icsiy tlneairn oaeeez hhit ttr ss -elodse tamolmtccheaa aitdghdrteotnaymmahlcana
.y tds hie l etx tdo rieosn eoluwl tiehetatpohmtneamt Tei droclweecipbtmpioulnsoce
, ft ylnsdt eeeniysmmaxtt no eiinoc clxi rf ipe:ioogml svweopemnttcmhreaotorcfts
yti x’.esrltop nimfavoopacihceibtrap
seec vi sslt naiec, gg sasnni d rreiisygn supg helna,toa ecDrigi tywaannesbeerirtaoaedl
w oelbei br e, cyh me eslcfoc.wef iosnodelIhegilwi rir bwed penxt Ieiymmil la r,u taan
leamca igstt ysfl ioassnmnaeo lcnb goxiresp let hkpde shc cmsfltioaoooihttcowwtta
st nle lmyiirpwrol ete.p ahnx,roesoicb t ialadmLatnotuannpoem cmo,eicyrreopexhet
, sd tn dh easyn,hnetwkaeietecierha vohawnatg eabwfmy lhfwpeioobrheaplc
s ttnaehymtan m os c rdli liolgpavh ielnnt.ewteoe eerahismcortunltaep stixurepempoxCe
.yllac i xtee ybleoolpvotamltnooacs
Market design:
n os i nfter oahen etcgt rnie, eacosk ss ucerdr rrndanedeoeM alnyfvt lauaaebrmsorfof
mt.rsnsoei nf r t o”s aensi eps e kattnAuaaele rcic e(nhbcrnaaaeeruimssvepnp“art
e, enrs smoentetn oih ou saoffstweiotihi ooahtberttectcanasth oureetalaeuktqrnaim
sn et egvs e knaid h)aihraret .tn oeemalgnelbaaiihmGustutenpd ey clt neseororcumapla
. s sst st t dene pnnte enkw ef aeoskehiro rofhrierstkan ehoretbaemkfrtefcmhoaPfutiad
, s s ettc, msoe irr unpkrre ooresrotwd fitcafconrtdcimepaoeaellbkrpearslam
:sseescunoehrgenfierra(elc o a n,hdo9Cns9al9i1W no7t9m9a1rC , edenfafAcM
nalliMcM ,6991 nall i,M4c9M9 1,5991 ,n , 7 oh;,9ms t989ondo991ranR99gra11leiPM
tn enh ricm eafesnf eo laef.nbhe i) go b,d9yir,89 rspn99 ae o91emd,s1hi9lTr9ip9W1
.eseht
1
la r ,ees dhe settd nfae notteii SihtmntcuU ur nat eeIco sheifatpdocsar
s,t ddssn t eeee e ou,sr rslmshoy tbmueegnlnattbyedvneerwoahroiocsebwtotgCivalog
n son waig. towt ieonhsnssteeg euiuif dc qs eeie eeihftdduhTfo nnc emoaeeotvsreiprar
se gdafekotcaalper -,rdeet tnya ircee i rvfeleuo ot pcdcoonmiest moorcinoicpodartrpcpua
s . eyses anln e mobet se n iacneubisgu ieratelmlroc hrauemengvrfBiitfrciedps
,ysyrr l a etweoso diott s tsd la denaislrnicowbeaa abei lpnhntrfdeotaionsneuihbbtmoc
e s e,snocge otingnnpr iaiispdm esk eee ngocar whownoaytottoahpaalhcwhlcta
. gnsn oei,ei grdhtsn uetdcnaedt nuohrpdaaiceontwduc aoura - ,ir ntosolFisuhamter
etcnierip ceditef odfo mnet”hoe s crty esupnt nflu miisgoucevair ohiwsnftteocda“
t ss ge erns n riidnsi ne eln eragit,haamcetnnyteoidriircrldet enficnyvobebocvcesripd
gnnei hdttdai“ be”h .ttestaulnim
, nsno iiig ht noeor ta sitmsecltaenalwis l bicaor ifuapt tgoscre eeeoktelrlfroheapTms
.noi teamn r ogrfe nfmSieoneoeoswehiireogtshfdpscim s rnee atweraost rpaoactpes
s eeg vnyaat h hioscctnxi oe rrio,to tdncfhs oetesil iucseewqish sit fymrohsepnwaorpt
sei tniil a e n ngheo mrntvin rei itoeotdtt cihf xuaafatthe lhgosscecteneannnageiirnltoc
gni tna o ioi,dtt seintmdie dkyartai mc. i ks rsr rrt g o feecosnweoshetuithutlhretoeTbn
sn nesoeriwe tty ,ceudsabbnr saeenlvalareht s nkoeortcionswa stleieahmnbtsnart
y tt,n iye en dclmevoodenalerritnta pa ruesaaeacfcssiuhcionnevqthieroeprdapargoeg
tsn te eenmseh eewstemro(sec lnrenkf oidiropuotsqweetrren oahC dn a,nos.l)i9W991
l raeon cboynai M el sn tninsgleir weiekesofsvr paoeeanxhrdlm eep-heytbritwne
. s yts t en , i ekaf 8nsrecrt i ot9 ibohnauecrs9. ojtimohioa1SwjaSbtsfv.emayUn(hp
hnd t gedeoeitn s Rssca0 oI( uee0)dhr odr0rewee hi,alprygd0elabn2yiif raaelc
,hecsi uhnowin h r. dgn,u)deno7t9 e c is99ttdanrrn99Ianlaeaa11dapderpelleurocP
, ndthoee cizkdditi reehal da rcwnamame eairohr,fldtr ecfprnfaviueoeetsrocsoceadhc
.seruliaf
,lano isn s eoese rm ternumnifailoouoic iq rasttp fn aI tsrentudusia ontedhfihrtoktooc
.s tlreeok vbr eaadllmn-Ay(rtne e ssuao hh ngtinnci eardefaeben lgyecilhswteedn
n o ei, s ctsstdnp n t eei oron ilktsydoiiy erprabsbrvao tasee mdan leblraeffmeoouhrntpo
s rsu enc)sic.uosonh agdin nciern a irhogntme saTfiaeehfyesckdt ohleirypcdrabemmA
gn ir sf hotmoscin dr atvecnid haaiiafesmhcg lteie o ebftyhtnkfarcirereiantvhmisw
.sr e e kns l trguakaoiopshw shiatee gcthdsnn Ti iit drr eeeapoktzetrailaelc mraacrtnec
d eez visi ltty an althrafnenttpo rve inireiie lwecottctelciflciehietaefptwdrffmafeopenci
.gn iltacraerttanloicb
d e, sde oe nve tsselrluatoalon sehiswgaen hi strt maadee hnlletabchtotsr rpyoelTdlnuuf
esmseeum ha i, ostcdtltte neia retamahluh itoftus tcss fssiropeigetlredeptnhaurts
d e t c,ayens h r detstdo sa ieee ntyum frkhreaseoeoertusihihpalehtrtxmihaeatvf
.evi t atn ared hev nsTtieenoiltphoyaco tie facntb eorsaamstzruti ooanffhaoggnrioraelc
tn e esknlvi riai.acg rm inetd a p ney ca eemrt i pfmsouer efooetBheehosrstmhtpiAth
ssn to l e se aodkrir,ctn r era)iueahh a4dommt tnp8,e foo,oim9)mhsR0o11t9c(9o99R11(
sneoria s sss te e r e f fdrr enk loy onuoyhirtertealb rt aevpehiaftoamkeitalonrlrfeaamv
dess uncis ihdto Rdn a g,n.4i)9X79919(1
2
s lceidt oe lmreaomn e aoedhsg iWltmn ti ea niudel cnod bnebdgawesonirotrasthxpeed
g nwio rh tte tisdg,s uingerd tn msinb inlaeynkiefaehb oohldtfacocpooltmmaims
d edde nvso el mtn t o l.e in xlvlat lrgheanaeeeboitcicdkho bsiiirtreaewdtaphldecmtmarp
gmeno lireatf rGasudlt ( ea f sdr dolei oenn avhsMteiecatiiek hihslbfttaoeb r eoagerhatl
dna , .y)ee2rl6 up9d ta1nla haar S ceh gittanrio iilRdwp(nomareg r0o9y9a1motoS
yevru shcum fo). esriuhttaretil
A simple model of matching:
erehT era owt tniojsi dstes fo ,sreya lspmriF =f{ ,..., f ,} dna srekroW =w{ ,..., w .}
1 n 1 p
ot evah yeht snoitisop fo rebmun eht si if mrif hcae htiw detaicossA ,reffo hca en ostne g .Aiq
ht i,wed irseh te o hnstotne grae vsoecnerefe r)ptcir td sneavitisn aer vt a(thekr ae m hfetodis
.g.e :stsil deredro yb detoned era esehT .dehctam eb dluoc yeht mohw
f(P w = ) w , w , ... , f , ...
i 3 2 k i
m t grdasn iahiisfetyaras f e c sit iosshr’wcif s r,e wfteirp otw de tonwed( f(P )w ,)
i 3 3 2 3 i 2
wtah tdn a,n oo sdna dlu o twtia hrtetf ay(olp m oegtnill i sw tiriekr oewlbaris etdsa eel h sti
k
rekro whca e,ylralimi S.)rekro welbarise dsse l ahti wt illi fnah ttnaca vnoitiso p aevae lrehtar
w mrof eht fo secnereferp sah (P w f =) f, ... , w ...
j j 2 4 j
a si emag eht fo emoctuo nA matchin,yllamroF .srgekrow dna smrif sehctam taht x
:xF ¨ W (cid:224) F ¨ ) thf,a c(Wh=uxts w )fwf (i=x , d frnloal f a | f nd)s sanfsr,iha(eowtxl|
ot lauqe q .w = )w(x ro F ni si )w(x rehtie dna
f ,
g n l d ixleio hibate cwsbAtam blocked by an individual deho ctk t gafsnmirin eeukfberp
ht idwehct agmnieb f i.e. i,)k(x s ixgnihct a .mA)k( x)k(Pk blocked by a pair of agents ( f )w,
fi .e.i ,x ta sehctam rieht ot rehto hcae referp hcae yeht fi
< |)f(x| fi f )f(P w ro )f(x ni 'w emos rof 'w )f(P w q
f
dna
.)w(x )w(P f
yt p smnowreatef e r,rfohpt idwehct ast’emii wm soowrstef e trfa phsty aesn itlsr iefhT(
).x ta hctam sti ot f sreferp w taht syas enil dnoces eht ;eno sah ti fi noitisop
g nAihc txam si stable fi ti td'enkscio lybb la uydnia vriodn iriap f.ostnega tahT ,sia
to nstneg af oria po nf idn a,hcta melbatpeccan un ao ttneg ao nsngiss at if ielbat ss ignihctam
.rehtona eno ot dehctam eb ot referp yllautum dluow rehto hcae ot dehctam
Some empirical evidence:
elbatsnU sgnihctam era drah ot ,niatsu ssseldrager fo rehtehw yeht era decudorpyb
d esznioliatratinteocgee dnro y.b sdeeszuiolhagrntinreace lc ,fI rof ,elpmaxe uoy eraa
sll aecno ho pwetk aoymtl neov au ho,ymr iefcio hdcri hrtu omyo rrfef fngoanidl orhekrow
odt ntiuf of iu o eytrra a ,fgp.ronei i. aokiadptc notiluf bof ien of ose mdhurltoiuyfow
referp ot krow rof dluo wreferp ot yolpme .uoy sA elbaT 1 d,eszwiolthaesrktrnaemc
3
elba tescudo rtpa hstesuohgniraelc es onh atyhltbai lee rrho cmduemdeec ceu vssaghnihctam
taht odton . elbaT( 1 si nwa r hddteo h bssmeiotlrobf nudpnnau mor fht o,R48,911991
dna ,4991 gniX dna htoR ,1991 htoR dna llegnoM dna nidoB ).9991 ,niknaP
4
1 elbaT se s u:ohgniraelC )dezilartneC( elbatsnU dna elbatS
tekraM ?elbatS ?)gnilevarnu detlah( esu ni llitS
:stekra mroba lsnoissefor phtlae hreht odn alacide mnaciremA
PMRN sey )7991 detpoda ngised wen(sey
seitlaicepS lacideM sey )stekram 03 tuoba( sey
eR latneD seicnedis sey )stekram 6( sey
)49 'erofeb (shtapoetsO on on
)49 'ecnis (shtapoetsO sey )stekram 2( sey
stsicamrahP sey sey
stsigolohcysp lacinilC )99‘ ni desu tsrif( sey sey
.K. Ueh tn istekra mlacide mlanoigeR
nidE )96'( hgrub sey sey
ffidraC sey sey
egdirbmaC on sey
latipsoH nodnoL on sey
mahgnimriB on on
)76'( hgrubnidE on on
eltsacweN on on
dleiffehS on on
( srotcoD naidanaC )SMRaC sey sey
)n ”ag sinsndiroaleincytaiwiCtasrLoap“(
Ontario sey sey
Alberta sey sey
ai bhmsuiltoiCrB sey de nn)oi6d 9no’anba(
seitiroroS muirbiliuqe ta( sey ) sey
sibbar mrofeR )89-79‘ ni desu tsrif( sey sey
5
ye tt rdre i tu eoks lsntfzbrA ,iiaaoiaaeesrb tellmhleaanrf atbketaoaraalsptTmcmniec
.esuohgniraelc l lt,’ueIbl bem ahotTtrnfe d n isas vihitethu tod ne bieartAaabcoosml
st elneka idr ce lia. ihgavmKtdta nno . aefior eUehmlnipthrteogi tesiemohytritmnlem
t sn,t melassmiht iiatse lnrfalsn eaaeuretelrhparu cbucxeoowiateelmbontamahsnnu
t i stmtenarooe endm.pidr e el e lpa cse lxr ntcel seeuteeuunbwawtshvBsoaoaetethnbs
r o ciyivl sgarfnuehaoeotelhiabuwrr catr i vsontlioraviauatp d ha(fieenovsbiiomdlancxie
.)yl t st ed eees reedlkt d dctcnuraynnnec naralai eAsueemomkevdbhithenvstoecb
. ge.ree— hsetnr ora tiesnthwea tomtlo liea rlrrre oaepulrfprtbexeaihetnstnsoiop
e l ln ahta drcg sheeiirdath zed uncty ihenbawayntm eneweaseiNhgewdtrctEoneebreffid
raend en.lmusu ot fo ene eypt esekrrleenehr oeebl ihpatfvhboomtmI eatsasrlxieaeht
sn odiet lin.ldiyonrro otcetnhaotrcobal
A laboratory experiment:
legaK dna htoR )9991( troper hcus na ,tnemirepxe ni hcihw a ,llamsdezilartneced
yrotarobal tekram saw .dehsilbatse tI decneirepxe yltsoc gnilevarnu revo emit ni
esnopser ot cigetarts roivaheb yb eht .stnapicitrap A dezilartnec esuohgniraelc sawneht
edam .elbaliava ehT latnemirepxe tnemtaert saw taht ni eno noitidnoc fo ehttnemirepxe
eht esuohgniraelc decudorp elbats sehctam ni( smret fo ’stnapicitrap detats—secnereferp
ees ,)woleb gnisu yllaitnesse eht mhtirogla deyolpme ni hgrubnidE dna ,ffidraC dnani
eht rehto ,noitidnoc eht elbatsnu mhtirogla dnuof ni mahgnimriB dna eltsacweNsaw
.desu s ed tdh eyleTewluvso lsr olfa e eyhloinrtsrtotiebo fnkote erahesarthsmodteblaelif
,stekram dna suht dda na tnemele fo ecnedifnoc ot eht noitaterpretni fo ehtlarutan
o ts uswoll ahcih w,yrotaroba leh tn ielbaliav alortno ce h .TK. Ueh tn idevresb otnemirepxe
kool t astek rtaa mhrteffid only ni r ,i gmesnshmiitrhnicaft hnatcomaechmt ehdtevresbo
.s mst se ndnig nee e nnamtreeeaac inocwhhheeruf nttcchbeoyeeeTpcb rbmxceeeahftfid
o ssllaae veemros fo se i ’tresioht xitn gevafnlapoiphirme cuobni dcoteirhtatipmsonrafrt
dezilartnec eodt dezila rsttneekcram taht spleh nialpxe eht scimanyd fo wohdezilartnec
.lia fr odeeccu ssesuohgniraelc
Stable matching mechanisms:
ds eme t svnnniaeei nhev s n eabno teotlhisye hsabcnks Tahaearitettmmaarsmht elbats
s e ghndn c aeiekt”c c kthlaaeuydcetome bdbeikfdfozmr“io riiawplmmoahr taneced
w h .o.gn dos l ruoses ef es a o iit s t osbaeethshaoi,aeiklatrttthsrnachlestieOmTavpo
e stsuae ohk s htastkdwgtauneonpabl inr iesdrimrbi eahcrzetsoil ieflcerd ahoartgtlnaec
n ors i et m ts sds,ohptsier isr tinmro slrfeoraredae hbcpiwn“k”tsifarf ecoiediwhttrap
,gd m nere nizehy iri dtgroel eroatdasoeko leirrthadgalstetmn nncnnfaaiaoefkccoaemd
c isgee it f ta .o,eeryttvit neerrsdeakkea ewmrrsveza absimf morlOnua(iorc t anleaceerd
,esme osfsusooihhgt n .ri rttmordu’ahia ecnhtvenzco tia liiodrhecloeha gbtrnltIanec
dr saoe eeic cktvanniasaliogtn hpieie esthfbi atoctr ea tk dhrsnsweatdrsr i.oolettats
e usdr nte ociezd ii tkiedvgeonrlznaettoaa i tAhtocmrdlhaeamtnatbronarotretbspcneedc
m)h. t 7 ,,i h 9d41rg, d t.9n99onheneoe1a 99githaeRgg11lXoTSanaRtisweivr eethnti
y dwlde o hesnly se gb oiebeilmuidpbharornotGorcarfsped Shapley (1962).
6
Deferred Acceptance Algorithm, with Firms making offers:
petS 1 .a hcaE mrif ftiw( h q )snoi tsirseofpfo meht ot sti q ts1eciohc
f f
pot eht ot .e.i( srekrow q .)tsil redro knar sti no srekrow
f
smr imfo rsfref f.oe. is(ref feolbatpecca nyu nsatcej errekr ohw c. abE
"sd l,odhe"v ir eesecfilefbroat p ,en )eed caftnrnrtchis ooae oatiknmdsnlnortaoir
.)deknar tsehgih eht .e.i( derreferp tsom eht
.
.
.
petS k .a y nmA rtiaf hdta hen od er tos ecrtre eaojpfmeef rto1ss-ekkam
s r peeuksl (rnb o ooar tswi t eertwp dbh eceefemtofencoru tfjcrn soeaettrfsieormp
.)deviecer
.b dn a,eta do treff oelbatpecc aderrefer ptso mre hsdlo hrekro whcaE
.tser eht stcejer
m rreoeihtk ftrh ochwac etd,ane madesarrmae fr fe:oh Pt n OroeTunhSfw
.gnidlo hs ieh sreff oesoh w)yn afi(
o tdehcta ms irekro wr omri fo nesuace b,elbat ss ignihcta mgnitluse reh ttah tee so tysa es itI
fmri fneh t, wrekro wo tdehcta me bo tsrefer p,ya s, fmri ff idn a,trapretnuo celbatpeccan una
.f ot dehctam eb ot referp t’nseod w os ,detcejer neeb dna w ot desoporp evah tsum
e hhtci h nw,imhtirog leacnatpec cdaerref erdalim i,srehto n saeire htta het e osyts aoes l satiI
r o”fylpp ar“ oe(sopo rsprekr oew hhtci h nw.ie .,idesrev eer rsarekr odw nsamr ief h ftsoelor
sq tsidl omfhr ihfc ade n)asnoitisop e bna ct .Itse reh tstceje rdn astnacilpp aderrefer ptso m
f
n wtoah hsl tls a regese hg nkt kt tnmiileraeiohl ulo hhsrcrsbwettofteeahpakrttomrsropw
d n,amhtirog lganisoporp-mr ief hmto rsftlus etra hgtnihct aem h stlal e swtasa e tlmahtirogla
.esoporp smrif eht nehw retteb od lla ylralimis smrif eht taht
m sh l dn t nlololideiht oiarnhwt eehseoewirhwudgtw etl l xehcfarestnoeeiovhecetnwoH
. tekr armob allacid eem h ntdinu osfnoitacilpm oec h fteomos sdn ilkarev es sa PheM hRTN
sr ieasp uha tc:oeb reebhirc s leh ldcIi iw ofh,wow)t”snoitai rhacvt a rmso“n(oitacilp mfooc
.stnacilppa emos fo secnereferp eht ni stnemelpmoc sa deknil eb ot snoitisop fo
Complexities of the medical market:
ehT tsrif fo es eshntoitac islepvmloo cvsntinacilppa ohw deen owt .snoitisop fOeht
s t hn ,ca trac0yg uaei0lnt oel0einnbyp,t t eeap0a opecta2mhtmrriceaexttpo atromaptpaa
ra etysr ieftisiuqere reapriuq eors llal iywe h,tdeecc uyse h ft,ita hhtc u,snoitis orpa edynoces
,tsi lyramir prieh ts itsri feh T.stsi lredr okna rf osdni kow ttimbu sstnacilpp aeseh T.noitisop
7
ri ennhootiti s ho. cp y ralaoeawF u essnhunitoiti sro epsveocneref errip eshettaci dhnciihw
yratnem etli pm ao pbys,uuelnsshaotit i rsta oseeprytiifsiu qsee rraei ru t pqtayeshrritalmirp
.snoitisop eseht gniknar tsil
A n ,otdi antrhoaawccle eiimsslmoipismso ctah ttuob ae vtinfecre pfo s tenhatcielrpapa
srebmem fo dei rsrealmpuoc ohw era gnikees o wyt csnneodiitsiesro pni eht emas.ytic
dekna rer ahcih wn o,tsi lredr okna relgni satimbu sselpuo cesehT pairsr oe fn,osnoitis ofpo
ri arpalucitr a sapeicio htcsr isf ttia h,telpma xre o,fetacid nyi aemlpu osac u. heTsuo phscae
s r sn,arno nl io inouda ifenti tcnp fdtociirsiasoniis weottosoosehBricohpiNtaepcopsna
.kroY
:snosaer detaler owt rof rettam snoitacilpmoc esehT
.1 dna ;tekram eht fo seitreporp eht egnahc yam yehT
.2 .meht etadommocca ot dengised eb tsum mhtirogla esuohgniraelc ehT
gnidrageR eht tsrif ,tniop nehw I saw deksa ni 5991 ot ngiseder eht esuohgniraelcrof
naciremA ,snaicisyhp I dah ot emoc ot spirg htiw eht tcaf taht eht ylno stluser nieht
gnitsixe yroeht fo gnihctam taht deilppa yltcerid ot taht tekram erew ehtselpmaxeretnuoc
ees( htoR dna ,royamotoS .)0991 ehT smeroeht erew lla fo eht mrof taht niatrecsgniht
always deneppah ni elpmis stekram ro( reven ,)deneppah elihw eht selpmaxeretnuoclla
dewohs taht nehw stekram evah seitixelpmoc hcus sa esoht debircsed ,evoba sselraluger
d lruooicvaheb sometimes .rucco tuB eht gnitsixe yroeht t’ndid evig hcum ecnadiugtuoba
magnitudes : woh netfo tnereffid sdnik fo ralugerri roivaheb thgim ,rucco dna tsujwoh
ralugerri ti thgim .eb revewoH snoitseuq tuoba sedutingam ylkciuq emoc ot eht erofni
.s e ncgginioishkecadm
oT xif ,saedi woleb era eerht smeroeht tuoba elpmisstekram esohw snoisulcnoc odton
sn o y irsrhtet r t aveehaoiPiokhcctwMrrttRaaaNvmm e vdoebbair csed .
nI: tgen kiearhlacpmtmaims
1. the set elba tfso sgnyi thsspciymtaeawnmloan
2. eht tes fo elbats sgnihctam syawla sniatnoc a "lamitpo-mrif" elbatsgnihctam
taht si decudorp yb eht gnisoporp-mrif derrefed ecnatpeccamhtirogla , dna natnacilppa"
"lamitpo elbatsgnihctam taht si decudorp yb eht gnisoporp-tnacilppa noisrev foeht
.mhtirogla
3. W neh eht tnacilppa gnisoporp mhtirogla si desu ( tub ton nehw eht mrif
gnisoporp mhtirogla si )desu on tnacilppa nac ylbissop evorpmi sih hctam ybgnittimbus
.sec n nte ma n rLo teseOrearifR fuhehesrtfritfpid
sel pnxmi ea elxsh pet temresnt loekmau ep ctrecoevmenarbsaisumoauhseoeahchctteB
sn ooi ttea ere wsosloloahnplnax coe,i tt d ealeekta iwrucnlapioemmdroecm
. ts exerkde oril ye fa vpnrhemd om ooteleroeiepihpcWthnmltatoiemsrixorppa
8
n ,so hs l iwdceeeinrtoe aceeaioalb hfeasrtftei lcolhe(ubryliptdpcl ihmsfewwoeebcdirb
htoR dna ,nosnareP.)9991
Computational experiments to assist in the algorithm design:
eshsTecorp d yeml n hhsgstgiiai uswrgoeonrdgilsaoporp -tn ahyc cbieilhhptwpa
. , s dtdslwnese aaogtr ttu ,liai r antdhlslFsoalepntoeuafumeaofdcwmmcRrron(iococfc
e vs lndoonsiaet radce i n ol lghtp.maitm)hesio6tdewc9i d 9r s1ots gIasl(paa-w iatlum
smht is reeeoin cgtotnlia aal , tiaed d pbmnse deaiaasntecttwair rcsban ranpoeeihfted
de b nihi rtdconsRaed ednaV ). 0 ge 9sr ntro 9iedoiaotn 1h detkVfnIetardribooocw
ec hnngc einie uihh, q nwtmse rrhes d ee tcaayb cfiihlmonoro futo oh,encegceibldhaacm
.d e s tdn sn clo natuu ienoc sdoes bwieon wbif otsMoocoehaectetvsrh dcaetoehpnfofe
en meet ohh cecwtyehtlftulfoaeit n, destlteuu o hboepec cm ltn ofpaoecommhtituso
,ny oltst tnn deoaesnwi runa l.eqo Plt Peie)MEnhstrIR(ecnaaNstoieaCrrmapv
st nle eargm n.onigosf irnieedceitcbenpkaimexatoruemuhoqpcfemrsoecp
g nseitvcnna neognsemio uuit l qrarateecunssp ioorxsdi ietnteflia h utfTesuosepermhotc
ta heth ttes eflobats tn e.rle l fg nt eaf noruo tmissituoteisDgaotbunwgqihctam
etlnbea rt eess cf ndufmdoe dihliefodtutdor ioanperciihortgalva sgnihcta mni( syawtaht
r edweetf c dey tlf l,o u fte t)nseso eteubt shnsi wthabunocraheithoimtuctlt atpammis
snoi ssgit n cnn si . eaaaecsredchmn eaui toe2cedln oc unypitttqe puaer,a ohseseTfihftid
,eerh ot.m srmetehr n htena rt iwoceer n r ihdufi eodltrFoehgnpont lapona sainueotht
, cd indt aean rm ioae gt etosn e psneie sepyccbdauasnni cdneeedourhutetqfefsid
d e y mecell hhn gti.tte ern agiuoweeofnrqtvutio enq hge soecllacstabnaaomtCs
ecne gmrh etn sdtv i iryean tnr, ead hosuwodedbweftcec ogehnmeomtdlltaupiiacnstyc
.g noi thec ltabaamts
Computational explorations of the data to assess the effect of the new algorithm:
lanoi t ,addt e euenotpw rtemm u lohntsep ctga cmeiiwfno hrsoOcetoehgdtla
.s rs, aut eo nd ryliI eeeolvnmthFieiottwrm i psms nbtr fousekeoisidnhtlrataorrolpxe
se c fn soet ei rn eh se eesbteyhefsaiu lt hee rrsearftrrkcttsneippnsseadeaeihrrrdlto
,n si d mannnnal e aiorp yheyigxtscthht oexintwcsrehe estpntddsin inelsadaeucrtisdem
,n osrieo tsf ea oohthpttecrriu phpeerwlwe b ttatnunoipon. stnaiaernu
d e y yrwb,nuo sashsem a a m,eee otmz hfce ie etotktnsleh ureIbltf oasapoamtmsis
,s en m daeotsecl cnesbtetehsa nburcetteoet ssar faese sfmvafsmii frrdedieicndkfearrow
d egrnr ieg sfn goe i snpdyreti obahlsdrptu onpmsfpa -oeooercr rheeptkh-rtmorwif
.smh t,ns i se id srethehneaon eWwtucwgosnk onlduoreafaaoahtt imtapfvdeoecrcpa
y.,el ee nnd. gn o oeisni syttadi b can hlhraeaecut afcbote f i wuyyatl0olap2bnhpaota
.dnasuoht
se ggnnai h hecscstto na hf rams, wIe ecitl r ebihelfeehmlt kaowltuparmpnpasmamis
g dnyli l usstpg ooetamnnwprnhiie oeat shsrhc o owlptihtepa lcwotmptriopipprawsfsoh
rnoei h vsctweae iim hm .eg i smeoesleoro tkaobctttttesrnwoastadloartiirrafrslltos
yl l .a nt cxie diekentl r thAap e awctmmthtmoe oo’tulrstcnBliiusodhaeftod
9
s e y c dge ei,eerslotita’ihnrat hcear nnwmvth ai isclchriaicehnlapwopexipetaatupmoc
n,r e eteelev cb gbhifdum,oritgolduttas unnnlae ooa ebgwctsf nsrnlineildohalctooh
stn an c isih.’lcarpatapeaeady elb aso lnt cio,giairngv teiearepvytohoedaftwurottHss
stsnta ncnei i ml l,ipsatrpineeah okpt eir xtltad eibametitv ns uooesnprtiogmpcpioiscfefde
d e, es ydr’ctkbnesosnadtriarnplroa cg inlli l ptnatpai aacgyhnebtubrt ylevitareti
s gerd,n nend i ei puescn ehms pottuoostrttu bandtoeeseecaehhtisr ncrwtelafuidorltppa
r ge s nb rtyimtinlt u iealaf knofhcalo mnhotiiurdoawrltpelrrppnidufpenroataocomp
tm hioycfrluoflsra pi. t ss ndttnoelsn e htuiarvwo olcee pecibfhlmoTpupna
d mdemheiot yr risoagfr ilvno0pigmsl eoaoptor p9- ts nnnnaoe iciheitwhlatplpuapinam
.ed hestnriameayxe
Theoretical computation on a simple model, to study the effect of market size:
snoi tf aolr aoenlh optaixt team a doet trh uxts fTepeeethmlkgatoprgh cmauteomshcttes
feolbats c isge ei r,ttyola ilflrd ngatnt unmsaas tishgerstnh oiitsprhippcortuasm
y.l lgnln oaisimdttsnn a o aylpecbusripealirpnrpaoamc eenmh aaTdecs(riboafs
hg u,o shIdm t eaetly;srvaa cesg ahtnruoeh,t oeecrenhndhspsoti isosddnRenarareP
. s. t)ll9au9ns9o e 1irst na toterteuiurohsBtpefgea mh ihneotrmtabcelhptxoe
dsclii u s ge oletebn c ahat oreith aesoh tote rna ftdnpwltOehneylsrcithaufomsps
ynd oasieatr halnlao u ir pdshtetieic atant urlf hacas uuaetmetnopvlaeialdenhobacm
c isge eirtt oa i.frnneteucs ktalarl atop ip ttpsean opr ha,aeeTtshhrsirtabeups
d e, t n yest o ebsuu nieveabeethahhmeatht xibl eetukwpo iotnl aaemht detti msbLuOsR
yll ancili agnm eaidtt eap yvros datteahsnveeaarb phl eiao s ct ,ueiehahthcctrtteaabpm
st .no eetelme bisfs irii lsehsauptinaxole ip.ty aaentwWr uuopttmoc
sdete l ethpykat mlr rieimasewvsomtnldneonnegv amnlriiarneopixte aethuTpmoc
.no e ilett bh ei fs aTe ssl okh tlo olm,s ecdsgtfpiosraeanno fhmeseainwrksirfow
sg nlilhicwt aem bl leaerm t oss;affedr iecete rntn weeeaeeyrhrlchlateenthfrogercirohpc
on .secn ed reetfaelreprrocnu e vtae hk e srefdenta hoinon m,tsoefe giss aainchIt
sr eeslc vtln eonae nh errot eege e)dhaf, hditetftee sreoothepkath rrtyaelmnmeogdnar(
ez if soe htete lsfboats sgnihctam e gss rwa) a o tslere elr ghfkaoehtoruchc aqtimehw(
s t : tnsere eewtgehtkmoarv tn rnrao0eta gg l 9cnmfissreosm r ersrdetpeainkeffargfoiwd
tsenelehbrcae ttfyasfbmi deh. t0e0m0i,t1=n
er utf tn orta aeeeelth vkfa r tnsereeotaiwartpaom amh0Hnopit0 ini0ec ,nin1otarcap
sert sr e i rtrtymookfmmakeseanr fnrorbndivhai, eoiuarlotmfsdrwfsrowneeahitvretni
. s,r seer tkceosrn wi oedl nwrn hee A dthfmeegw eu wt nxrmktee ipiimlrfxmooabsfmus
. wseo r l ryerp s g lkemd msfdrb ineraoiomsSahipwuktfa nn rtideearnrhhhiottsfc
e lesbz tainhe rsickfa(i rophe amwwwmoocn kegw nei rkt”aoa ,oeelhutrt“
t i )bes iheeh tcmxen aezess irtdse ee festfelaorblpautpsinamnu s gs naeeiwenhsictam
y l e teh.nzt seiftus oeqel kehat rstceyanistmofd lC oe,ae mPihdrMctneR ealNnplisams
elbats , sdetnecsa hnist elg n hrnso te t eiiif ezdgffh toekinnoecachrsaertntalpaummf
y lden sooop tlss cet l seredalehrkei lttorvce aac ariznmmnmefiosiisist btseorehaattad
.st e l k m al rsoec lea irrieah md hfodrmtsnyTceutsiatmto (rc nfte uaoeperkohtrrtsapm
.)s tee ls cz tlifn eeniecaloIthlesha metbrtffssaeo tfdseertpalup ifnoam sgnihctam
10