Information Exchange and Competition in Communications Networks

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1 Inomon Ehnge nd Comeon n Communons Newoks Clo Cmbn Poleno d Tono nd Tommso M Vlle Imel College London nd CEPR Ths eson: Jnuy 005 Abs We deelo model o nomon ehnge beween llng es We heze he equlbum when newoks omee o suh uses h n be hged boh o ougong nd nomng lls We show h when lls ogned nd eeed e omlemens n he nomon ehnge hen newoks he edued nenes o use o-ne e dsmnon o ndue onney bekdown Ths bekdown olly dses oeos e llowed o negoe eol ess hges We lso show h bll-nd-kee sysem oe ess hges n ome n een egme nd we dsuss when hs sysem emeges om e negoons JEL Clsson Codes: L4 L96 Keywods: Ineonneon Aess hges Reeon hges Bll-nd-kee Inomon ehnge We hnk Luen lohel A Hyynen nd semn ns n Helsnk Keele P nd Toulouse o useul ommens nd dsussons Poleno d Tono DSPEA Cso Du degl Abuzz Tun Ily e-ml lombn@olo Coesondng uho Imel College London Tnk Busness Shool Souh Kensngon mus London SW7 AZ K e-ml lle@uk h://wwwmsuk/ommso

2 Inoduon Peole use eleon ommunons n ode o ehnge nomon Ths ehnge my ke ey deen oms Tke s n emle suon wh wo ndduls A nd B A nd B e dems yng o wok on on e bu le n deen les hus hey ely on elehone onesons nd e-ml ehnges o ondu he wok One dy A nd B e sugglng o sole n equon A nds he soluon nd lls B: B s obously hy bu hen does no need o ll A bk sne he oblems hs been soled Anohe dy A hs n embyo o n de nd lls B B needs some me o onde oe hs udmenl de nd hen lls A bk o ell wh he hnks bou : n hs seond se B s sll hy o hng eeed ll om A sne my led o n moemen o he e bu now he ognl ll hs ned hn eon h hs led B o eun he ll These smle emles lluse moe genel eue nmely h ommunons sees e no onsumed n solon nd nole nedeendenes beween lles They lso eemly henomenon whh seems ully elen o busness uses whee n ehnge o nomon my ee he need o uhe ehnges o nomon ledng o smulon o lls om heoel sndon wo hngs e woh nong sly eees o n eleon ommunons enoy ose bene ll eenly Seondly eh nddul hs demnd o lls h deends no only on he e she hs o y bu lso on he moun o lls eeed om he ohe y Thus he demnd unons deend on he es hged o boh es Ths e sudes model o newok omeon when demnd unons deend on he wy nomon s ehnged beween uses Esng models o newok omeon ylly ssume h onsumes dee uly only om mkng lls Ths leue ned by he semnl woks o Amsong 998 nd Lon e l 998 sks ee negoons oe ne-e wholesle ess hges n led oeos o hoose el ees h e demenl o sol wele o nsne beuse hey my be used o susn olluse lne es n he el mkes o beuse oeos o deng sze my he degen neess oe he leel o eol neonneon ees Ce nd Wgh 003 o beuse neonneon ees ode ommmen mehnsm o lm omeon oe nesmens n nsuue Vlle nd Cmbn 005 Howee hese woks gnoe he ole lyed by ll eenles whh s we gued boe e ese n eleon ommunons See he sueys o Amsong 00 nd Vogelsng 003

3 Cll eenles e elen mssng ngeden om he leue gen s nome nen sne hey he song m on he eeny oees o he omee oess Reen leue hs sed o look no he oblem o how o se el hges n n enonmen wh ll eenles Km nd Lm 00; DeGb 003; Jeon e l 004; Bege 004 These woks howee gnoe he nedeendenes beween uses nd ssume h he ses o lls/messges sen nd eeed e ndeenden o eh ohe An eeon s eesened by Hemln nd Kz 004 who nlyze wo-wy ommunons The ous s on he ossble seg gme beween he ommunng es s o who wll be he sende nd who he eee The onen o Hemln nd Kz 004 s on ng unde uneny bou he es lues o n ehnge whle hey do no nlyze mulle newoks nd he oblem o neonneon Ou wok s heoel bu s lso moed by ndngs om n eml leue on eleommunons demnd sed by he wok o Lson e l 990 on on-o-on demnd Ths mewok dsggeges no wo dsn elemens: uonomous ndeenden o he leel beween he newoks nd ndued whh s nluened by he olume Indued sly deends on how nomon beween wo usomes s ehnged Tylo 004 eews he eml leue om he ely 90 s h led on-o-on models o ommunons beween y s n Cnd neonl nd n he S ne-lata nd beween ounes Cnd/S mong ohes Ths eml leue ees sebly beween ougong nd nomng nd nds song nd sslly elen eese-llng henomen Clls n one deon end o genee lls n eun h e ndeenden o e nd nome These des ound lons n sudes o long dsne elehony n monools mkes bu he no been led o omee enonmen In hs e we ke e lue hese eml ndngs h he been negleed by he heoel leue h hs ehe gnoed ll eenles o modeled hem n smle shon by ssumng ee sebly beween nomng nd ougong lls We s by sudyng he oess o nomon ehnge whh s he me h leds es o enoy uly om lls ly s no geneed by lls e se bu he lls e nus o he oduon o nomon Clls mde nd eeed ould be subsues he nomon eeed does no eque he eee o ll bk o omlemens nomon be- As summzed by Tylo 004 9: ll n one deon smules somehng lke one-hl o wohds o ll n eun

4 omes odue only by esondng o quees ned by one he es Thus we do no ke ll eenles s gen bu he onsde he wy lle nd eee genee nomon We hen embed he undmenl oess o nomon ehnge beween wo es llng eh ohe no he IO mewok o newok omeon Jeon e l 004; JLT heee s he e loses o ous They deemne omee el nd eeon hges when he uly unon s eely seble beween ougong nd nomng lls e hee s no ndued They show h n he esene o eeon hge he ll e goes down s eles euny eenly: when newok lowes s e he subsbes o he l newok wll he o y moe s hey eee moe lls Hene n nese n he l s eeon hge mkes moe desble o newok o end s ouu JLT lso show h n he esene o newok-bsed dsmnon boh on nl es nd on eeng hges onney bekdowns se In n em o dsouge subsbes om onneng o he l newok hs n nene o hge eemely hgh o-ne ll es nd o-ne eee es By dong so he subsbes o he l newok ould no bene om mkng o eeng lls o-ne In ul onney bekdown n ou odng o deen mehnsms: When he bene om eeng lls s smll omed o ognng lls hen s he een newok h wns o edue o-ne lls s hey would bene mosly he ognng l; he nsumen o hee hs uose s ey hgh o-ne eee hge When he bene om eeng lls s hgh omed o ognng lls hen s he ognng newok h wns o edue o-ne lls s hey would bene mosly he een l; he nsumen o hee hs s ey hgh o-ne ognng hge These esuls e woyng om oly esee nd ll o some so o neenon eg egulon o eeon hges We ssess he elene unde moe genel omulon o he nomon ehnge oess We lso onsde mld oms o neenon mgh llow he ndusy o sel-egule sly we show h when ess hges e ken s gen he sk o onney bekdown s muh dlued omed o JLT when ndued s ose e lls mde nd eeed e omlemens n he nomon oduon unon Seondly we show h hs sk s omleely elmned oeos n se eol ess hges JLT do no endogenze ess hges Inu- 3

5 ely lhough eol dels ge ms n nsumen o ly ollude hee s no need o desoy o-ne On he ony oeos ee o hoose ey low ess hges so h o-ne es e lso ey low: n hs wy he nensy o omeon o he mke s edued s usomes nd bg newok less elng hn smll one Whle onens o bekdown e wekened we sll show how hee ess some lmed oom o neenon o moe he ouome o e negoons o nsne by usng suble eeon hges nlly we onsde he neon beween emnon hges nd el es boh o ougong nd nomng lls We show h he leel o eeon hges deends que ully on ess hges 3 om he ose on o ew ou e s bou omee ng n he esene o eenles Ou nlyss s lso elen om he nome on o ew o ssess he m o een eguloy neenons oe ne-newok hges The debe on he egulon o ed-o-moble emnon hges n Euoe whee Cllng Py Pys CPP sysem s n le nludes he doon o hges bsed on Long Run Inemenl Coss LRIC nd he noduon o RPP Cndll nd Sdk 004 The deemnon o moble-o-moble emnon s ylly less nuse nd nludes eol ngemens nd n some nsnes bll-nd-kee dels Bll-nd-kee hs been doed s wy o shng eenly he lue eed by ll when boh lles nd eees bene om DeGb 00 We ge ondons unde whh hs sysem s ndeed een nd we sudy n ee emege om e negoons We lso show how RPP nd ess hges e eled o eh ohe The emnde o he e s ognzed s ollows Seon nodues model o nomon ehnge beween llng es Seon 3 soles model o newok omeon wh unom ng Seon 4 nlyzes he se wh newok-bsed e dsmnon Sne e dsmnon ylly does no ehb he esul o o neuly wh ese o ess hges n seon 4 we lso sk wh leel would be hosen by negong o oeos s oosed o beneolen sol lnne Seon 5 onsdes he se o mke-deemned eeon hges nd seon 6 onludes 3 The oeos e o hgng usomes boh o ognng nd eeng lls s usully eeed o s he Reee Pys Pnle RPP whh s led n he moble mkes o ounes suh s Cnd Chn Hong Kong nd he ned Ses Clely ose eeon hges mke sense only he eee es bou beng lled ohewse no one would ee nswe ll 4

6 The nomon ehnge oess nd ll eenles Imgne hee e wo uses One use subsbes o newok nd he ohe use o newok nd hey ommune wh eh ohe o he momen ssume he newoks e deen hene n lso denoe he s use nd he seond use Eh use s ssumed o dee uly om he moun o nomon eed om ognng nd eeng lls n yl on-o-on onneon Inomon o use denoed I s odued odng o he ollowng oduon unon: I whee s he quny o ougong lls use ognes o on use nd s he quny o nomng lls h use eees om use The oduon unon s one o he mon mes n ou model nd n desbe deen ses when lls e subsues o omlemens n he nomon eon oess nd I / denoe eseely how nomon I / hnges he mgn wh lls sen nd eeed by onsume when ommunng wh nd hey e boh ssumed o be ose We use suess o denoe he ehnge o nomon beween he ogno nd he eee Ths noon n lso ommode he se when boh uses e onneed o he sme newok n whh se nd I Denoe wh eseely he e hged by newok o lls ogned by use ses he denl eeenes oe onsumon o nomon nd I denoes he uly unon o use when ommunng wh use We ssume o he momen h uses nno be hged o eeng lls ses nd deemne smulneously he quny o lls o onsume by mmzng he ollowng oblems: se : m I s I se : m s I I The s-ode ondons e eseely nd whh deemne he equlbum leel o lls ogned by use deed o nd use deed o : nd In genel he quny ogned by use s eed boh by he e she ys nd by he e ohe eole y Le / denoe he de e ee on qunes nd / he ndued e ee The sgn s ound by olly deenng he s-ode ondons Denong wh 5

7 A < 0 he seond ode dee wh ese o own es nd B he oss dee wh ese o own nd l es esuls: A B B A d d d d In symme equlbum wh hen A A A B B B nd: A / A B / A B B I boh uses e onneed o he sme newok e lls e on-ne hen o on-ne lls he ol ee o e hnge s: d / d B / A In summy on-o-on ehnge o nomon beween wo es leds hem o ll eh ohe geneng demnd unons nd These demnd unons e deemned s Nsh equlbum o he gme lyed by he wo uses whee eh use onols only one nu o he nomon ehnge Demnd unons hus e o he sgn / sgn A es hged o boh es The de ee hs sndd sgn: [ ] [ ] [ ] 0 sgn < [ ] Thee s lso n nde ee h ndues ddonl : sgn[ ] / sgn[ B] sgn The sgn o B s mbguous nd deends on he oees o he nomon oduon unon I uns ou o be zeo only when he uly unon s eely seble beween he bene deed om ougong nd nomng lls s s ssumed by JLT As ned by he Inoduon sebly s song ssumon nd does no seem o hold n he d Aodng o he eml leue lls end o genee ddonl lls n eun hus sgn[b] > 0 Ths mles h nomng nd ougong lls should be omlemens n he nomon oduon unon > 0 I s esy o ommode he mewok o nomon ehnge lso n he esene o eeon hges I newok hges s usomes o eeng lls e 6

8 e ll hen he eous Nsh equlbum h genees nd s un- hnged s long s usomes e eey ll whh ndeed would hen nd We ll hs suon whee eeon hges do no bnd ehe beuse hey e zeo o low enough suon o sende soeegny When eeon hges do bnd he sme nlyss n be led In ul boh eeon hges e hgh enough omed o sendng hges hen eh usome eeely onols he moun o lls eeed The s-ode ondons n hs se e eseely nd whh deemne he olume o lls he Nsh equlbum: nd Ths suon o eee soeegny ses when sendng hges do no bnd: nd nlly ls ossbly ses when he bndng es boh o sendng nd eeng lls e se by one newok lone Ths se s denoed s suon o newok soeegny o nsne newok s soeegn hen use hooses boh nus n he nomon ehnge The s-ode ondons n hs se e nd whh deemne he olume o lls: nd Noe h hs s smle omzon oblem ondued by use sne use s sse Ths suon o newok soeegny ses when use es ll lls eeed nd nno send ddonl lls sne hey e uned by The ou suons o sende/eee/newok /newok soeegny ehus ll ossble ses o he deemnon o he olume o lls Mos o ou nlyss n he emnde onenes on sende soeegny sne s he moe elen se om n eml sndon We do so by onsdeng eeon hges h e eguled nd low enough so h hey do no bnd Howee we do emne lso he ohe suons when we nlyze mkedeemned eeon hges n Seon 5 3 The model o newok omeon Demnd o lls beween o uses s geneed odng o he model desbed n he eous Seon nd summzed by he e ees o eq The model o omeon ollows Amsong 998 Lon e l 998 nd s eenson by JLT Thee e wo ne- 7

9 woks deened à l Hoellng omeng n ommunons mke A un mss o onsumes s unomly loed on he segmen [0] whle he newok oeos e loed he wo eemes We denoe by eseely he m loed he ogn eseely he end o he lne Cusomes y hee- T q q o q whee he ed ee n be neeed s subsbe lne hge s he mgnl e o ognng q o lls s he un e h newok s onsume ys o eeng q lls 4 When onsume loed l buys om m loed l he uly s gen by y 0 l l /σ w whee y s he nome 0 s ed sulus omonen om subsbng suenly lge suh h ll usomes lwys hoose o subsbe o newok nd w s he nde uly deed om mkng nd eeng lls h we desbe below The mee σ eesens n nde o subsubly beween he newoks The onsume ndeen beween he wo newoks deemnes he mke she o he wo ms In ul m s she s whee: w w / σ w w whee: 3 w 4 5 Ths sysem o equons desbes suon whee usome hs mny on-oon nomon ehnges A usome belongng o newok hs ehnges on ne nd ehnges o ne Eh on-ne ehnge genees quny o lls ogned by he use onneed o newok nd desned o use onneed o he sme newok Ths quny deends only on nd s he oesondng nde uly deed om he sngle on-o-on ehnge on ne Smlly s he nde uly deed 4 The se wh newok-bsed e dsmnon s onsdeed n Seon 4 8

10 om eh o-ne ehnge h noles lls ogned by he use onneed o newok nd desned o use onneed o newok hs deends no only on bu lso on sne he eese s ogned by he l newok Boh newoks he ull oege Seng usome noles ed os o onneon nd bllng The mgnl os s e ll he ognng end nd he emnng end The ol mgnl os o ll s Newoks y eh ohe eol wowy ess hge denoed by o emnng eh ohes lls Thus newok s o s gen by: 6 { } Newok s o n 6 s gen by he sum o he ollowng omonens: he o deng om ognng lls emned on he sme newok nludng he eeon hge he l newok ; he o om ognng lls desned o nd emned on ; he o om emnon nd eeon o nom- ng lls ogned by usomes o he l newok We onsde he ollowng mng o he gme s neonneon nd eeon ems e se n sge I Then oeos omee n wo- es nd n sge II In ul we ssume h eeon hges e lwys se low enough In hs wy we n onene on he se o sende soeegny only Ths nlyss obously nludes he se whee eeon hges do no es 0 s s he se n mny ounes h do CPP I lso dels wh he se o eeon hges eguled n sge I by beneolen sol lnne h mkes sue h hey do no bnd n sge II 3 Equlbum wh unom ng unde sende soeegny In he Aend we obn he ollowng eesson o llng es equlbum: 7 Φ Γ Φ Φ Θ 9

11 whee: Φ o whee o denoes he ol quny o lls ogned by newok nd desned boh on-ne nd o-ne Φ eesens he o beween he mgnl hnge n ougong o-ne lls nd he ege mgnl hnge n ll ougong lls boh o- nd on-ne nludng he eun ee on he le used by n nese o e ; Φ s summy o he ougong eun henomenon Γ o s he o beween he mgnl hnge n nomng o-ne lls nd he ege mgnl hnge n ll ougong lls used by n nese o e Γ s summy o he nomng eun henomenon Θ wh denong he ol quny o lls eeed by o uses onneed o newok Θ eesens he o beween he ege mgnl hnge n ll nomng lls nd he ege mgnl hnge n ll ougong lls used by n nese o e Θ s summy o nomng-o-ougong lls Eq 7 n be neeed s ollows: Φ Γ eesens he newok s de eeed mgnl os The ossble emnon mk-u o o-ne lls s mulled by he deene beween he one ougong nd nomng os eleng he wo-wy ee o ll ogon; 5 Φ s he euny eenly due o he esene o he eeon hge Ths s mulled only by he o Φ he ougong eun o om o sne hs s he only deon h mes o he euny eenly mosed on s usomes Φ Θ eesens he deene beween he mgnl uly o use om eeng nomon hough lls ogned by uses hs s why he mgnl uly e on-o-on ehnge s mulled by he o-ne ougong o Φ nd by s she nd he mgnl uly o eeng lls by use use eees nomon boh on- 5 One would ee Φ Γ Also noe h he sgn o he emnon mk-u does no me Φ Γ 0

12 ne nd o-ne hus he mgnl uly e ehnge s mulled by he nomng-oougong lls o Θ Eq 7 genelzes eous esuls obned n he leue When he uly unon s eely seble beween ougong nd nomng lls s s n JLT esuls nd 0 so h he nomng o s Γ 0 nd he ougong o s Φ whle he nomng-o-ougong o smles o Θ Then eq 7 smles o h oesonds o nd ly mends he esul o JLT 6 I uses do no eee uly om beng lled 0 nd e no hged o eeon 0 hen 7 beomes smly s n Lon e l 998 nde ou moe genel seon we obn he ollowng: 7 Pooson nde sende soeegny he symme equlbum wh unom mul ng s hezed by he ollowng ondons: he ll e s gen by: 8 whee s ogon o gen by: Γ Φ ; b he ed hge s gen by: / σ ; eh newok s o s equl o /4σ The esul o o neuly s ommon n symme models o newok omeon wh mul- unom ng The moe neesng eue o Pooson les n he eesson o he ll e gen by eq 8 whee we he nodued new elemen he ogon o Ths denoes he o beween he hnge o o-ne lls when he l e hnges nd he de hnge o on-ne lls when he own e hnges In ohe wods he ogon o mesues he ele m o he eese henomenon 6 Pooson o JLT 95 msses he ls em n bkes whh s zeo only n symme equlbum Ths em eesens he deene n uses mgnl uly o eeng lls I shows h he mgnl uly om eeng lls s hghe o l use hn o own use hen ees bus newok would nese s own e n ode o edue s ougong lls nd edue he benes o uses o he l newok 7 JLT show h symme equlbum ess σ s smll enough o s smll enough

13 sng eq nd he noon om Seon he eesson o he ogon o n symme equlbum s: B A Sne A s nege he sgn o s he sme s he sgn o B As we gued n he Inoduon he eml edene lble o us suggess h nomng nd ougong lls e omlemens n he nomon oduon unon hene should ke ose lues lhough hee s nohng n heoy o een subsuon ees ledng o nege lues o I s lso els o mgne h < whle oesonds o he se o ee omlemens Ths o edues o zeo when he sebly ondon on uly holds s n JLT n whh se eq 8 edues o / The m o he ogon o on he oeos ng s wo-old On he one hnd hghe ends o deese he e n ode o ndue he ll genees lls henomenon whh s enoyed by usomes: hs s he ls em o he sque bke n eq 8 On he ohe hnd ll ogon lso ms on ll es ess mblnes nd eeon hges The eeed o-ne os / s ushed down he hghe s he ogon o s eey ll o-ne o whh s d ndues on o eun lls o whh s eeed 3 Wele nlyss We now ome he equlbum ll hges wh he sol omum Ths s ound by mmsng ol wele e he uly o he llng nd he eeng es mnus he ol os ledng o The oml ouome eles he eenly nd unde sende soeegny e ould be mlemened by seng he ollowng ll hge:

14 The oml ll hge should be se below he mgnl os ounng o he ose eenly om eeng lls By equng eq 8 o he oml hge one dees he ollowng ondon h would ensue eeny: 9 Sne hee e wo es o be se nd seel ses n se: Imgne hee s no eeon hge 0 s s he se unde CPP sysem hen eeny n be ensued only wh below-os ess hges In hs se n om eq 9 one ges / < To undesnd hs esul ell h eeny des h he ll e s se below os: whou eeon hge he only wy o deese he el e s o u he eeed mgnl os o newok hus < I he bene om eeng lls s hgh hs mgh mly bll-nd-kee 0 Imgne emnon s se he LRIC leel hen eeny n be ehed only wh ose eeon hge; howee hs s no omble wh sende soeegny < In hs se n om eq 9 one ges The leel o he eeon hge deeses wh he leel o he ogon o Howee he eeon hge should be se so hgh h oles he onsn Only he se o ee omlemens mkes LRIC egulon omble wh eeny nd sende soeegny In he ls esul s moe genel: eeny n lwys be ensued o ny ess hge s n be seen dely om eq 9 A oolly o he eous se s h eeny nno be ensued unde sende soeegny > sne om eq 9 > ; hus no eeon hge n ndue o ll moe sne he eees would hng u Imgne he eeon hge s se he newok emnon os hen eeny n be ehed only ess s ed below mgnl os In hs se n om eq 9 one ges 0 Noe h hese ondons mly nd < hus hey us ssy he onsn o sende soeegny When he eenly s hgh hs mgh mly zeo emnon hge nd eeon hge equl o he mgnl os o emnon 3

15 4 Newok-bsed dsmnon nde unom ng oeos e ndeen wh ese o he leel o he eol ess hge Ths mkes he model no ey neesng o undesnd he ndusy ould sel-egule wh mnml degee o neenon eg by smly mosng eoy luse To ddess hs queson we now onsde he se o newok-bsed dsmnon boh on nl es nd on eeng hges In ohe wods usomes e oeed e- s o he om: T q q o o o eeng lls ogned on newok nd q q q m s she s sll gen by eq whee now: whee s he un e s he un e o o-ne lls w s he ne sulus o usomes onneed o newok Noe h wh he noon boe we he gn mlly ssumed h eeon hges e low enough so h hey do no bnd n deemnng ll olumes h e deemned nsed by lles lone Newok s o beomes: 0 { } { } [ ] The mng o he gme s s beoe s neonneon nd eeon ems e se n sge I Then oeos omee n mul- es nd n sge II 4 Equlbum n sge II: e omeon Oeos n nenlze eeyhng on-ne esulng n n een moun o on-ne lls On he ony hee e unnenlzed eenles o-ne nd hus neeny n se wh o-ne ommunons In he Aend we oe he ollowng: 4

16 Pooson When symme equlbum wh sende soeegny nd emnon-bsed dsmnon ess hs equlbum s hezed by: he on-ne un e s he solly oml lue: ; b he o-ne un e s gen by he ollowng eesson: ; he ed hge s gen by he ollowng eesson: / σ ; d onney bekdown s less moe lkely o se when he ogon o s ose nege JLT nd h when he uly unon s seble nd he uly om nomng lls s on o he uly om ougong lls hee s lwys onney bekdown nnely hgh o-ne es To ome ou esuls wh JLT denoe wh / so h om eq he equlbum o-ne e s e-wen s: bs whh kes ne lues o < 0 Then een ends o we do no he onney bekdown he ogon o s ose In ou mewok he bekdown es nd s een moe onouned when lls e subsues < 0 n he oduon o nomon sne ould ou lso o lues o < whle he henomenon o newok bekdown s less lkely when lls e omlemens > 0 Noe h when e when hnge o e ndues he sme hnge n ougong nd nomng olumes hen he o-ne e smles o The ess hge does no me ll sne o ny ougong ll o whh hs o be d hee wll lso be n nomng eun ll o whh wll be eeed A ose ogon o hels ensue h he o-ne ehnge o nomon s no u bekdown ndued by hgh el hges when sendes deemne olumes 8 A mo esul ses n he se o eee soeegny when llng es do no bnd In 8 Sne we he ssumed h he olume o s deemned by lles mus be whh om eq bs n be e-wen s [ ] / 5

17 JLT onney bekdown would ou > nnely hgh o-ne eeon es In ou model een ends o we do no he onney bekdown he ogon o s ose sne eeon hges ke ne lues o > 9 All n ll he mgnude o he onney oblem s edued omed o JLT lls ogned nd eeed e omlemens n he nomon oduon unon To undesnd hs ell h he bekdown ylly hens beuse one newok sy he eeng hs he oose nees o he ohe newok sy he ognng Howee one lls e omlemens o genee nomon hen he eeng newok wll need o llow emnon o lls wns lso s own ognng lls o beome odue 4 Sge I nd he ole o ess hges We now sk wh leel o ess hges would be hosen n he s sge by negong ms s oosed o sol lnne o see nd how e nd sol neess dege In se o dseny n sge I beneolen egulo my lso se eeon hge The sge-ii o n symme equlbum s gen by: 4 4 whee he eessons o he equlbum o-ne es nd ed ees e gen eseely by eq bs nd : hese e he only es eed by ess hges nd by o-ne eeon hges We mgne h n he s sge newok oeos e ee o negoe eol ess es We lso suose h low-enough s se eogenously nd my be onolled only by he egulo Gen he symmey negoons oe ess hges e equlen o mmzng eh oeo s o Thus he eol ess hge s se suh h The ee o on he olume o o-ne lls s: 9 A oml oo s lble om he uhos 6

18 4 [ ] The ee o on he o-ne e s que ne n genel We nno suose h he o o mgnl ules does no hnge wh sne hs would be ue only by kng he sel seble unonl om o JLT To smly he oblem we ssume om now h he ogon ee does no subsnlly hnge wh hnge n es In ohe wods lls oge en eo o es o nsne eey ll sen ndues 05 lls n eun hnge o es would no hnge he nomon ehnge nd lls would sll oge n he sme mnne wh 50% Ths ssumon s ese bu s gubly els o smll e hnges nde hs smlyng ssumon we obn he ollowng: Pooson 3 I n neo soluon ess newok oeos only gee on he ollowng eol ess hge: 5 3 In ode o undesnd eq 5 onsde he sndd se wh no eeon hge 0 nd no bene om eeng lls 0 Then eq 5 smles o / < Ths s he ndng o Gns nd Kng 00: ms ollude by seng below-os ess hges n he lm by dong bll-nd-kee sysem Ths s beuse he o-ne llng hge beomes hee hn he on-ne hge nd usomes hen ee o belong o he smlle newok so h hey mke mny he o-ne lls Oeos e less ggesse sne ys o be smll In equlbum hs esuls n hghe os Ths mehnsm es owd o ou moe genel mewok The s em n he sque bke o eq 5 s nege when usomes e bou eeng lls: o hs bene s nenlzed by he oeos nd hey end o ush o-ne llng es down lowe ess hges The seond em n he bke eles he m o he eeon hge As oeos y o od omeon by ushng o-ne es down nd s he eeon 7

19 hge ledy hees hs he euny eenly hen hee s no need o ush oo low when hs ee s ensued by he eeon hge The ls em s he ee o Gns nd Kng oeed by he ll eenly nd by he ogon o Eq 5 s only ndde equlbum hge sne s we dsuss n he Aend esons e needed o ensue h o s one n Also hs soluon holds so long s he eeon hge does no bnd e When ess nd s ose n neesng mlon s h onney bekdown would no hen een when s ey hgh: when s endogenzed nd kes he lue o eq 5 hen beomes: 6 h does no go o nny o ny lue o he ogon o nd o he uly om eeng lls Ths onss wh Pooson whee we ound h unde some mee onguon onney bekdown would hen The deene s h now oeos n dus he ess hge s well: s he uly om eeng lls neses o s he ogon o goes u he ess hge s ushed down so h he o-ne e lwys kes ne lues In s esy o see h he eeon hge s zeo hen om eq 6 he o-ne e s sly lowe hn he on-ne e: < / Ths esul hs wo mmede mlons sly onney bekdown onens e olly elmned oeos e llowed o negoe oe ess hges Seondly n he bsene o eeon hges negoons would no neessly dele een ouomes sne hey would esul n o-ne es h e oo low The le on leds o ou mn oly queson How does he ely hosen ess hge ome o he solly oml one? The ess hge h mmzes sol wele s he one h mkes he ely oml o-ne e n eq bs equl o he solly een e: Thus he solly oml ess hge s: 8

20 7 W Noe h W he so-lled LRIC ule s ylly no solly oml n he bsene o eeon hges s we ledy dsussed n Seon 3 unde unom ng I 0 hen W < s solly een nd so s bll-nd-kee sysem when s suenly hgh The sme gumens ly hee Elung he deene beween eq 5 nd eq 7 we ge: W 8 Eq 8 s nome bou he deene beween e nd sol oml ess hges Noe h n he sel se when / hee s no wedge beween he wo hges: he ndusy would sel-egule wh no need o neenon Howee hs esul does no hold n genel In he bsene o eeon hges negoons oe eol ess hges would se hem oo low om sol on o ew s boh he s nd he hd em o he RHS o 8 e nege Sll hs my no be oblem he sollyoml hge om eq 7 s ledy equl o zeo: oeos ould no go below hs leel hus hey would gee on n een bll-nd-kee sysem whou hng o mnde I on he ohe hnd boh nd W ke ose lues hen ossble o he egulo o use eguled eeon hge o hee eeny Ths leel o he eeon hge s deemned by leng he LHS o 8 equl o zeo ndng: 9 W Ou esuls on wele e summzed n he ollowng ooson: Pooson 4 In sge I o he gme: uneguled negoons oe eol ess n elmne he onney bekdown oblem o o-ne llng hges; b n een bll-nd-kee sysem n be hosen by negong oeos; 9

21 when negoons led o ose ess hge he egulo n use ose eeon hges o ge lose o een hoes lhough he nee hees he s-bes In summy we he ound wo enougng esuls nd mldly enougng one om oly esee we he shown h ee negoons oe he eol ess hge would ensue h onney bekdown oblems dse Ths s he s enougng esul The nuon n be obned one gn by ellng h oeos e bee o by yng no o omee oo hd gns eh ohe: only by llowng he o-ne lls hey n ensue h hs s heed The muul nees goes oose o bekdown h s equlen o nnely hgh o-ne hges We he lso seen h unde some umsnes boh egulo nd e ms would hoose bll-nd-kee sysem n whh se een ouomes e ehed wh mnml neenon only eoy luse s needed Ths s he seond enougng esul When negoons e no een s sll ossble o egulo o moe eeny wh n oe eeon hge lhough lo o nomon on oss nd demnd s equed on he egulo s sde o hee hs ouome: hs s ou mldly enougng esul In my be mossble een o eely nomed egulo o hee he s bes he egulon o eeon hges: hey should be se so hgh h hey would ole sende soeegny The bes egulo ould do s o se eeon hges he hghes ossble leel suh h ll lls eeed e lso eed 5 Mke-deemned eeon hges In he eous seon we dsussed he ole h n be lyed by eeon hges when se by beneolen egulo I hey wee nsed negoed by oeos n sge I s le h oeos would he n nees degen om he egulo s The nuon h we ge o negoed ess hges would y owd o negoed eeon hges s well Oeos would y o obn he o-ne lls o edue he nensy o omeon When o-ne hges e ledy he lowes ossble e bll-nd-kee o 0 hen he o-ne e om bs s [ ]/[ ] : oeos would hen s nodung ose eeon hges s hs llows hem o ush o-ne el es een lowe he euny eenly Ths ylly esuls n eeon hges h e oo hgh om he sol on o ew Conesely he eely negoed ess hge s ose 0

22 bu oo low om sol on o ew hen eq 6 holds nd he o-ne es neses wh he eeon hge The egulo nd he negong oeos he onlng neess: he ome would lke o nodue ose eeon hge s he oell esul s o ush u he e bu he le he ely he oose nees nd hey would se he eeon hge o zeo he lowes ossble leel I s doubul howee h oeos would be llowed o negoe oe eol eeon hges s hese e el es ony o ess hges h e wholesle es An nus uhoy would lmos suely obd hs knd o el ons gen he olluse nue In hs ls seon we sk wh ye o el eeon hges would be hosen nddully by omeng oeos In ode o nswe hs queson we mus mend ou model sne s elned n Seon he moun o nomng nd ougong s deemned by wo bndng es only o nsne unde sende soeegny only ougong ll hges me s long s eeon hges e low enough bu he e leel o eeon hges s ndeemne Smlly unde eee soeegny only eeon hges me s long s ougong hges e low enough In ode o deemne smulneously he ou ll es ougong nd eeon hges o boh oeos we ollow JLT by nodung some nose when eeng lls Ths ues ndom elemen o nsne he een o ll my no be n he del suon o nsweng he ll eg beuse dng o engged n ohe es Is ehnl ole s h boh he sende nd he eee he ose obbly o ung ommunon We suose h he uly om n ehnge o nomon s s n seon lus n dde em wh nose om eeng lls o onsume he goss uly s I ε whee ε hs dsbuon unon G wh wde enough suo [ ε ] ε zeo men nd sly ose densy g oe he suo ε s d o eh o usomes Consde n nomon ehnge beween nd : I ε ε nd ε ε hen hee s sende soeegny egme h genees lls nd ; I ε < ε nd ε ε hen hee s newok soeegny egme h genees lls ε nd ε ;

23 I ε ε nd ε ε < hen hee s newok soeegny egme h genees lls ε nd ε ; I ε ε < nd ε ε < hen hee s eee soeegny egme h genees lls ε ε nd ε ε We now lluse he equlbum n sge II when oeos omee n e- es As beoe on-ne es e een s eeyhng s nenlzed nd he eessons e no eoed The ollowng ooson hezes o-ne es: Pooson 5 As he nose nshes he only symme ndde equlbum whou onney bekdown when sendes e soeegn mos o he me s gen by: 0 < nd < ; 0 nd < / The only symme ndde equlbum whou onney bekdown when sendes e soeegn mos o he me s gen by: < nd > ; 3 [ ] 0 nd > We bely dsuss eq 0 nd s hey ele o he se o sende soeegny mos o he me whh s he se eole e ml wh n l ems s he numbe nd lengh o lls s edomnnly se by he lle nd no he eee o e esons The nge o ldy o he wo equons s lso loed n gue whee we he u he

24 mgnl uly om eeng lls on he hozonl s nd he leel o he ess hge on he el s Conney bekdown ous n he boom le one he lowes ue desbes he lmng ondon o hng sende soeegny mos o he me nd o he gh o he dgm he el lne s / In he ohe egons hee s ndde o symme equlbum wh sendes deemnng olumes mos o he me Eq sys h when emnon hges e se o boe os LRIC hen omeng oeos should se nege eeon ees By yng onsumes o eee lls oeos dely omoe nesed emnon eenue Howee nege eeon hges se seel oblems o nsne some me go n Ily moble oeos dd se nege eeon ees o whle only o nd h eole wee llng he moble hones om oe lnes so s o obn hese ebes The shemed hd o be whdwn Thus n Pooson 5 nd gue we lso mose non-negy onsn on eeon hges Ou esuls hen eln why onsumes e no hged o eeng lls n ounes wh hgh emnon hges een hee s nohng n nle o een oeos om nodung suh hges Ths s n lne o nsne wh he Euoen eeene o ed-omoble hges On he ony emnon hges e se below os hen oeos my s nodung eeon hges hey he he bly o do so Ths s n lne wh he Noh-Amen eeene o moble elehony s we dsuss n he onludng seon LRIC > be gue Mke-deemned eeon hges unde sende soeegny [Pmee lues: ] 3

25 6 Conlusons Ths e hs deeloed model o nomon ehnge beween llng es nd used o nlyze omeon beween newok oeos We he ound h elen ole s lyed by he ogon o whh mesues how eun s ndued by sendng lls When ne-newok ess hges e ken s gen we he shown h he onney bekdown oblem hghlghed by Jeon e l 004 s enhned when lls mde nd eeed e subsues n he nomon oduon unon nd edued when hey e omlemens When ess hges e endogenzed nd hosen by negong oeos we he lso shown h he bekdown oblem n be olly elmned: oeos e bee o by llowng he o-ne The eml leue hs ound h lls genee lls e he ogon o s ose As menoned by Tylo 004 he ele leue hs used ggege d nd mgh he ued boh he ogon o nd newok eenles I s n neesng queson o uhe eml eseh o sudy he nomon ehnge oess nd oely deny he ogon o usng mo-d nl bee nlyss s lble howee he edene lble o us so ons o ose ogon o hus ou esuls sugges h onney bekdowns should no be seen s mo soue o onen In hs ese he ndusy s que lkely o be ble o sel-egule Howee we he lso dsussed how he ndusy would lmos nee hee he s-bes when oeos n negoe oe ess hges To he een h eguloy uhoes e ylly woed h o-ne es my be se oo hgh o nsne hgh emnon hges we he no ound suo o hs onen unde mld om o egulon eoy I nyhng negong oeos would gee on dels h end o ush o-ne es oo low om sol on o ew Ou esuls lso sugges h he debe o he mes o CPP esus RPP mus be ssessed gns he leel se o he ess hge When he bene om eeng lls s suenly hgh below-os emnon hges n he lm bll-nd-kee sysem he good oees nd my be seleed by oeos hemseles We he lso shown h n he esene o below-os emnon hges oeos my lso nodue eeon hges Gen h oml egulon s ey dul nd osly o hee ou oly messge s o llow oeos o negoe oe eol ess hges Only eemely hgh 4

26 o-ne hges my be sube o uhe suny eselly hey e ey deen om on-ne hges We onlude by eong some edene lble om he S h seems o suo ou ose ndngs Mus 004 dsusses how he ll emnon sysem n he S hs song endeny owd symmey n he es hged o eol omenson nd owd denl ess hge es o wed es n he sme geogh e In ul he shows h: ILEC-CLEC nd ILEC-moble eol omenson es e genelly symme nd se e h eles he mgnl os o he ILEC 0 ILEC-ILEC CLEC-CLEC CLEC-moble nd moble-moble eol omenson es e deemned hough oluny negoons nd n mny ses e se o zeo bll-nd-kee n ul o ILEC-ILEC nd moble-moble neonneon The moble seo s ully good ndde o es ou ose ndngs sne s ndeed se o newok-bsed omeon whee oughly symme moble ms he o emne lls on eh ohe s newok The e o eol omenson s esblshed hough uneguled ommel negoons These geemens e genelly on bll-ndkee bss Moble oeos lso hge he usomes o eeng lls RPP: hs s eeed om ou nlyss only n he esene o below-os emnon es Ou ndngs n be led when oeos e symme nd llng ens blned I wee sgnnly mblned oluny negoons o symme es would be moe dul o hee We belee h uhe wok s needed n hs e o see lgh egulon eg eoy dels ould wok lso n symme sengs 0 ILECs e he numben ed-lne oeos whle CLECs e he omeos n he ed-lne mke Ths s n sk ons wh mos Euoen ounes whee lge symmees n emnon es es beween ed-lne oeos who e ylly sube o emnon e egulon nd moble oeos who hsolly he no been sube o emnon e egulon CC In he Me o deelong ned Inee Comenson Regme CC Doke

27 Reeenes Amsong M 998 Newok Ineonneon n Teleommunons Eonom Jounl 08: Amsong M 00 The Theoy o Aess Png nd Ineonneon n M Ce S Mumd nd I Vogelsng eds Hndbook o Teleommunons Eonoms Noh- Hollnd Amsedm Bege 004 Aess Chges n he Pesene o Cll Eenles Conbuons o Eonom Anlyss & Poly 3: Ale Ce M nd J Wgh 003 Asymme Newok Ineonneon Reew o Indusl Ognzon : 7-46 Cndll R nd JG Sdk 004 Should Regulos Se Res o Temne Clls on Moble Newoks? Yle Jounl o Regulon : -46 DeGb P 00 Cenl Oe Bll nd Kee s ned Ine-e Comenson Regme Yle Jounl on Regulon 9: DeGb P 003 Een Ineonneon Res o Ineonneed Comeng Newoks Jounl o Eonoms nd Mngemen Segy : Gns J nd S Kng 00 sng Bll-nd-Kee Ineonneon Angemens o Soen Newok Comeon Eonoms Lees 73: Hemln B nd M Kz 004 Sende o Reee: Who Should Py o Ehnge n Eleon Messge? RAND Jounl o Eonoms 353: Km JY nd Y Lm 00 An Eonom Anlyss o he Reee Pys Pnle Inomon Eonom nd Poly 3: 3-60 Jeon D-S J-J Lon nd J Tole 004 On he Reee Pys Pnle RAND Jounl o Eonoms 35: 85-0 Lon J-J P Rey nd J Tole 998 Newok Comeon: I Oeew nd Nondsmnoy Png; II Dsmnoy Png RAND Jounl o Eonoms 9: -56 Lson A Lehmn D nd D Wesmn 990 A Genel Theoy o Pon-o-Pon Long Dsne Demnd n A de oneny MH Shugd nd DS Sbley eds Teleommunons Demnd Modellng Noh-Hollnd Amsedm Mus SJ 004 Cll Temnon ees: he S n Globl Pesee mmeo Tylo LD 004 Cusome Demnd Anlyss n M Ce S Mumd nd I Vogelsng eds Hndbook o Teleommunons Eonoms Noh-Hollnd Amsedm Vlle TM nd C Cmbn 005 Inesmens nd Newok Comeon RAND Jounl o Eonoms 36 Vogelsng I 003 Pe Regulon o Aess o Teleommunons Newoks Jounl o Eonom Leue 43:

28 7 Aend Deon o eq 7 ollowng Jeon e l 004 we sudy he omzon ogm o newok ssumng h s gen Le [ ] ~ be genelzed ed ee noong lso he os o eeng lls Gen eq we n we σ / / w w nd usng eq 3 we obn: / / ~ ~ σ Newok s o n eq 6 n be enged n he ollowng wy: [ ] { } [ ] ~ The OC wh ese o s gen by: A ~ whee ~ ~ ~ o lls ogned by newok nd emned on newok he nde uly s gen by eq 5 Thus esuls: The ee o e hnge on he nde uly o usomes onneed o newok s gen by he sum o wo os: sndd loss n uly on eh ogned ll nd em h eles he hnge n uly due o wy he een es odng o he nomon ehnge unon hus ledng hm/he o hnge he numbe o lls sen o usome /

29 8 o lls ogned by newok nd emned on newok whee esuls: In hs se he mgnl hnge n nde uly deends only on he m h newok s e hs on he lls eeed by uses o lls ogned nd emned on he sme newok whee he nde uly s gen by eq 4 esuls: d d Noe h n he ls em he ee o nluenes no only ll ognon bu lso ll eeon d d Ae subsung he eous eessons n eq A one ges eq 7 ED Poo o Pooson In symme equlbum ½ We lso he nd Thus esuls sym sym sym Θ Γ Φ whee s ogon o dened s Γ/Φ / Subsuon no eq 7 ges eq 8 The leel o he ed ee s deemned by sudyng he dee w : [ ] { } { } [ ] / / ~ σ Sne n esuls d d we he: [ ] { } { } [ ] [ ] { } 0 / / / ~ σ σ In symme equlbum he boe eesson edues o: 0 ~ σ sym

30 9 whee ~ nd gng b nlly subsung nd n eq 6 ges : σ 4 / ED Poo o Pooson We ollow he sme oedue s n Seon 3 wh gen Resul s sndd s o onne es newok mmzes on sulus wh ll usomes hene ehng he solly oml lue To ge esul b onsdeng only he o o o-ne lls boh ougong nd nomng Ae mnulons o eq 0 we ge: A [ ] { } { } ; Cony o JLT s no ossble o sl n ougong o eled only o el es nd nomng o eled only o eeon hges The OC s: [ ] { } [ ] h n be ewen s: [ ] { } whee / s he ogon ee Solng 0 we ge: h symme equlbum ess edues o eq In ode o show unde wh ondons hs e s ndeed mmum we he o deemne he SOC Denoe wh / suh h In he sme wy dene / Sne / nd / esuls: [ ] { } h edues n symme equlbum o:

31 30 sym 4 Consde s he se o JLT wh ndeenden ougong nd nomng ll e 0 The SOC beomes < sym Moe n genel ellng he denon o he ogon o we n we: In symme equlbum he SOC beomes: [ ] 4 sym Suose h lls e ee omlemens e A suen ondon o he 0 < sym s h 0 e he ogon o s no eed by hnge n es Sne we he ssumed sende soeegny mus be h he eeon hge s low enough e n symme equlbum nlly o deemne he ed ee o he mul- we mmze newok s ol o gen by eq 0 w o : A3 { } 0 wh [ ] σ σ In symme equlbum A3 s { } 0 sym Ae mnulons we obn eq ED Poo o Pooson 3 The o-ne e s gen by eq bs nd unde he ssumon 0 we he:

32 3 A6 [ ] [ ] whee Noe how / s ose unde he genel ondons sues h / s ose o no oo nege om eq he ee on s whee [ ] Theeoe esuls: A7 [ ] Subsung eq 4 A6 nd A7 n eq 3 we obn: A8 [ ] { } 0 whh ges eq 5 n neo soluon when In ode o deemne he oml ess hge s lol mmum we onsde he sgn o he SOC Denong by [ ] Ψ he SOC elued n edues o Ψ Sne / s ose we need o sudy he sgn o Ψ / : [ ] Ψ Ψ The sgn o he ls eesson s no obous o I demnd unons e lne nd / s ose o no oo nege hen esuls 0 / < Ψ nd he ess hge n 5 s lol mmum Howee hs s no genel oey ED Poo o Pooson 4 Ps nd b e ledy dsussed n he mn e To omlee b mgne bllnd-kee sysem s n le 0 om 7 he egulo n ndue eeny by hoosng eeon hge equl o: W

33 whh sses he onsn / 0 In ohe wods he s-bes n be heed ehe he ogon o s o < nd < In ul s suenly low eeon hges my no be needed ll 0 nlly ons o oenl oblem h he egulo es when yng o nodue eguled emnon hge n ode o de owds eeny Suh hge ess s gen by eq 9 when boh nd W e ose Ths hge hs lso o ssy sende soeegny whh s wen s when he een el e s ndued I s sghowd o see h hs nequly s lwys oled by 9 unless he ogon o s nnely hgh Thus he egulo ses he hghes ossble eeon hge h does no ole he onsn ED Poo o Pooson 5 skeh A oml oo lble om he uhos s ey long nd noles de mmzon o he o s he nose nshes whle keeng lge suo o od e ndeemny Insed o ondung he ull nlyss we skeh hee moe heus oo We s onsde eh one o he ou egmes o sende eee newok nd newok soeegny ndeendenly As he nose nshes we hen onsde he equlb n whh he olume s deemned by sendes eseely he eees mos o he me Sende soeegny The nlyss wh ese o ougong hges when sendes e soeegn mos o he me llels he nlyss ondued n Pooson nd we eo hee he eesson o he symme equlbum o onenene: bs Reee soeegny Ths se s mo o sende soeegny nd he sme nlyss ondued n Seon les hee wh he oe hnge n noon The nde ules om he nomon ehnge beween nd e: Sne when he eees e soeegn esuls: To ge he esuls we mose eguly ondon Gen unon egul sequene o dsbuons G n ε o he ndom ble ε wh zeo men sses: lm G n ε ε ε 0 ε ε 0 o ε 0 > 0 lm G n ε ε ε ε 0 o ε 0 n 0 > 0 n 3

34 33 Ae he oe hnge o noon om A he OC o m s: [ ] { } whee / / nd / s he ogon ee when he eee s soeegn Solng 0 we ge: [ ] h symme equlbum ess 3 edues o: A9 ; Denong / eq A9 n be e-wen s: A9bs [ ] 3 Newok soeegny Ths egme ses when newok neses s eeon nd ougong hges o suenly hgh leels suh h deemnes he olume o ll lls The nlyss o Seon hs o be moded sne s only deemned by The s-ode ondons e nd whh deemne he oml leel o lls nd The eessons o he hnge n o-ne qunes used by hnge n e e: d d d d C B B A whee A < 0 C < 0 nd B The nde ules deed om he nomon ehnge beween nd e: 3 The sudy o he sgn o he SOC s he sme s n he oo o Pooson Suen ondons o hng 0 0 < sym e h ehe s smll o h s lose o nd 0

35 34 Ae he oe hnge o noon om A he OCs w nd o m e he ollowng: Denoe wh n A B he nomng ogon ee eled o he lls eeed by newok who soeegns he nomon ehnge nd le ou C B be he ougong ogon ee eled o he lls ogned by newok Rellng h he boe OCs n be ewen s: A0 [ ] [ ] { } n n A [ ] [ ] { } ou ou ou 4 Equlbum nlyss when he nose nshes We onsde nddes o symme equlb Consde s he se whee nd sendes deemne mos olume n equlbum Then he elen ondons e bs nd

36 A0 whee he le smles o [ ] In sym- me equlbum nd Ths sysem ges eq 0 s he neo soluon Ths soluon s ld < nd omble wh he egme o sende soeegny > > / The eeon hge mus ke ose lues 0 I s boe hs heshold hen he eeon hge s zeo nd s obned dely om bs In hs se he nge o ldy s < / The se whee < nd eees deemne mos olume n equlbum n be nlyzed n sml mnne gng eq nd 3 ED 35