three essays on market structures with pivotal player · 2 the mode1 \!*ir ti ()!ir pi~rticiiiar...

$: Three Essays on Market Structures with Pivotal Player · 2 The mode1 \!*ir ti ()!Ir pi~rticiiiar fi~ri(~t~c)ti;il forrri3.inmn-;~riori n-ii1 II*)$
Three Essays on Market Structures with a Pivotal Player

National Libfary !*l ofCanada Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibliographie Servicss se ruices bibliographiques 395 Wdington Street 395, nre Wellington ûtiawaON K1AON4 -ON K1A ûN4 canada canada

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Résumé 1

Résumé II

Summary

Avant-propos

Contents

Table des hIatières 10

Liste des Figures I l

1 rit roduction 12

2 Optimal Licensing Contracts arid the Value of a Patent

3 Licensing a Non-drastic Technological Headstart through Linear Contracts 103

List of Figures

Introduction

Chapter 1

Exit and Products Selection

1.1 Introduction

"T!i:> 1 3 4 iiticm~lt f'rorri t f i t h .rpprmch c.ikcnri II\- Fr!tv iniiiti , i r i c i Tlirsw 1 !)!Ji 1 . I I I i i i t ~ r pirptnr. ( - imsi ir i~~~rs. wiiir-ii ti;rvt.

. : f i l ! i i r * ! : ~ . t r ~ ~ f . !)II\- t I I C ~ r i t ~ c l \\-1:Ii th^ i w ~ r filtl prlct3 if t h fidl prict. <!ut? twt cxcced riie constirriers' rcsc.rv;rtiuii pricv f f r . ~ ~ t . t ' . t . , i r l ~ t m t 6 r ~ Il.tvt1 t ic) 1ri:ritisir prt+rrtii-c for protf i i~t (tifftretitiatiim. Aiiotlier weil-knowri ciuc wiicrv i-onaiiriit3r. i ~ , ~ v t s . L I I i i i t r i i l s i c prt~ftlrtnriccl for prmfiirr ~i i t f t~rr~it iar roll 15 t. tir litlt' corisiclrrerl in nixit anri Stiglitz i Il)';';!.

1.3 Products select ion wit h cost less reent ry

1.1 Products select ion wit h unprofitable reentry

1.5 Concluding remarks

1.7 Appendix B: Proofs

1 . 7 1 Prouf of Lenrnm 4

.ïl , r t b t j l i ~ r thtl rpsrric-rions , ) 11 ( j i ~ t i ~ l . i l , in Clair11 1 art> rilosta rmluirrvi for - h s ~ i r n p t i o t i 1

i b t . - : i r i ~ h t ~ ( l " 1 . t1t1 . 4 1 , p t ~ r l ( l i s ..\ 1 . .\(x.i,r(liiig!y. i i s i t iq C'l.iiiii 1. n - t b 6)ht;iiii rii;tr. 1iii<li1r . \ s s i i r ~ i ~ i t i o ~ i

1 ,/:, l!' .oli?.' 1 \[ i f . i ~ i i i 0 1 1 1 ~ 1: ilit.rt1 4txiir. \' 2 0 -ii(.Ii t i ~ i t 1 1 ; . dl;. \ ' i? . t -011it i o r i 1 ) t ' t i l t a

. - !; 1 1 1 1 n v 1 1 1 g .vs:tyll , ) t t ~ ~ 1 1 ; ~ t p ) i l $ - '

R t > 1 1 1 ; 1 r k t ~ ~ ~ r ~ ~ t ~ ~ l i ~ t t t ~ i ~ rl i ;tt t l l i ~ l t ~ f t - l l i ~ ~ \ t i h1tit1 I 1 - 1 l ! rt)t1(1> T O mru i i - i t t w t ~ ï x ~ r .+ l , r t h ~ ~ ( i > 1 1 )

1 d Zr! 1 I I . 0 1 1 r lit' I )t I L C T l i ; t l l ( i . ' . ~ I I ~ ( v \ cli I . i l , . q i~ ..;tri(-t lv ( t c v . r t * i f i i i i g iri . f i , : w t 3 C ' l i ~ i ~ i i 2-i i i i I 1 .

( 1 , I i: , I J , fi,, ( 1 - t j i f ~ ) r ,111 -jl,, < ( : 0 - 2 t / 1 ci. L 1 . H ~ ~ t b \ . t ~ r . t d k i ~ ~ g 11110 ; t t x s o 1 m t t 1 1 i ~ 1 t j ; - 1 1 . = 11 2

: i i i i ~ i i i ~ i - t ~ i . . i l ; = 1. v t r i 1 i t , , 1. j = t - t 2 . C ' i ) r i s t ~ ( l i i t ~ i i t l y . t lit. r i g l i t -

! i . i i i i i - i t l i I 1. 14 1 I t r i t i L I I 1 ) t . G i : d - 2111 11. l i. r i i i . r t l f o r t s . fi,r . i l [

J! -. : tj :{. d 2 ; - ! I ( . j l l . t i 1 -. 0 for . j! , ~ ~ ~ r h . i t ~ ~ i t l>- t - i o s t a t.0 tl - 2rj I t j .

43

Cliapter 2

Optimal Licensing Contracts and the

Value of a Patent

I Introduction

I ' i i ~ ? iviII bc t l i t s I-;LW wiwritt\t~r r h c irivtlritur i i tb~tiier .in ititir.pr.ri~i'rir rmeiirch !ab or. 6)r in5t.\iirtB. .i ilonitut K- i irrii

: i i ~'11.-11iz Ir' tt~L~rit)Iiic! t t ) fort*~qi firin_s thcil . L W .ic.t:vv OII tt\it~k<i~'t> wtwrt. tl1t3 ~Ii>n\t.attç tirm i:, ,ihwnt

2 The mode1

\!*ir t i ()!Ir pi~rt ici i iar f i~ri(~t~c)t i ; i l forrri3. inmn-;~riori n-ii1 I I * ) <iri~st i ( . ~rhtmt-vw- ( tt - 1 . 1 t 5 1.

Tl111 iritt>r;ir.riort I > t ~ t ~ r m m tir1115 ;trlti t h i r i t l t p ~ n ~ i t ~ r i t riwb;~r(.li Lit) . l i t m d t t ~ r rc~fvrrcd t o ;LS t l ~ r b

li,.tm31 N. 1 . ~ forr11:~ilf- 4 Itwrilwti h v r iltb i l d l tw i rq r tirw-sr aqtl gilnltx. .At r I I P tirsr .st;~gt.~. t lit1 l i ( ~ ~ i s ( x

, . I l t ,, b:.t*> ,: t .( )ri t r i i~.r . Thi> l i c - t ~ r l ~ i ~ i ~ 4 - t mtr:icSr 1 . 4 111sists of il11 111)-front t k m i f ~ t ) t L ~ i ( 1 i l r~ pyidt v ~ (4 i t~11 i t~

-,ci. r p . S o r t 3 t1i;ir t t l t ' . L I I ~ I ) I I I I ~ rov;iltit%s piici I ) v tirtri Ii mit! dq~rrici on t ~ o t f i firrxi h ' s o i i t t ) i i t

i i r i t i T I htid I u ~ r ~ ) i ~ t Q. Tl115 11;1/1 111 1)iirt !(-i~l;lr 1 1 t h t t i ~ (.;t.<tb ~ v h t ~ ~ w v t ~ rov:dtit>s :LIT !miibii ~ ) I I tir111 t i . ~

-;lilb~ r ~ \ - t ~ i ~ l t ~ ~ P ( Q I , ~ ~ ~ . For t t i v +&il , , f yriilrality. sliiili rmt rtTtr1c.t r o y d t i m t o pos i t iv~*

3 Fixed fee plus linear royalty contracts

4 Optimal licensing contracts and the value of a patent

4.1 Optimal licensing contracts

I X ~ i i i l i i ioii I t ir ruri rit triiisiiiiiz;itit~ii ih .;rtisiit>(i for d l 1 - 1. - . r l - 1. 011 tlic o ~ i i i ~ r h d . ivit 11 t!, = (1;'

t'or i - I . . - . . r~ - 1 . tirst-orclt'r ~ o w l i t i o i ~ for profif rr~;ixii~iizi~tic)r~ of t h ) 1ast tiriri wiII t.licii \ ) t t

1 2 p " : . C ( 1; + 1 1 - r l - 2p0\ - 2( 1 .- p'' )q,,. which is strictly ~wg:~tivv for d l qn w l w ~ i e w r p" > 1 2 .

' 1 n I ( ' t J 1 l > l 1 ~ j l l ~ ' ~ ~ ~ ~ ~ . i f l ; ) ! = , . 1 1 I is C L C'o~ir~iuc t$(!i~ilit)r~urli. :\s shc.nv11 in ciitb ; i ppwl ix . tu tblitniriiit~b t11L

l i l i l t i I ~i t ~ ~ t i ~ l i b r l ~ i ~ r l . t 1w licx~rlsor (.;LN sl lgi~t ly m o ~ i i f ~ . t 1 1 t h ( u i l ~ r a c t by i i ~ l p o s i ~ ~ g a p t~ r~ i1 t . i~ 1.. :LS >tl~iiII

'L- i~.;iiit> I J I ~ ~ 3 t rwr ly ~ ) o ~ i r i t r . i f tlits l i c * [ * ~ l s c s ( * t i ~ c ~ l l ~ ~ r \1ro4ktic-(\. .A I i ~ i f ~ l i t ~ ( ~ c ~ l i ( x ~ ~vl t t i t i l t . I ;LM%

i v i l ~ ~ r t ~ 1; -- 1 :> t h ) p w , i b i l ~ t v r h t . ~ v i ~ t ~ ~ i t ~ v t ~ r ) 1 - 1 tir1113 ~ c q ) t t.iitb t x ~ ~ i t r ~ r . rlltb ~ - o r i . t * ~ ~ ) t ~ r l ~ ! i r l ~

4.2 The value of a patent

. - l ~ . ~ . f i ) t - ( i i ~ q l y . t1 \ . cb~~ ~f r l i t b ~ ) ; t t t > r i r t ~ ~ l 1rlrio\xt1oIl ; i l lo~vs ti)r 'ui i ~ i t i ~ l i t t ~ ~ i ~ ~ ~ i i l tSost rtd11(-r~o11. th tb

l l l r l o ~ - ; i r o r ' ~ r t ~ - f ~ ~ i ~ l t l n i I I t ~s (+c~t r h t * l)r~)!-i? t h i t ;i r ~ ~ o t ~ o p o I \ - 7 . i - i l 1 rri:dw ~ v i t t i o ~ ~ ï 11si1iq tilt1 i ~ i t i t ) v ~ i t l o t ~ .

- r l l l? titit.~otlc;lv 1.011rr;itiic-ts tilt. tirliiiriqc; i ) t i t ; t i ~ l t ~ l i m i ~ r thtt ;t=;i;itrripticiri thtir rtit. i r i~iov; t tor (-;tri risth

tb!rIit.i. tist*ci ! i b t b tililv 4 ir iirit3:ir t irl t~)ti t-I)i~.<i~t 1 ri iy;ilt\. 1 . t irirr;t~.ri; t ) ~ . f ; ) r irlsr;t~lc-c~. K ~ L I I I I ~ ~ I I ,i11t1 T ; L I ~ ~ I I ; ~ I ~

l!)a~i ; . I r 1 r i l t w > [ . ;LS~~S. t j i t ~ li t-tq~sor 's rtlixlIilitl t t~rit is t o m r o ~ i s t h > t.03; r w i i ~ ( - t i o r ~ id10w-d hv r h >

:1 l~l~l \~;~t10[1 rt111tls r~ L t * r l t . .-!t t i rsr qi;~ri(.fb. r h (XI I sh11i >(i111t% cto1111rs ri oiir :tndvsi0;. B11t tilib

] ) i ~ t ~ n t i ~ i l t ~ r i o ~ i IF * t t . t I ~ i i l I ~ (1111tt. ~ r i t i~ i r iv t l - I r i ( l t ~ i . w t i t w a ~ f x r th fa i r i n o ~ ; i r o r lsitIi tlsfl tistv! ffvb pll10;

ra ~ i . ; ~ l t ~ - ~ . ~ , t ~ r r ; ~ , - t . - . f i i t b l I~ r i~ lv ; i r~ , r i> ; ~ \ ) l t > t ( i t ~ i ~ t ~ l l [ ) ~ i I i i t ~ ~ ti;fb t~l:trgi~iii l (*i)sr ot -1 h - t i ~ i w t t ;L< i1ts i ~ i > I ~ t * s .

n-t1;~tt~\-clr r tic. c~ii;ilirv o f Ili.; iririo\-:triori. Tilt. lic-cm..;( Ir c-;iri r1itwîi)ri~ ~li*sigri ; L (*otit rm-r 5t1('h t tiiit . for

t . ; t i . l~ tir111. - r i 1 a~c.c.cyi r 11,' (.c )rirr;tt.t" l ) t . o t . ~ t l i b - ;L 1;irgc~- profit t IMI Y I ) r t b . j w r r hi* c'or~triic.~" I ) I I ~ . i f

, l i ~ pi-rr; + .ii*r*ttpt t i l t * (.ont r;i(.t rhbv 111,riiiri ;i protir .+tri(-tlt. l ~ s s : ; i c ~ i t ; i l l i - ;i zcro profit t t i m t h i b 4 i r i t l

tj! 1

Related literat ure

Concluding Remarks

7 Appendix

7.1 Proof of Proposition 3

1'1 "it ive (\ttant ity ~t cqiii1it)riiini so chat. hy t hta hrst-urcicr t-oridition giveri in t 3-13 ). iiriy Lictmst~?

[ ~ i t l > r ~ ) r o i i u ~ ' c thci same ([iiaritity a r eqiiilibriiini. ;ml (b) wtl stiotv tliiit iu~y tiorilicenst~ prcitlucw


A (2';. ; . i i i i l Q'.. ~ r ; t i i d bir t i l t * s t i i i i of ~ ~ i i ; r i i r i r i i ~ ' ; p r i ) t t ~ a . f v i ; i t ;i ( ' o i i r ~ ~ i r i * ( p i l i l ) r i i i i i i 1,. tirni'

i i l . 1 6 ) i igin?: t t i .\- 5 .~11ri 3'. n - h i l t - A.'' i' r 1111 c v ~ ~ ~ l l i l i r i t l ~ ~ i i l 1 1 1 t i l ) t ~ o f l i ( . t ~ ~ l ~ t v ~ . i . Sm-. ri 1 i ~ ~ i p h t s : ,

; i i , ~ t . fibr ( a ) . i i i c l ( b ) t o ticilci ~ t i i i i i l t , ~ r ~ t ~ t ~ i i ~ l y . A-" 1iliic;t l ) t ~ t ~ ~ i i i i l r o r r . On t l i t l o t l i t t r i i i ~ i t i . f r u t t i t h .

. - . m

Tlit~>t~ t - o r t ~ p u t i ~ [ ~ o ~ ~ ~ 'ire . i v x l ~ i ) l c I ~ I ~ I r c q ~ w t

œ P .a Proof of Proposition 7

\ \ - t l ?iltb~i ( i t w ~ r t * 1)v r t i l t ) r iglit-l~i~ticl s~c!tb oî' i 2.5ii 1 . It ih q ~ i i t i ~ i b i ~ s y r o ~ v r i f y t h t F 13 btril*tly p o s i t ~ v t ~ .

i:;iri itlso c.oriipiitcb t lic. ~ i t r t i i ~ l c l~rivi t t ivc~ o f t hi.; c-spri~ssic)~~ [vitIl wspcc't t o <)o. r~ i~ll(1 r t . This

glY4'h:

t h x + s ~ ~ ; ~ ~ ~ t l < tv1t1i rtL>[)tv-t t o t . . , m t l 15 . ~ t r i ~ t i ~ i l i t * ~ t b ; L ~ i t l ~ i l1 r i i~licl t l s t t l c ~ (20 !s ~ , l ~ v i o ~ t ~ l ~ strit-rl\-

~ I I ~ , I - ~ ~ , L ~ I I ~ : i t i ( 1 6 ~ ~ ~ ( i r j .mi 15 >tr î ( - t lv dtnt>i~sirlc 111 t . .

( i i ) ;incl ( i i i ) Tilt, priv;ttt1 v;tliit' t j t ' ;i p i~ t t~r i t tvill t~xct~tvl its . ; o c - i d i-;~Itic* ~vhtwta\-tar w t i s i i r i i t n '

-t~ri>l115 t i ( ~ ~ * ~ ( ~ i ~ + ~ ~ \vit11 rtlt* i t t Iopi i~~t1 o f r l u t i ~ ~ ~ l o \ . ; i r i o ~ i . This \riIl I N - t h (*;LW ~ - i w ~ i v v w (20 --, (2.".

L I - . . i v I ~ t ~ t i t ~ i + f ~ r t - ! I - l ! , l - ( - 1 - I ; . > t > t 3 ! 2 . . 5 2 ] .

8 Complements to the Appendix

c ) ~ k k ( x' . /) r k - - , 1 A. - 1 , 2 ] l e i h - ~ h i - I 1 - ? ~ p i

? [ < ; J I - 21 Tl,,, = il. I I - 1

Chapter 3

Licensing a Non-drast ic Technological

Headstart through Linear Contracts

1 Introduct ioii

\ \ ' t k c.c,li:iilt>r ;i 111;~rkr~t t ; )~ . . L ticrr~ioqc~~it~citis proc111t-t ~virli A sibr .Y .= ! 1 . . . 1, 11 2 . o f firr~is t I i i ~ t f i i ( , t b

-111 l[l\ 'i1T!4' c ~ ~ 1 1 1 i i r l r f filrlc't ioll P t (2 I \vtlixrt' (Z 5t: i~lci~ for t o t d o l l t pllt. \\-P 511pp)St' tflilt Pi (2 ) = ( 1 - q.

n ~ r t i ( 1 % 1 ) . wtliqitq-~br ,I (2. ;~11(i 1'1 (2 ; - 1 ) o t ht~tv is t ) . ~ r i i ~ i d v . pro(iu(=t~oii ( .o?t5 of iiIiy hr111 1 1 .

1 - . L Y I i c i O 1 1 ; ~ r l ( f rlh i;r;ui(iing f;)r h i Il 's qu;mtity.

[ ~ l , L I l(11t 1, ) I I t~ 1 t f i t> 1 ) fir1115. t h t~rv 15 1111 i t p ~ r ~ ~ l + ~ r i r r + ~ w ( * l i Iat ). ! i t w : d r tbr ~ ) f t ~ r ~ ( l t o :LY 7 l i t b

1 i t ~ ~ ~ l ~ ~ ) r . I V ~ ~ O O I Y ~ ~ S :L p;it1>11r for , i r t ~ - h r l t ~ l ~ ~ q - r t 1 ; ~ r r t~ i t~ i~tbs r h ~ 11ixq111a1 (-ost of prt)cl~i(.tiori h m 1

, r l l , - t ~vit l l I I + t - ,.- T t l t b li(-tylst~r i ? 110r , L ttli-ntl)ibr of t h > iri~11istrv iiti(1 wt*ks t o lit~arist* 1115

~ 1 1 1 1 ) \ . : ~ t 1011 r i 1 t l i t > firnw.

~ I L T ~ T ; L C T t( 111s I , tqtvc~*t1 t i r~~i . ; ,iri<l t t i t * lic-t.ti.s~ )r , u t 1 tiiwril)t*il I I V T t i r . fol11 )u-iriq îi~t>-c;t;igi. q i ~ i i t ~ . 111

T r . t t I I r t t - 1 1 i 1 I r i t t t t f i t .~)+~c.ititbs ;i tisc~1 h.1. ( 1 . .iricl C L

; . I I \ , , L ~ ~ i. ~ i t t t ' ,). Tilt' < t l t , ) t ' ;~t1~1115~il)lt~ t . ~ ~ i t ~ . ; t ( . t ~ 1 0 . I I ~ [S ~ I I ~ ) ~ ) o ~ ~ ~ I ~ t~ I ) t b { \ O . O 3 O iLti(i 1 1 C O . 1 .

. \ r rlio \)iyi~i;lirig t,f tilt' w 3 o r i c 1 -;r;lgtl. tir1115 I )iistbr~.r' r ht- 'ipi>(.ific,'; I j f t l i t * prcyio.;cv 1 (-oritrwt ;L*

x - t ~ l l ,L- t kit.- ri~irqi11:~l 1.1 )sr rtb(l~i(-tit ciIl( ) \v t~ l ln- t t if> i:i~io\-:it ion- t . TIlt11i. tirtx~s cltv-idt~ s i ~ t i t ~ l t i i ~ ~ v ) I I S ~ V

a - t i t l r tl@>r r t ) ;i(.(,~bl)r ) r rttjt-i-r ri:il li(xt~isor'+ ~.otitr;u.r. If :L tirrn. SAV 1 . ; ~ t ~ v ~ p t . - riiv (xmt r:icSt I 1 1 . , J 1 .

* iitw ~t i 11i;iryr~;il i.ost l ) t ~ ~ o ~ x i t ~ ; t T , 1; - e . I f :L îis111. 5;iv J . rtljw't5 rhcb rontr;u,r. rhctri its ni;iri.$ri;d

l . 4 F F 1.- 1 . . -- 1' . H t w v . t Ilil ;tlt -\- = i 1. . . :) 1 1 )i tirms is pi~rtiriorityi i r i r t I t\vo ~11l )s t~ ts . .5 ;~ i i ( i 5 .

(.( I F K I ~ ~ I ) ~ )tiifirig t ~ ) t iitb r u - ( ) p~ ' i s ik)b i)rc ~(lirct iim tdiriologiei;. Th* stlr S I-onsists of t i i t l lir.r~isec~s. i . r . . .

3 Firms' Decisions

1 Equilibrium contracts

. L I . i ( ' w i r i i o i t v l ~ i i l i ! i r i i i i i i . i . t8 . . k . p. r r . (.: = ~ * q : ( k. p. ( ~ * i ) ~ , - . y 1 - 1 1 - A.~t !y[k . p. ( c ; ~ ),,.-*y I n - i t l ~

I . ' 1 , , i ~ i d i t i : . e ~ l - t ~ i i ln- 1 i1.2 ,,ri11 [.l.:i) r w p t v t ~ v ~ i v : Q:.'( k . /,. (-:. , + - ~ t m ~ l s for A,!:'{ A-. 1 1 . 1 t - i : l hL y 1 . c ~ ~ ~ t i . 1

1 I L v v 1 3 ! 1 1 , . b-or i . o r i v i l r i i t w c i ~ . wb &i c l t ~ h r i t ~ fi ith f l ic . hrst tc3riri 111 i :3.:II 1 .

Tiitw. ~.oriip;t i- ; i t ivt~ ..;tatic rrsiilt.; c ~ c . i - ~ ) r ~ l r o r h . iritiiitioris qivtlri ; t t ) o v ~ . Tiicr-il is ho\vt~rr*r o r i t l

111 ) r ~ ( . t h ; l t ) [ t b t - x ( -q ) t iîm. r i ~ ~ n t l I \ * . f h . i v h n t ~ v f ~ r r i i t ~ ~ ~ ~ ~ t t i l i h - i ~ ~ r i ~ ~ ~ o n t r ; ~ c t k o f T v p ~ 111. t h t b +v\~ i i i i l ) r i i i~ t i

1-1 ji.:i/tv r ; t t t b / ) * is t i t v m w i r l g [IL 4- i . t l . . 111 P . F r i m o \ \ r : i l~)vta t i i s c t i s s i o ~ ~ . I V ~ ~ t ~ x p t v S t t ilikt i t irlcrtb;~w>

x . i r l ~ t 7 -in1-t1 l~avib : i r q ~ i m i \ ~ i t - . v t ~ w u - k l ST:W \vit11 ;LI: t ~ ~ ~ ~ i l i t ~ r i i ~ ~ r i 11f T v p v 1 I I I i v ~ t h , I 3 t r i t 11.

I H 1>1t i ~ . , ~ rl n - i ~ l t ~ riitt* UV +ilil11 t ~ ( 1 111) iv i th t v ~ ~ ~ i l i ~ ~ r i i ~ r x ~ 1 )f T v p II ! w i r h i i ZWO r o v d t y rat(%! [f

4 ~ ~ Y w ~ : L ~ I ~ > . .1p[)iirf1nt ( X )c l t r iukt11 111 ( ~ ) t n t ~ i1c.t 11;dlv f r o r ~ ~ t tit* fi\(-t t l i i ~ t . ~ L G ; d r ~ a c i v I1ltlllt i o~ i tv i - i\.f1

~ h t l 111,r r i d a - ir;to d ~ t x x ) i i r i T 111 oltr id)ot*tb ( [ k - i i ~ i o i l o f tllfl i~l(-i(itmcth of [*Iiii11qt3 iti m a r g i ~ i ; t l c o s t s t ~ t i

6 -4ppendix: Proofs


5iiit-(3 IVP 2lavtl ;~ii;~init.tf t h;ir 1; 2 r l 17. t hta Co i i r t ior t ~ i i i l i b r i u n i q i i m t i t i r s ;irv irniqiit?ly g i v w 1 n-

:1.2. . i r i t i i 3.3 i f or m v X - , , I . .trici i (.h lhe.y. I n t htb f i ~ i i r r l i stage o f t h ditrile. firr~i.; ~~i ioow thcl rriiugiiiii i

1 ~ p r I t t i . t & ! r o I I I ; L Y I I I ~ I Z ~ * ~ h r protir. For t i 1 r : h t ~ wfwmct~s. let 11s (itqlott~ riiis protit I I \ . for al1

- 7 ) - -1- \ \ . t b r t i tmf, 1i;ivt~:

d ~ ( i-. , j , ( i ) - = o.

i lk

(iii) 1 . , rX.2

I r i5 tl ic.rcti>rc i i i i i l i d i a t c ! t t iat . p' is i lcrrrc-uir ig iri !i m d t l i c r c f o r c iti t t i c rii itrkct sim ( 1 . 1 ~ i i r t l i t ~ r i i i c ) i c ~ .

L: 13 cliritt* t1i&v Ci, vm-ify t t i i t t :

Conclusion

References

. - \ r r o ~ + . K . I 19ti2 i +,Ec'i,~lo~llc. \\'tllt'iiït' ;i~lcI t h ' .-\llorxtiotl o f Rt..;oitr(v.s f o r Irivcwticms." in Tht R d t

,lrjtî Dlr-vctlurt of 1ni~r1 t t1 . t . - l ( ~ t ~ ~ ~ ~ t ! , , 1 > ( 1 . R.R. Stllsor~. P~-irictvi)n: Priri(v>tori L'tu~twtty Prt~ss-

three essays on market structures with pivotal player · 2 the mode1 \!*ir ti ()!ir pi~rticiiiar...

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