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Strategc E n Deterrene an the B ehavi of
i try c d or
P harmac eu c alI c u en ri to P aten E x rati 1
ti n mb tsP or t pi on
G l nE lis
en l on
M I an NB E R
T d
and
Sara F is E lis
her l on
M IT
Apri 7 99
l2 ,19
P rel in
im ary
1
e il e l n mite u liso @ mite u h ¯sta t o ' w r a su re by N a io a
ma :g liso @ .d ,se l n .d .T e r u h rs o kw s ppo t d t nl
Sc n eF u a io r n
ie c o nd t ng a tSB R 95- 50 7 a daSl a e a c e l w ip a dt ese o da t o '
1 6 n o nR se r hF lo sh n h c n u h rsby
g a t f o t eSl a F u d t na d El L ilyt heN B ER a d t eD e n s F c lyD e e o
r n s r m h o n o n a io n i l ot n h a ' a ut v l pme t
n
F n a M IT .W e t a k A l n So e se , Eme B a e n D a id H w n f re c le t r se r h
ud t hn a rn n k sk ra d v a g o x el n e a c
assist nc , G ilia Cu r f rh l in c n r c in h d t se , Ka ie M a f ra e f rg id n e o
a e l n rie o e p o st u t gt e a a t t ca l n o u a c n
in it t n ld t il n it s R ia n h aM ih l nf rt e ssist n eo a aissu s.W easo
st u io a e a s,a dD a da dR e aiso o h ira a c nd t e l
t a k Fio a Sc t o t n f rh rpa tin o rj in a a c le t n e o t a f rpr v ingo h r
hn n o tM r o o e r u o td t ol c io ® r s nd o o id te
d t ous.Final ,w ha kEr ieB e n tf rma yu f lc mme t
a at ly et n n rd o n se u o n s.
A bst a t
rc
Thepa re a
pe x mine h h v ro
st ebe a io fpha ma e t a c mbe t
r c u ic lin u n sinthepe io u
r dj stbe o e
fr
t e l se pa e t pr t c io . B e a se t e st a e ic in e t e t de e n r is a n in
hy o tn oe t n c u h rtg c n iv o t re t y bse t
ma k t w ic r
r e s h ha esosmalo a g s t
l rl r ea oma ee t yd t re c n c ssa yo
k n r e e r n eu ne e r rimpo ssibl ,
e
itis pr po d t to e w y t l o f re id n e t a r a e in ue c d by a d sir t
o se ha n a o o k o v e c h t¯ms r ° n e e e o
d t re t y is t v st a e w e h rbe v ris n n no o icin t e size o h ma k t
ee nr oin e ig t h t e ha io o mo t n h ft e r e .
T h a ac n a d e t g o c oif r t na
ed t o t ina v r isin ,pr du tpr l e a io ndpr in f r t nf rasa eo
ic gin o ma io o mpl f
d u s w ic l stpa e tpr t c io be w e 1 986 a d 1 992.A mo gt e¯ ing c nsist n
rg h h o tn oe t n t e n n n h nd s o et
w ha n r e e r n emo la et tin u
it ne t yd t r e c de r ha c mbe t inma k t o t r d t
ns r e s fin e me ia esizea et e
r h
mo ik l or du ede a d e t ga dt c e set epr l e a io fpr se t t n in
stl e yt e c t ila v r isin n oin r a h oif r t no e n a io s
t ey a f r pa e te pir t n
h e rbe o e t n x a io .
G l n Eliso
en l n Sa aFish rEliso
r e l n
D e rme to o o s
pa t n fEc n mic D e rme to o o s
pa t n fEc n mic
M a c u t s In it e o e h oo y
ssa h se t st ut fT c n l g M a c u t s In it t fT e hn l g
ssa h se t st u eo c oo y
50 M e r lD r e
mo ia iv 50 M e r lD r e
mo ia iv
Ca id e A 0 21 42- 347
mbr g ,M 1 Ca id e A 0 21 42- 347
mbr g ,M 1
1 I trod u ti
n c on
P r rt 984 albu h
io o1 l tt emostpo l rd u s t n e or t int e
pu a r g e d dt e a h irmo o l
n poypo io o g
sit nl n
a t rt e
fe h irpa e tpr t c io x e .FD A r g a io sr q ir da y¯m w n in opr d c
t n o e t ne pir d e u t n e u e n r a t gt o u e
ag n r
e e icsu it e t e a h l n t y pr c ss o e s a d cin a r l t h h t e
bst ut or pe tt e e g h o e ft st n l ic lt ias ow ic h
in u
c mbe tha be n su e t d be
n d e bj c e ing al w d t c mpe e T h g c ng d d a t al
lo e o o t . in s ha e r ma ic ly
in t e mid- 980 ' t e W a ma - a c A c 1 984)g e ty r du e r g l t r ba r r t
h 1 s: h x n H t h t( r a l e c d e u a o y rie s o
g n r n r n it h oif r t no a el w ma d t g al w gg n r
e e ice t ya dw ht epr l e a io fst t a s n a in / lo in e e icsu it -
bst u
t nbypha ma ist itbe a
io r c s c mec mmo o e e ic t a nama o it
o nf rg n r s oe r j r yma k tsh r
r e a esho ty
rl
a t re t y
fe n r .In t is pa r ee pl r wph r c ut a c mbe t h v d atw h t e
h pe ,w x o eho a ma e ic lin u n s a e e l it h
t r a fe t y
h e to n r .In pa t ul r sin
ric a ,u ga pa lo r g t a o
ne fd u s h tl stpa e tpr t c io be w e
tn oe t n t e n
1 986 a 1 992 w d sc ibe pa t r s in a v risin ,pr d tpr l e a io a pr in ,a d
nd e e r te n d e t g o uc oif r t n nd ic g n
l o o v e c h tin u
o kf re id n et a c mbe t ma h v st a e ic ly d o t d t e \ in e me t
n s y a e r t g al ist re h se v st n s"in
a a t mptt e e e r n r .
n te od t rg ne ice t y
R e e ty a l r e n mbe o t e r t a pa r ha e d sc ibe h w ¯ms ma ma e
c nl ag u r f h o e ic l pe s v e r d o r y k
\ st a e ic in e me t in c pa it , a v r isin , c pit lst uc ur , c n r c u lpr c ic s,
r t g " v st n s a c y d e t g a a r t e o ta t a a t e
d t )t e n r fpo e t lc mpe it r 1 T h
e c,t t r( ra c mmo a e h e t y o t n ia o
t . ode e o c o t o s. ena u e o r t -
t r fst a e
g in e me tmo l ma e t e d u tt t stdir c l , h w v r a r l t e y l te
ic v st n de s k s h m i±c l o e e ty o e e , nd e a iv l it l
e id nc h s a a e .T h a o c w t k in l o in f re id n e o r t g in e t
v e e a ppe r d e ppr a h e a e o k g o v e c fst a e ic t n
is t t y t e pl it t e f c t a t e in e t e t d t re t y w lt pic ly be l r e
o r o x o h a t h t h c n iv o e e n r il y al a g rin
in e me ia e size
t r d t - dma k t t a
r e s h ninma k t w ic a esu ie tysmal l r esot te t y
r e s h h r ±c n l l/a g ha n r
d t r e eis u ne e r /
e e r nc n c ssa y impossibl .
e
W e be in in se t n 2 w h a d u n o r t g
g c io it isc ssio fst a e icin e me tmo l me n oh l
v st n de s a tt e p
ca if h
l r yt ispo t sin
in .U gast c a icmo e h hiso l ig tyd e e tfo t e t o
o h st d lw ic n ysl h l i® r n r m het x bo k
t r e st g mo e , w ¯st r v w w a is me n by a \ st a e ic in e me t a d n t
he- a e d l e r e ie ht at r t g " v st n n o e
w y d e t t st o st a e ic in e t a e d u t W e ne t po to t t a , a n e t y
h ir c e s f r t g t n r i±c l. x in u h t bse t n r -
d t r e emo iv t n q ibr m in e me tl v l r f e
e e r nc t a io s,e uil iu v st n e e sa eot nmo o o ic lyr l t dt h
n t n al e a e ot e
a ta t e e o h
t r c iv n ss ft ema k tt
r e opo e t le t a t
t n ia n r n s.W et e in r du et n r e e r n e
h n t o c hee t yd t r e c
1
See, f ex pl B u ow , G ean opl , an K l perer (19 85), Fu en erg an T i e (19 83 19 83 ,
or am e, l ak os d em d b d rol a, b
19 84 ),Di i (19 80 ),Sc hm al s (19 7
xt enee 8,19 81),G el anan Sal (19 83 u d (19 85
m d op ),J d ),Ag onan B ol
hi d ton
(19 87 ),Cooper (19 86 ).
1
mo iv t n,d u w yitt nd t
t a io isc ss h e s obel r e
a g stin in e me ia esize ma k t n ilust a e
tr d t d r e s,a d l r t
h wt is c n l a t
o h a e d ono nmo o o icpa t r s in in e me tl v l
n tn te n v st n e e s.
T h ph r c ut a
e a ma e ic lind st y pr v e a n e o ru y t st y e t y d t r e e
u r o id s ic ppo t nit o ud n r e e r nc .
L o k g a d u s w h e pir pa e t o e c n c nst u t a siza e sa e o
o in t r g it x ing t n s, n a o r c bl mpl fsimil ry
al
sit t d e t a t f c gat r a fe t y hea a a eda aal wu t o ka o r
ua e n r n s a in h e to n r .T v il bl t lo s ol o th w¯ms
u an
se umbe fpo e t lst a e ic t os, incud gt ot pe o d e t g h n mbe
ro t n ia r t g o l l in w y s fa v r isin ,t e u r
o o ms in w ic ad u
ff r h h r gis sod nd pr e
l ,a ic s.A n n e a it n lf a u e o h ind st y is
ic dd io a e t r ft e u r
t a n r be o s po
h te t y c me ssibl n a l rt a a
e oe rie h n tak w pa e te pir t n d t .T h f c
no n t n x a io a e is a t
al w u t o kf re id n eo r t g
lo s s ol o o v e c fst a e icdist rio n to l
o t ns o n ybyl o in tc o se t n l
o k ga r ss- c io a
pa t r in in e me tl v l
t e ns v st n e e s,butasoby l o in tho
l o k ga win e me t c ng o e ime a
v st n s ha e v rt s
pa e te pir t n d t s a o c .
t n x a io a e ppr a h
A n c ssa y pr c so o a e a
ee r e ur rt n x mina io o o inc mbe tbe a io a ie w h t e
t n fh w u n h v rv r s it h
a ta t e e o
t r c iv n ss fama k tt
r e opo e t le t a t is ame sur o
t n ia n r n s a e fma k ta t a t e e
r e t r c iv n ss.W e
t u be inbye ima ingamo e fg ne ice t y ol w gG r bo sk a
hs g st t d lo e r n r .F lo in a w i ndV e n n( 992)
ro 1
a d Sc t o t n ( 995) e u pr - x a io r v n e a d o h rma k tc a a t r ic
n o tM r o 1 ,w se e e pir t n e e u s n t e r e h r c e ist s
t x a
oe pl inad pe de td mmyv r bl o he he e e ice t yo c r w h h e e r
e n n u a ia ef rw t rg n r n r c u s it int r ey a s
o t n x a io .G e e ice t yo c r f ra u
fpa e te pir t n n r n r c u s o bo t60 pe c n ft edr s ino
r e to h ug ursa e
mpl .
Themo e ' e ic io sa esu ie tyst o gsoa oal wu oca yan mbe fd u s
d lspr d t n r ±c n l r n st lo st l ssif u ro r g
a be
s ingu l e y o e y l e y t a e e t y h w lal wus t o
n ik l rv r ik l of c n r .T is il lo oc mpa e t be a io
r he h v r
ofag o p o
r u finc mbe t f rw ic e t y d t r e c is n tac nc r w h t be v ro
u n s o h h n r e e rn e o o e n it he ha io f
in u
c mbe t f c ga in e me ia epr ba it fe t y
n s a in n t r d t o bil yo n r .
A d e t gpl y a impo t n oe in ph r c u ic lma k t a otc e st t ic
v risin a s n ra tr l a ma e t a r e s| n f - it d a ist
by c it s o t ph r c ut a in u r is t t mo e mo y is spe t by t e ind st y
r ic f he a ma e ic l d st y ha r ne n h u r
n r e in ha n e a c n v l pme t2 O ure
o ma k t g t n o r se r h a d de eo n. mpir a n l sis f c se o t e
ic la ay ou s n h
q e io o h t e d e t
u st n fw e h ra v risingl v l a e u u a
e es r n su lin \ in e me ia e
t r d t "ma k t
r e s.W e dot is
h
2
See U .S.Con res, O ± c e ofT ec hn og Asesm en (19 9 3 B ilCln , i
g s ol y s s t ). l i ton na 19 9 3 s peec h, s d that
ai
the pharm ac eu c ali d u try s d s\$ 1 b i l
ti n s pen l onm ore eac h y
i ear onad verti i g an l b yi g thani d oes
sn d ob n t
ond evel n n an b etter d ru s....W e c an ot have pro¯tsat the ex s ofou c hid ren" (T he
opi g ew d g n pene r l .
W allStreet J ou al Feb ru
rn , ary 16 19 9 3 Sc hw ei er (19 9 7 provi esa thorou h d i c u sonofres h an
, ) tz ) d g s si earc d
m ark n ex d i resofpharm ac eu c al¯rm s
eti g pen tu ti .See Caves W hi s , an Hu i (19 9 1), Hu i an
, nton d rw tz rw tz d
Caves(19 88),Le² er (19 81),an B ern t, B u ,R eil,an U rb an(19 9 5 f d i c u son
d d i ly d ) or s si sofother as tsof pec
pharm ac eu c alad verti i g
ti sn .
2
in t o w y l o in c o se t nal a d e t
w a s: o k g r ss- c io ly ta v rising t sae r t s, a d l o in a o
o l s a io n o k g th w
a v r isin
d e t gis c a g dimme ia e ypr rt
hne d t l io opa e te pir t n ne¯ ingc n e tw h
t n x a io .O nd o sist n it
a e t yd t re emo iv t n is t a c
n n r e e r nc t a io h tin umbe t in in e me ia ema k t a emo el e y
ns tr d t res r r ik l
t e uc dv risingo e ha e e pir t npe io h n a ein umbe t in ma k t w h
or d ea e t v rt tpr - x a io r dt a r c ns r e s it
ah h o o n r pr ba it .
ig rl we t y o bil y
M a y pr sc ipt n d u s a e sod in al r e n mbe fpr se t t n
n e r io r g r l ag u ro e n a io s.T h t a q il r
e r n u ize
H ad l f re a e is sod in 1 , 1 , 2, 5, 1 0 a 20 milig a t bl t a a c n e t a e
l o, o x mpl , l 2 nd l r m a e s, s o c n rtd
l uid in bo te a a a sou io f rin r v no use in v l a
iq t l s, nd s l t n o t a e us ias, mpu e a d d
l s n ispo bl
sa e
sy in e
r g s.W h e w ha e se n l te w it e a u e n a io pr l e a io a ast a e ic
il e v e it l r t n bo tpr se t t n oif r t n s rtg
t o, a in u r so r e w c nsu t d me t n d l e e t n n a t e ¯st t in t a
o l n d st y u c e o le n io e in x e sio s s h r h g h t
w ul c me t
o d o omin w n o e be a t a f rg ne ice t y n po
d he n g n opl n o e r n r .O e ssibil y is t a
it h tby
in r a g t e v r t o e n a io sod a inc mbe tw ul in r a t e c stt a
c e sin h a ie y fpr se t t ns l , n u n o d c e se h o o n
e t a to e o c g t e pr du tl e a d mig tt e e d t re t y f e e n in
n r n fr pr du in h o c in n h h r by e e n r .A t rpr se t g
so su
me mma y st t ic o t e t pic ll v l o nd t e ds in pr se t t n pr l e a io ,
r a ist s n h y a e es fa rn e n a io oif r t n
w o ka o
el o th wpr se t t npr l e a io a ie w ht el eih o fg ne ice t y g in
e n a io oif r t nv r s it h ik l o do e r n r .A a ,
w ot is in t ow y o k ga o
ed h w a s:l o in th waH e ¯ a lin xo e n a io bypr se t t n
r nd h de fpr se t t n e n a io
r v n e a ie c o r g n o k ga hic r g r e din oin r a
e e u sv r sa r ssd u s,a dl o in tw hd u sa et n gt c e sepr l e a io
oif r t n
a te
s h irpa e te pir t n da e a o c .
t n x a io t s ppr a h
T h ¯ a r t g v r bl w e a u n s'pr e 3 H e e w d u h w
e n lst a e ic a ia e e x mine is inc mbe t ic s. r , e isc ss o
pr e c a e be o e a d a t rpa e t e pir t n f rd ug w h l w me iu a d h h
ic s h ng f r n fe t n x a io o r s it o , d m, n ig
pr dic e pr ba it s o n r
e t d o bil ie fe t yin t ed u st r a h spit lma k t
h r g o e nd o a r e s.
Ourpa rc nbese na r l t dt w mpir a it r t r s.Fir ,an
pe a e s e a e ot oe ic ll e a u e st umbe fpa r
ro pe s
h v pr v u y e pl r d pr ing a v r isin , a d e t y in t e pha ma e ic lin ust y4
a e e io sl x o e ic , d e t g n n r h r c ut a d r .
M o l se y r l t d t urw r is Ca e
stco l e a e oo ok v s,W h st n ur it ( 991 )
in o ,H w z 1 ,ade r iv st dy
sc ipt e u
ba d o t iry d u s w o pa e t e pir be w e 1 97 a d 1 987 T h y l o mo l
se n h t r g h se t n s x e t e n 6 n . e ok sty
3
Inad d i onto ref c esm en on ab ove,s M asonan Stei er (19 85
ti eren ti ed ee s d n ),Com an (19 86 an Fran
or ) d k
an Salever (19 9 7 f d i c u son pharm ac eu c alpri es
d k ) or s si sof ti c .
4
Som e n otab l papersi
e nad d i onto thos m en on ab ove are Caves W hi s , an Hu i (19 9 1),
ti e ti ed , nton d rw tz
G rab ow s i an Vern
k d on(19 9 0 ), Sc ott M orton(19 9 5), G ri i hesan Coc k u
l c d b rn(19 9 4 ), Fran an Salever
k d k
(19 9 2 ),an E li on
d l ,Coc k u ,G ri i hes
s b rn lc ,Hau m an 9 7 here are a n mb er of ook i teres ab ou the
s (19 ).T u b sofn t t
ec on i sof
om c pharm ac eu c al nl d i gW aler (19 7
ti si c u n k 1),Sc hw artz m an(19 7 ),T em i
6 n(19 80 ),an Sc hw ei er
d tz
(19 9 7 ).
3
a v r g be a io finc mbe t be o e a d a t re pir t n,at o g t e d pa a e
ta e a e h v ro u n s f r n fe x a io lh u h h y ose r t
d u sin ol wa
r g t o ndhig e e u a e o ie n eifin u
hr v n ec t g r sa dse c mbe ta v r isin
n d e t gbe a io i® r
h v rd e s.
Sc t o t n( 995)f c s o h
o tM r o 1 o use nt ede e min n s o e e ice t yw had t tsimil rt
t r a t fg n r n r it a ase a o
or
u s.In a d io t o k
d it n ol o inga x g n u ma k tc a a t r ic
te o e o s r e h r c e ist s,sh asol o s f re e t
e l o k o ®cs
o c mbe t a v r isin x nd u e nt epr ba it fg n r n r .G r bo sk a d
fin u n s' d e t ge pe it r so h o bil yo e e ice t y a w i n
V e no ( 992)aso st dy a pa e fdr s w h e pir
r n 1 l u n lo ug it x ingpa e t a d f c s o po - n r
t n s n o u n ste t y
be a io fbo h in u
h v ro t c mbe t a d g n r n r n s.
n s n e e ice t a t
Se o d, a n mbe fpa r h v e a e st a e ic e t y de e r n e ( n e t y a -
cn u ro pe s a e x min d r t g n r t re c a d n r c
c mmo a io )ino h re v o me t
o dt n t e n ir n n s.A s weme t n da v ,itis d u tt e ir c l
n io e bo e i±c l ot std e ty
w e h rpa t u a v st n s a e st a e ic T he o e pa rw a e a a e o hic h s
hte ric l rin e me t r r t g . n pe e r w r fw h a
t ie t is is Ka iy l ( 996) a st dy o he ma k t f r¯m, w h e ima e pr e a d
rd h d ai 1 , u ft re o l hic st t s ic n
a v r isin l st it s a d a g e t to r e l v l o ic nd a e t gbyEa ma
d e t ge a ic e n r u s ha bse v d e e s fpr ea dv r isin st n
Ko a e einc n e tw h st t
d kw r o sist n it a icmo poypr ¯
no l o tma imiza io
x t nbu o sist n it e -
tc n e tw h n
t y d t r in
r e e r gbe a io .Smil y ( 988)r po t e ide c fo sur e s o r a u h t
hv r e 1 e rs v n e r m v y f¯ms bo tw a
st a e ie h yuset e e n r .Inpr c ic ,ith sbe nmo ec mmo opr v ein ir c
r t g st e od t re t y at e a e r o nt o id d e t
e id nc t a v st n s a e c o n st a e ic ly by sh w
v e e h tin e me t r h se r t g al o ingt a v st n s d a e t
h tin e me t o ® c
f t r c mpe it n ( h h w ll a u t c ncu e t a v st n s mu
uue o t io w ic il e d s o o l d h tin e me t stbe st a e ic if
r tg
¯ms a e r t n la d a a e o h e e to c mpe it n) O n c n t in o
r r a io a n w r ft e ® c n o t io . e a h k fCh v l rs
e aie '
( 995a 1 995b)st die o he e e to a a e r c u in o e t y a d e ita su r
1 , u s ft ® c fc pit lr st u t r g n n r n x nd pe -
ma k tpr in ,L ie r n s ( 987 isc ssio o h r spo s by inc mbe t in c e a
r e ic g be ma ' 1 )d u n ft e e nse u ns h mic l
in ust ie or as' d io fc pa it ,a dSc t o t n s( 995)d u no h ® c s
d r st iv l a dit nso a c y n o tM ro ' 1 isc ssio ft ee e t
o d e t go n r s pr v in v e eo his so t ie r nasol o s f re ide c
fa v r isin ne t ya o id ge id nc ft r.L be ma l o k o v n e
o n r d t r in
fe t y e e r gbe v rin c o se t n lpa t r s in e a in h t e h r is mo e
ha io r ss- c io a t e n x min gw e h rt e e r
e c ss c pa it
x e a c yin ma k t w ic a emo ec n e t a e .
res h h r r o c n r td
T h o g niza io o h pa ris a f lo s.Se t n 2 disc
e r a t n ft is pe s ol w c io usse e t y d t r e c a d
s n r e e rn e n
t e mo o o ic yo h v st n - r e
h n t n it ft ein e me tma k tsizer l t nsh
e a io ip.Se t n 3 de r s o rd t .
c io sc ibe u a a
Se t n4 pr se t t epr bitmo e it h hw st t h ik l o do e e ice t y
c io e ns h o d lw hw ic ee ima et el e ih o fg n r n r .
Ev e c na v risingisinSe t n5; e n a io oif r t nisinSe t n6; n
id n eo d e t c io pr se t t npr l e a io c io a dpr in
ic g
is in Se t n 7 c io 8 c ncu e
c io .Se t n o l d s.
4
2 Strategc en d eterrene
i try c
Int se t nw isc ss w yitis d u tt e
his c io ed u h i±c l ot stdir c l he h rin e me t a e\ st a e
e tyw t e v st n s r r t-
g "a d t n d sc ibe a ide f rh wo e mig tl o f re id nc o r t g n r d -
ic n he e r n ao o n h o k o v e e fst a e ice t y e
t r e c by l o ingf rn n n t n it s in t e r l t nship be w e in u
e rn e ok o o mo o o ic ie h e a io t e n c mbe t c io
n s'a t ns
a d t e a ta t e e o h
n h t r c iv n ss ft ema k tt
r e opo e t le t a t
t n ia n r n s.
2.
1 A m od el d e¯nti san d i c u ti
: i on d ± l es
In t is subse t n w sk t h a t pic lmo lo st a e ic in e me t" a de r w y
h c io e e c y a de f\ r t g v st n , nd sc ibe h
t st
e ingdir c l h t e n in e me tis st a e icis adi±c te
e tyw e h ra v st n rtg ul mpir a a .
ic lt sk
t= 1 t= 2 t= 3
In u
c mbe tmo o l
n n poist P o e t le t a t
t n ia n r n M oo l
n poy
c o se in e me tA
h o s v st n o re A t n
bse v s he or
a o ( )
tc stc A c o se w e h rt
h o s hte o do l
u poy
e t ra o
n e tc stE
T h pr t t pic lmo lo r t g in e me tis a t r e st g g me l e t tsh w
e o oy a de fst a e ic v st n he ae a ik ha o n
a v .Int e¯stst g t= 1 ) h c
bo e h r a e( ,t ein umbe t¯m ( r 1 )c o s a v st n e e
n r ¯m ho se nin e me tl v lA
atac sto ( ) ssu t a 0 A )> 0 a d c0 A )¸0 .In t se o d st g ( 2) h
o fc A .A me h tc( n 0( he c n a e t= ,t e
po e t le t a t( r 2)o r e h c
t n ia n r n ¯m bse v st ein umbe tsc o eo a dt e h o sw e h ro
n ' h ic fA n h nc o se h t e r
n tt n e hema k t h hr q ir s pa in
o oe t rt r e ,w ic e u e y gasun o fE .Inasl h e rur r m
kc sto ig td pa t ef o
t e w y st a e icin e me tmo e s a e u al pr se t d e w la me t a h e t y
h a rtg v st n d l r su ly e n e ,w il ssu h tt e n r
c stE is st c a ic w h CD F F ( ) a t a h t u v l e is r v ae t he po e t l
o o h st it E , nd h tt e r e au e e l d ot t n ia
e t a tbe w e h r n c n a e
n r n t e nt e¯sta dse o dst g .Int et ir a e( 3) it rt ein umbe t
h h dst g t= ,e he h c n
is a mo o l
n poisto he inc mbe t a d e t a t c mpe e a du poist Ift e in umbe t
rt u n n nrn o t s o l s. h c n
is a mo o l , a me t a
n poist ssu h o s me c io m A
h titc o se so a t n x ( )in t e t ir pe io a d a a
1 h h d r d n s
r su te r s pr ¯s,¼1 ¤( )´¼1 ( m ( ) )
e l an o t m A x A ;A .Ife t yo c r ssu
1 n r c u s,a met a h n u a
h tt eu iq eN sh
v l e he r ho c io s ¤ A n ¤ A
e uil iu o h t ir st g g me in ov s t ¯ms c o sing a t n x ( )a d x ( )
q ibr m ft e h d a e a 1 2
a d r c iv g pr ¯s ¼i¤( )´ ¼i( ¤( ) ¤( ) ) A ssu t a 1 ¤( )a d ¼i¤( )a e
n e e in ot d A d x A ;x A ;A :
1 2 me h t¼ m A n d A r
5
c n a e a d t a h ¯ms'be e nse a e aw y in e io nd g e by t e u iq e
o c v , n h tt e r str spo s r l a s t r ra iv n h n u
sout n t he¯sto de o d io s.
l io ot r - r rc n it n
In t is mo e , t in u
h d l he c mbe ts in e me t d c n is sa t be \ st a e ic in t a
n ' v st n e isio id o r tg " ht
¯m 1 t pic lyd o t it in e me tl v lA a a r m t e e h hma imize pr ¯s
r y al ist r s s v st n e e w yf o hel v lw ic x s ot
( odingsubse u n c io s ¯ e )in o de oa e tt
hl q e ta t n x d r rt ® c hebe a io f¯m 2.M o epr c l ,
h v ro r r e ise y
w ala in e me tst a e icift ee uil iu v l e o di® r fo t a h h w ul
ec l n v st n r t g h q ibr m au fA e s r m h tw ic o d
h v be n c o n in a mo lw e e ¯m 2 d n to r e ¯m 1 ' c o e o . In o
a e e h se de h r r id o bse v r s h ic fA ur
mo e ,w e ¯m 1 c o s in e me tl v lA it e pe t d pr ¯s a eg e by
dl hn r ho se v st n e e s x ce o t r iv n
E ( 1 ( ) F ( 2d ¤( )¼1 ¤( )+ ( ¡F ( 2d ¤( )) 1 ¤( )¡c A )
¼ A )= ¼ A ) d A 1 ¼ A )¼ m A ( :
e r r e o it n iv g¯m s q il ium in e me tl v lA ¤ is t e
T h ¯sto d rc nd io g in r 1 ' e u ibr v st n e e hn
@¼ d @¼ m
c( ¤) = F ( 2d ¤( ¤) 1 ( ¤;x ;A ¤)+ ( ¡F ( 2d ¤( ¤)) 1 ( m ;A ¤)
0
A ¼ A ) x ¤
1 2 1 ¼ A ) x
@A @A 1
@¼ d d¤
x
+ F ( 2d ¤( ¤) 1 ( ¤;x ;A ¤) 2 ( ¤)
¼ A ) x ¤
1 2 A
@x 2 dA
d d¤
¼
+ ( 1 ¤( ¤)¡¼1 ¤( ¤) 2 ( ¤) ¼2d ¤( ¤);
¼d A m
A ) A f( A )
dA
h r e v r tn ¤ n m o ¤ A
w e e w ha e w it e x a d x f rx ( ¤)a x ( ¤)t sa e spa e In c n r st if
i 1 i nd m A
1 o v c. o ta ,
¯m 1 ' in e me tl v lw r u bse v bl , t e ¯sto d rc nd io g in t e o ima
r s v st n e e e e no r a e h r r e o it n iv g h pt l
in e me tl v l u o l j stbe
v st n e e ,A ;w u d u
@¼ d @¼ m
c( u = F ( 2d ¤( u ) 1 ( u u u ( ¡F ( 2d ¤( u ) 1 ( m ( u ;A u ;
0
A ) ¼ A ) x ;x ;A )+ 1 ¼ A )) x A ) )
@A 1 2 @A 1
h r u n u r h q il ium c o e in t h d st g ft a
w e e x a d x a et ee u ibr
1 2 h ic s het ir a eo h tmo l
de.
T h d e e c be w e t e t o¯sto d rc n it n is t e pr se c o h t ir a d
e i® r n e t e n h w r r e o d io s h e n e ft e h d n
f u t e ms w e
o r ht r h nA is o r a e h hir e m is t e\ st a e ice t ya c mmo a io "
bse v bl .T et dt r h rtg n r c o dt n
e et
® c .Co dit na n ¯m 2 e t r ,¯m 1 w lbebe t ro
n io lo r n e ing r il t e ®ifit in e me tha c u d
s v st n s a se
¯m 2 t le s a t n in t e d e t n w ic inc e se ¯m 1 ' pr ¯.T h f urh t r
r oat rit c io h ir c io h h r a s r s ot e o t em
is t e \ st a e ic e t y d t re e e e t B e a se ¯m 1 ' pr ¯
h r t g n r e e r nc " ® c . c u r s o tis h h rw e it is a
ig e h n
mo o l , itha a in e t e t
n poist s n c n iv odist r s in e me tin t e d e t n o e u in ¯m
o tit v st n h ir c io fr d c g r
2' pr ¯ w ic r d e t el e ih o o r 2 e t r g .
s o t( h h e uc s h ik l o d f¯m n e in )
6
T h mo ir c
e std e tme h d f rt st gw t e
t o o e in he h rapa t u a v st n
ric l rin e me tis st a e icw ul
rtg o d
be t v l a e t e t r in t e e pr ssio a v t e
oe au t h e ms h x e n bo e ot stw h ¯sto d rc n it n h l s.
hic r r e o d io od
T h h w v r w lu al be e t e l d u tin pr c ic . En r d t r e c c n o l
is, o e e , il su ly x r me y i±c l at e ty e e r n e a ny
o c rw n in e me t ha e l n e m c nse u n e
c u he v st n s v o gt r o q e c s.In r a o l ma k t w e e e t y
e lw rd r e s h r n r
d t r e eis apo
e e r nc ssibil yt e ew lt pic lyasobeu e t in ya u n r n s' a s.A s
it h r il y al l nc r a t bo te t a t pl n
t e ¯sto d rc n it n ma e ce r sse gdir c l h t ra in e me tis st a e ic
h r r e o d io s k l a ,a ssin e tyw e he n v st n rtg
w l r q ir e ima e n t o l o t e l ng r n e a ic y o pr ¯s w h r spe t t t e
il e u e st t s o n y f h o u l st it f o t it e c o h
in e me t bu l o h in u
v st n , taso ft e c mbe ts pr ro t l e iho d o n r a o h tt e
n ' io n he ik l o fe t y nd fw a h
ln u
o gr nbe e to h v st n o dh v e
n ¯ ft ein e me tw ul a ebe nint o n e f c u lst t ft ew rd
hec u t ra t a a eo h o l
w e e e t y h d h d n to c r e . Ca r in o tsu h c l u a io s t a y pr c n w l
h r n r a / a o c u rd ry g u c ac l t n o n e isio il
t pic lybe v r d ul.
y al e y i±c t
2.
2 M onotonc i of n tm en ab s t s
i ty i ves t en trategc en d eterrene
i try c
In t is se t n w d u h w in e me t l v l mig t be e pe t d t v r in a c o
h c io e isc ss o v st n e e s h x ce o ay r ss
se t n o
c io fma k t w n in e me t se v s n r l in de e r g e t y In pa t ul r w
r e s he v st n r e o oe t rin n r . r ic a , e
d u c n io un e h h in e me tl v l w lbe mo o o in a pa a t rw h
isc ss o dit ns d rw ic v st n e e s il n t ne r me e hic
r ° e t t t r c iv n ss o h
e c s hea t a t e e ft ema k tt
r e opo e t le t a t
t n ia n r n s.
2. 1
2. A pr po io
o sit n
Co sid ramo e e t a ot a ft
n e d lid n ic lt h to hepr v u se t n,bu it t d it n lf a ur
e io s c io tw h hea d io a e t e
t a h o ta
h tt epr ¯ ndc stf c io s d pe d asoo ac a a t r icz o h
o un t n e n l n h r c e ist ft ema k t .. h
r e ,e g,t e
n mbe fpo e t lc n
u ro t n ia o sume s in t ma k t ssu t a h v r bl z is no maize
r he r e .A me h tt e a ia e r l d
sot a a g rv l e o c r e n t
h tl r e au s fz o r spo d oma k t w ic a e mo e pr ¯a e f r¯m 2,i..
res h h r r o t bl o r e,
@
@z ¼2d ¤( ;z)> 0 .T oca if t e l kbe w e st a e ice t y d t re e a d t e n n no
A l r y h in t e n r t g n r e e r nc n h o mo -
t n it o v st n , w f c in t is se t n o a mo e
o ic y fin e me t e o us h c io n d lin w ic n e t y d t r e c
h h o n r e e rn e
e e t r e n .Inpa t ul r ec nsid r¯m 1 ' h ic fa v st n e e h nt e
® c sa epr se t r ic a ,w o e r sc o eo nin e me tl v lw e h
in e me tc o e is r v ae t r 2,bu nl a t r¯m 2 h s ma it e t y d c n
v st n h ic e e l d o¯ m to y fe r a de s n r e isio .
( o e t a s a r su tin e me tl v l in t is se t n w lr ° e te t y a c mmo t n
N t h ta e l v st n e e s h c io il e c n r c o da io
mo iv t ns.
t a io )
In t is mo l e t in fin e me tl v l a c a g
h de,w h ko v st n e e s s h n ingw h z f rt or a ns.Fir ,
it o w e so st
7
@2 ¼ 1¤
d @ 2 ¼1 ¤
m 2
w r f rt ( 2¤)@z
e e e oF ¼ @A + ( ¡F ( 2¤) @z
1 ¼ ) @A ¡ @z@ @A a t e \ d e te e t fz o A .Itis
c
s h ir c ® c "o n
po iv
sit eifin r a gz r ise t ema g a
c e sin a s h r in lmo poyo u poypr ¯ r m t ein e me t


Use: 0.4614