Munich Personal RePEc Archive

New exports from emerging markets: do

followers benefit from pioneers ?

Wagner, Rodrigo and Zahler, Andrés

Harvard University

January 2011

Online at https://mpra.ub.uni-muenchen.de/30312/

MPRA Paper No. 30312, posted 23 Apr 2011 21:55 UTC

①♣♦rts r♦♠ ♠r♥ rts

♦ ♦♦rs ♥t r♦♠ P♦♥rs ∗

♦r♦ ❲♥r

PP

♥ ♥rs ❩r

rs♦♥ s ♦ ♥r②

strt

♥ rr♦ s♣♦rs r♦♠ ♣♦♥r t♦ ♦♦r ♥ ♥♦♥① ♥♥♦t♦♥s r♥tr t♦ ♦r ♥rst♥♥ ♦ ♥♦♥♦s ♦♥♦♠ r♦t ♦♥tss ♥ ♦ tss♣♦rs ♥ ss♦♣ ♦♥♦♠s s ♥ s r ♣♣r ♦♥trts ② s♦♥♥♦ ts ♦♥sst♥t t ①tr♥ts ♥ ♥ ①♣♦rt ♣r♦ts ♦ ♦ ss t♦rs①♣♦st ssss s t ♦♥ t ♥rs ♦ st♦♠s tr♥st♦♥s r♦♠ ❲ ♥ tt rst ♦♦r r♠s r ♠♦r ② t♦ ♥tr ♣r♦t t ♣♦♥r r♠srs ①♣♦rt♥ ♦r ♠♣♦rt♥t② s♦ ♥ tt ♣♦♥rs ♥tr ♥ r♠♥ s♠r t♥♦♦rs s ♥t tt t rst ①♣♦rtr ♠② ♥♦t t r♠ tt ♥ts t ♠♦str♦♠ t s♦r② s t s ♥♦♥sst♥t t t rr♥t② st♥r ♥ ♥tr♥t♦♥tr ♥ t rst r♠ ♦ t rst ♥ t♦ ♣② ♦♠♦♥♦s s♥ ♦st ♦①♣♦rt♥ ♥ ♦♥trst ♦r ts r ♦♥sst♥t t t tt s♠r ♣♦♥r ①♣♦rtrsr t ♣r♦rs ♦s s♣♦rs ♥t rr ♦♦rs ❲ ♦r s♠♣ ♠♦ t♦♦r♠③ ts ♥tt♦♥ s ♦♥ t tt r ①♣♦rtrs ♠♦r ♦s ♦♥ ♦ t♦♦t tr ♠♥r ♣t② s r ♦♣t♦♥ ♠s r ①♣♦rtrs t s t♦ ss♥tr ♠r♥ ♠♥r ♦♥ t st ♣♦ss ♣r♦t ♥ ♦♥trst s♠r ♥ ♠♦r ♦sr♠s ♣rr t♦ ♣♦♥rs

sst♦♥

② ♦rs ♦♥♦♠ r♦t ♥♥♦t♦♥ ①tr♥ts rst♠♦r♥t

∗❲ r ♣② ♥t t ♦s r♥r r t③ ♥ ♥ ♦r s s ♦r t r② ♥stsss♦♥s t r♦ s♠♥♥ ❲ s♦ r r♦♠ sr r P♦ ♥trs ♠sr ♦♠s rr♦s r rs② ♥ rs ❲♦♦r s s r♦♠ ♣rt♣♥ts t rr ♥tr♥t♦♥♦♥♦♠s ♥ ♠♥ ♦♥t♦♥s ♦rs♦♣ ❯ ♥ ♦t♦r ♦♥s♦rt♠ ❲ t♥r♦ ♦♥ ♥s ♥ st♦♠s ♥ ♥ ♣rtr s r♣ ♦r t ss ♥ ♣ t ①♣♦rt♥ ♠♣♦rt t sr ♦ ① ② ♥r ♥ rt♦ ♦ ♣ s tt♥ ♠♥strtt ♥ ♦♥tr♦s ♦s Pr③r s ♥ ①♥t ♣rt♥r ♦r sss♦♥ tr♦ t ♦ ♣r♦ss r ♥ t♥ Prt♦ r ①♥t ssst♥ts sr♥ r♠ t s s ♥② ♦♣♥♦♥s ♥♦♥sst♥s ♦rrr♦rs r ♦♥② t t♦rs rs♣♦♥st② ❲♥r ♥♦s t r♦♥t♦♥ r♦♠ ♦st Pr♦♠s♥ssrtt♦♥ Pr♦♣♦s ♥ t ♥r♦s s♣♣♦rt r♦♠ ♠♥ ♦♥t♦♥ ssrtt♦♥ ♦s♣ ♦rrs♣♦♥♥ ♠ ♥rsrr

♥tr♦t♦♥

♠r♥ ♦ ♥ ①♣♦rt ♣r♦ts s ♥ ss♦t t ♦♥♦♠ rt♦♥s ♥ ss

♦♣ ♦♥♦♠s s ♦ ♥ ♠s♥ ♥ ts ♦♥t①t t s

r♥t t♦ ①♣♦r tr t ♣r♦ss ♦ ♥ ♣r♦t s♦r② s ② ♥tr♥③ ② r♠s

♦r ♥ ♦♥trst s♣②s s♦♠ t②♣ ♦ ①tr♥ ♦♥♦♠s

♥ ♣rtr s♥ rr♦ s♣♦rs r♦♠ ♣♦♥r t♦ ♦♦rs ♥ ♥♦♥① ♥♥♦t♦♥s

♥ ♥tr t♦ ♦r ♥rst♥♥ ♦ ♥♦♥♦s ♦♥♦♠ r♦t ♥② t♦rs s♥ t♥

r♥ ♦ s♠♥♥ ♥ ♦r ♣♣ t♦ ts t♦ ①♣♥

② ss ♦♣♥ ♦♥trs ts r♦t♥ t♦rs ♥t♦ tts t ♣♦t♥t

♦♠♣rt ♥t s ♥ ts t♦rs s tt ♣♦♥rs ♥ ♥ ♣r♦ts r t

♣r♦rs ♠♣tr r♦♠ t ssq♥t ♦♦rs ♥t ♣r♦♠ s tt

♣♦♥rs ♦ ♥♦t ♥tr♥③ t s♦ ♥t ♦ t ♥♦r♠t♦♥ t② rt s rst tr

♦ ♥ ♥r♣r♦s♦♥ ♦ ♥♥ts t♦ ①♣r♠♥t ♥ ♥ ♣r♦t r ♦ ♥ ts ♣♣r s

t♦ ♠♣r② ①♣♦r ts ♣♦♥r♦♦r ①tr♥ts ♥ t ♦♥t①t ♦ ♥ ♠r♥ ♠rts

♥ ①♣♦rt ♣r♦ts t s♥ r♥♥ s ♥♦t rt② ♦sr ♦r s♠♣ ♠♦ tt

♥ rt♦♥③ ♦r st②③ ts s ♦♥sst♥t t ♣r♦t s♦r② ①tr♥t②

s♣t t t♦rt ♣st② t ♠♣r ♥ ♦♥ s♣♦rs r♦♠ ♣♦♥r t♦ ♦♦rs

s ♥ rr t♦ ♦♣ t② rss r♦♠ t ♠♥♠♠ t rqr♠♥ts t♦ ①♣♦r

t ss ♦♥ r♦ s s t ♥s t♦ t r♠♣r♦t s♦ ♥ st♥s r♠

♦r r♦♠ ♥str② ♦r ♥ ♥ ♣r♦ts♣r♦sss r tr s ♦t s♦♠t♥

♥ t♦ r♥ ♥ t s ♣♦ss t♦ ♥t② t r② sq♥ ♦ ♥tr② ♦♥ t st ♣♦ss

♥rs ♦ ♣r♦ts t♦ ♦ ♥st ss t♦rs ① ♣♦st sss ss ①st♥ ♠♣r

sts sss ♦ s② ♦♥ ♦r ♠♦r ♦ ts ttrts ♥♦t ①♣t♦♥ s t

♣r♦ ♥ ♦ rsr ♣♦♥r ② rt♥r ♥ ♥rs♦♥ tst♥ ♦r♣

s♣♦rs ♥ ♣t♥t tt♦♥ ♦♥ rt② ♦ ♥strs t ♦♦♥ t ♣t♥ts ♦s ♥♦t s♠

s t♦ ♥rst♥ ♦ ♠r♥ ♦r ♦♣♥ ♦♥♦♠s t ♣ ② ♦♣t♥ ♦t r♦♥tr

♥♥♦t♦♥s r ♣♣r s ♣rs② ♥ ♦rt t♦ ♥rst♥ s♦♠ ♦ ts ♥♦♥♣t♥t s♣♦rs ♥

♦r r♥t ♠♦s ♦♠r r♥ t tt t ♥♦♥① ♣♦rt♦♥ ♦ ♥♥♦t♦♥s ♥ ♥ ♥♦♥♦s r♦t

♥ tr ♥♦♦ ♣tr rrs♦♥ ♥ ♦r③r r ♣r♦② t ♠♦st r♥t r ♦ ♠♦s♦ ①tr♥ts ♥ ♥ ♣r♦ts ♥ ss ♦♣ ♦♥♦♠s ♦s♥t ♥ tr♥ ♦♠♣ ♥ ♦♥♦♠rt♦♥ s♣♦rs t ♦ ♥♦t ♥ ♥ tr ♣♣r ♥② ♥ ♦r ♥ tr ♣r♦ts ♥ ss♦♣ ♦♥♦♠s ♥ ♦♣♥ ♦♥trs rtr tr s ♥ r♥t trtr ♦♦♥ t ①tr♥ts♥ t ♦♠ ♦ ts trtr s r♠r ② ♦str ♥ ♦s♥③ s tt t♦ sttst② ♥ s♦♠r♥♥ tr ♦t t♦ s♦♠t♥ ♥ t♦ r♥ ♦r ①♠♣ ♦ r♠r ♥ ♦♥s♦♥ ♦ ♥♦t ♥r♥♥ r♦ss r♠s ♥ rt③t♦♥ ♦ ♦ r♦♣s ♥ ♥② ♥ ♦♥trst ♦r t ♥ ♥ ♥♥♦♥ ♣♥♣♣ r♦♣♥ ♥ ♦♥② ♥ ❯r② ♥ st♥s r♥♥ r♦ss r♠s s♣rt ♦ ♦r ♠♣r strt② s♣rs② t♦ ♦s ♦♥② ♦♥ ♥ ♣r♦ts t♦ s tr ♥ ♥ ♥ ♦ r♥♥ ♦♥ r♦♠ t ♣♦♥rt♦ t ♦♦r

♥ t rt♥r ♥ ♥rs♦♥ r♦♥③ tt ❬❪ tr r ♥ ♥♦r♠♦s ♥♠r ♦

♥ ①♣♦rt ♣r♦ts ② s♥ ♠t♦ tt ♥ ♣r♥♣ ♥ ①t♥ t♦ ♦tr ss♦♣

♦♥♦♠s

r rst st♣ t♦ st② t ♦r ♦ ♣♦♥rs ♥ ♦♦rs s t♦ tst ♦ r②

♥ ①♣♦rt ♣r♦ts r♦♠ s♥ t tr♥st♦♥ t r♦♠ ♥ st♦♠s

♥ ♦tr s♦rs ♦ t st ♦ ♦r ♥♦ r t rst ♣♣r ♦♦♥ t

s♣♦rs s♥ t tt ♠ts tr ♣r♦s② ♦t♥ ttrts r♠ t ♥

rt② ♦ ♥ ♣r♦ts ss ♦r♥ t♦ st♥r ♥♦♠tr tr trs ♦ ♦r t

s♠ ♣rtr② st ♦r ♦r ♣r♣♦ss ♦r ①♠♣ s s♠ ♦♣♥ ♦♥♦♠② s♦ ts

r♠s r ♣s② ♣r trs ♥ ♥tr♥t♦♥ ♠rts s r② s♠♣s t strt

♥trt♦♥ ♠♦♥ t♠ ♥ ♦r s♠♣ ♦♥ s t♦ ♦s ♠♦st② ♦♥ t s♦♥ t♦ ①♣♦rt

❲ ♣r♦ t♦ ♠♥ rsts ♦♥sst♥t t t tt ♦♦rs ♥t r♦♠ ♣♦♥rs ♥ t

r② sts ♦ ♥ ①♣♦rt ♣r♦ts rst t sr ♦ ♣♦♥rs s ♣♦st② ♦rrt t

♥tr② ♦ ♦♦rs s ♣s ♣rrqst t♦ t♥ tt ♦♦rs r♥ r♦♠ t ssss

♦r rs ♦ ♣♦♥rs ♦r ♠♣♦rt♥t② ♦r s♦♥ ♥♥ s tt ♣♦♥rs ♥tr ♥ r♠♥

s♠r ♥ s③ t♥ ♦♦rs ♥ ♦♥tr♦ ♦r ♥♦sr s♦s t♦ ♣r♦ts ♥ ②r

s rst ♠♦r s♥t s ♥♦♥sst♥t t ①t♥s♦♥s ♦ rr♥t② st♥r ♥tr♥t♦♥

tr ♠♦s t③ ♥ t rst r♠ s t rst ♥ t♦ ♣② ♦♥st♥t

s♥ ♦st t♦ ♥tr ♥t♦ ①♣♦rt♥ ❲ ts st♦♥ t ♣trs t st② stt ♦

①♣♦rts ♥ rr r♠s ♦♠ ①♣♦rtrs t ♦s ♥♦t t t r② ②♥♠s ♦ ♦r ♥

①♣♦rt ♣r♦ts r ♣♦♥t s ts ♣♣r s tt t ♥♥♥ ♦ ♥ ①♣♦rt ♣r♦t s r♥t

r♦♠ s♠♣ ①tr♣♦t♦♥ ♦ t st② stt

♥ t ♦r st②③ ts r ♦♥sst♥t t t tt s♠r ♣♦♥r ①♣♦rtrs r t

♣r♦rs ♥ ♥t rr ♦♦rs ❲ ♦r♠③ ts ♥tt♦♥ ♥ s♠♣ ♠♦ ♥

rr ①♣♦rtrs s♦ r st ♦ ♣♦t♥t ♥ ♣r♦ts t♦ ♣rs ♥ t② ♥♥♦t ♦♣

♦ t♠ s ♦ rs♥ rtr♥s t♦ s♦♣ tr ♣r♦♠ s t♦ ♦t ♥ ♥s sr

s♣♦rs t ♥♦ tt♦♥s s♥ ♦♥② s♠ rt♦♥ ♦ rsr ♦t♣t s r ♣t♥t♥♦tr ♣♣r♦ t♦t ♥ r♠ t s ♥ t♦ s rt ♦♥tr② ♦♣t♦♥ ♦ ♣rtr

t♥♦♦s ♦♠♥ ♥ ♦♥ ♦r t ♦♥tr② s♦r② ♦ ♥ ①♣♦rt ♣r♦ts s♠♥♥ ♥♦r ♦ ♥r rs ♥ s♠♥♥ ♥r ♥ r♠♥ ❯♥ ts ♠r♦ ♣♣rs s r♠♣r♦t t tr②♥ t♦ ♥rst♥ tr t ♦♣t♦♥ s s♣♦r r♦ss r♠s ♦rs♠♣② s♥ r♠ ♥rs♥ ts s③ r♦ss♠♥ ♥ ♦ss♥sr r tt ts s r st♥t♦♥♦r ♦r ♥rst♥♥ ♦ ♠rt rs ② r tt ♣♦♥r r♠ s t ♣♦t♥t t♦ r♦ r② r t♥ ♥tr♥③ t ♥str② r♥♥ ♥ r♠s ♦♥st♥t rtr♥s t♦ s t♥ ♠♥② ♠♦s ttst② ♣♦② s ♦♥ ♥rs♥ rtr♥s t ♥♦♥ ♠♦ ♦ ♣♠♥ ♥ r♠♥ ❬♣❪ ♦r tt ♥♦ ♦♥r ♦r ♥trst♥② ♦r rsts r② s♦ tt t ♣♦♥r r♠ s ♥♦t ♦♥② ♦r t♥ ♠rt sr ♥ ①♣♦rts r♦♠ t ♦♥tr② ♥ t ♣r♦t t s♦ tt t s s♠r t♥ ♦♦rs s ♦rrsts r② ♦ ♥st t ♦r ss♠♣t♦♥ ♦ r♦ss♠♥ ♥ ♦ss♥sr ♥ ssts ♣r♦ s♦r ♠rt rs ♥ ♥ ①♣♦rts ♦♥tss ♦r ♥ rsts ♦t r s ♣r♦rs s ♠♦r sst ♦t ♥ ♦ r♠♥t ♥ ♥ r♦ss♠♥ ♥ ♦ss♥sr t♦ ♦r stt♥ s r♥t s ♦♥② ①♣♦r t ①♣♦rt♥ ♦ ♣r♦t ♥♦t ts ♣r♦t♦♥

❲ tst ♦r ♠♥ rsts s♦ ♦r t ss♠♣ ♦ ss r s ss t♥ ♠rt sr ♥ t♠♣♦rt st♥t♦♥ ♥ st t tt ♣♦♥rs ♥ ♣ ♥ s♠r t♥ ♦♦rs

♦r ①♠♣ rs ♥ ②♦t r♥r ♥ ♥s♥

rs♦r ♥ ♠♥r t♦ t st ♣♦ss s ①tr ♣♦t♥t s♦♣ ss s♠r

♥ ♠♦r ♦s r♠s ♥rts r ♦♣t♦♥ tt ♠s rr r♠s strt② ② ♥tr②

♥ ♦♥trst s♠r ①♣♦rtrs t r ♦♣t♦♥s t♥ t♦ ♥tr s♦♦♥r r♥ ♥♦r♠t♦♥ t♦

♦♦rs ♦t ♣r♦t ♣r♦tt② ♥ s♦rt ♦♦rs rr ♦♥ t ♣♦♥rs ♦rt

♠♥s♠ ♦t♥ ♦ s ♥♦ ①♣♥t♦♥ ♦r ② rst ♠♦rs ♠t ♥ ♣ ♥

s♠r ♣②rs s ♥tr t♦♣ ♥ s♥ss trt② r♠♥ ♥ ♦♥t♦♠r②

♥ ♣rtr t st♥r ♦rs tt rt♦♥③ ② t s♦♥ st s rr t♥ t

♣♦♥r ♦ ♥♦t s♠ t♦ ♣♣② ♥ ♠♥② ♦ ♦r ♣r♦ts rs ♥ r♦s ♦r ①♠♣

t ♥♥③t♦♥ ♣r♦♠s sss ② r♦♥ ♥ ③r ♦♦ ss r♥t t♦ ①♣♥ ②

rr ①♣♦rtrs ♦ ♥♦t ♥tr s ♣♦♥rs s♥ ♦r r♠s ①♣♦rt t♦ r ♥tr♥t♦♥ ♠rt

♥ t ♣r s ♠♦r ② t♦ ①♦♥♦s t♦ t ♦r ♦ ♥ r♠s ♠r② t

♣r♦ts ♥②③ r ♥ ♥ tr ♣r♦t ② s♦ t s♠s ♥② tt t

♦♣t♠ ♦r♥③t♦♥ ♦r♠ s t♦ s♣rt t st r♦♠ t ♣r♦t♦♥ st s sst

② ♦♥ ♥ r♦ r t♦rt ♠♥s♠ ♣s s s♦ rt♦♥③ t t♥♥② ♦

rr ♥ rs ♦r♥③t♦♥s t♦ ♣② ss tt♥t♦♥ t♦ ♥♥♦t ♦♣♣♦rt♥ts s s♦♥ ②

r ♥ rs♥♥ r♥st♥ ♥ ♥rs♦♥

r tr ♥ ♥ rst ♥s t tt ①tr♥ts r ♦♠♠♦♥♣ r♦ss ♣r♦

ts ♥ t ♥ ♠♦r t♥ ♦ t ♥ ♣r♦ts t sst♥ ♣♦♥rs ♦ ♥♦t ♦sr

♦♦r r♠s ♥ ♥ ss r ♥♦t ♥♦r♠t♦♥ ♦♥sst♥t t ♣♦st ♣r♦ts

❲♥ r② ♥tr♥ts ♥♦② r rst ♠♦r ♥t tt ♣r♠t rtr ♥tr② s ♥ r

♠♥ t s ss ♣s t♦ r ♥ ♦r ♦ t♥ ♣r♦t r♥♥ ①tr♥ts ❲ s♦

♥ s♦♠ s♣♣♦rt ♦r t tt ♥ ♦♦s t r s ♦ ♣r♦t♦♥ ♥ t ♣♦♥r

♦♠s ♥tr ♠♦♥♦♣♦② ♥ t ♦♠st ♠rt t s ss ② t♦ ♦sr ♥tr② ♦ ♦♦rs

s ♥ s♦ ♥tr♣rt ♥ ♦r ♠♦ ❲♥ tr s s♥ ♣♦t♥t ①♣♦rtr ♦ ♣r♦t

tr s ♥♦ rs♦♥ ♦r ts r♠ t♦ ② t ①♣♦rt ①♣r♠♥t s t ♥ ② ♥tr♥③

t ♥ts r♦♠ ts rs② ♥♦r

r♦♠ ♥ ♠♣r ♣rs♣t r ♠♦st ♦s② rt t♦ ♣♣rs ①♣♦r♥ s♣♦rs ♥

♥r t trtr tt ♦♠♥ts ts ①tr♥ts ss ♥str② ss ♥♦r♠② s

t♦rs sss ss ♦r ♥strs tt r ①♣♦st P♦rtr ♥r r♥

♥ Pr♦ ♦s♥ ♥ r♦rt ♦ ♦♥tr♦ r② ♥ r③é

♦♥② ♥ ❯r② ♦st ♥ ♣♣r s ss r ♦ ♦rs ♥trst♥ t

tr ♠t♦♦♦② ♥rts t ♦r r ♥ ♥rt♥t② ♣rs♥t ♥ t ♦♣♠♥t ♦

♥ ①♣♦rt ♣r♦ts s ①♥t r② ♠♣♦rt♥t ♦r ♥tr♥t♦♥ ♥tr♣r♥rs ♥ ♦♥trst

♥ ♦t sss ♥ ♥sss ss s ss t♦ t ♥rs ♦

♥ ♣♦sst② s tt t② ♦♥t♥ s t s♥ ♦st s ♣ ♥♦t s t s ♦♦ ♣r♦t r♦♠ ♥① ♥t ♣rs♣t t♦ ♦ ♥♦t ♦sr r♠s ♣r♦ts ♦r ♦r s♠♣ s♦ ♥♥♦t ♠ tt t P❱ ♦t ♣r♦t s ♣♦st st tr ss ♦ ♦♥② ♣♦♥rs tt ♠ t♦ ♣② s② tr ♥st♠♥t♥ t♥ ♦♥t♥ ①♣♦rt♥ ♦♥

tr♥st♦♥s ♥ ♦♦s ♦r t ♣r♦ st② t♦♥② ♣r♦ t s

♠♦r r ♥t♦♥ ♦ ♥ ♣r♦ts ♥t ♣♣rs s s♦rt r♥ ♥t♦♥s ♦r

♥ ♣r♦ts r♥ ♥ Pr♦ ♦♦♥ ♥ ♦r ♥ ♦♥trst ♦r ♦♥r

♣♥ ♦s s t♦ t ♣rs♠♣ ♦ ②rs t♦t ①♣♦rts t♦ ss② ♣r♦t s ♥

s rs t ♣r♦♣♦rt♦♥ ♦ ♦ ♣r♦ts tt r ♥tr♠tt♥t② ①♣♦rt ♥ tt ♠②

♠ssss s ♥ ❯♥sr♣rs♥② t qt r♥t rsts r♦♠ t t♦ ♣♣rs ♦

♦♦♥ ♥ ♦r ♥ ♠♥② ♣♦♥rs ①♣♦rt♥ ♥ ♣r♦ts r♦♠ ①♦ t♦ t

❯ ♠♠t② tr ♥ ♦r♦r t② ♥ tt t rst ①♣♦rtrs ♥tr

rst ♦r♥ t♦ tr t♠♥ ♥ ♦♥trst ♥ ♦r s♠♣ ♦ ♥ ♣r♦ts ♠♦st ②s ♥

s♥ ♣♦♥r ♥♥ ♣r♦t t rst ②r ♥ ts ♣♦♥r t♥s ♥♦t t♦ t ①♣♦st

rst ①♣♦rtr

r rsr ♥ s♦ t♦t ♦ s ♥ ♦s♣r♥ ♦ t ♥ ♥ ♥tr♥t♦♥ ♦♥♦♠s t

tr♦♥♦s r♠s t③ ♣rtr② ♦ ♠♦s t ♠t♣r♦t r♠s s s

♦ ♥ ❨♣ r♥r ♥ ♥ ♦tt ♥ r② ♥

②r t③ ♥ tt♥♦ ♥ ts trtr t rst ♥ st ♣r♦tt②

r♠s ①♣♦rt ♠♦r ♣r♦ts ♥ r t ♠♦st ♥ t♦ ♣② s♥ ♦st t♦ ①♣♦rt ♥ ♣r♦ts

♥ ♦ ♥♦t ♥ s♣♣♦rt ♦r t ♣rt♦♥ tt rr ①♣♦rtrs ♥tr rst ♦r ♠♦

t♦ ♥rst♥ ② ts rr ①♣♦rtrs ② ①♣r♠♥t♥ ❲t♥ ts tr trtr ♦♥

①♣r♠♥tt♦♥ r rt t♦ ♥ ❲ts♦♥ ♥ ❲s ♦r♥♦③

♦r♦s r♥s ♥ Pr♦ r② ♥ ❱rr ♥ t♦♥ s

r③♥ r ♥ ②♦t

♥② r ♦s② rt t♦ t ♥♥♦t♦♥ strt② trtr ♦♥ ♦ t rst ♠♦r ♣s

ts ♦r♥ ♥t rt ♥ r② ♥rs♦♥ Prs ♥ ♠t③

❲ sr t ts trtr t s♣ ♦s ♦♥ t sq♥♥ ♦ ♥tr② ♦r ♦♥sr

♣r♦ts tt r t♥ t ♥tr♥t♦♥ r♦♥tr ♦ ♥♥♦t♦♥ ♥ r② ♥♦♥♣t♥t ♥

tt s♥s ♦r ♣♣r s s♦ ♥ ♠♣r ♦♥trt♦♥ t♦ t ♥tr♥t♦♥ rt♥ trtr

② ♥rs ♠♥ r♣♦rt ♣r♦ts ①♣♦rts s♥ t ♣r♦t ♥t♦♥ ♦ st♦♠s t r♠♦♥③②st♠ t t r t ♦s ♥♦t ♥ srs

♦r ①♠♣ ♦♦♥ ♥ ♦r ♥ ♥ ♣r♦t s ♣r♦t tt s ♥♦t ①♣♦rt ② t♦♥tr② ♦♥② ♦r ♦♥ ②r r♥ t ♥ ♣r♦t t♦ ♥② ♦ tt s ♥♦t ①♣♦rt t t rst ②r ♦tr s♠♣ ♣r♦ ♥ tt s ①♣♦rt ♦r t st ♦♥st ♣r♦s tr

r♥ t s s♠r tsts s r♦s sr♣t ♣♣rs tt ♦♦ t t ②♥♠s ♦ ♣r♦tsr♠s ♥ st♥t♦♥s ♥ ①♣♦rts r ♠♥ r♥ t t♠ s tt t② ♦ ♥♦t t t ♣rs♣t ♦ ♥①♣♦rt ♣r♦ts t♦♥ s r ♥ ②♦t t♦♥ ♦rt♠ ♥ r♠r③ ss ♥Prs tr t♦rs ♦♦ t ♥ t t♦ ①♣♦r ♣ttr♥s ♦ tr ♦r ①♠♣ srs ①♣♦r ♥str② ♥② tr tr r③t♦♥ ♥ t t s ♥ r② s s s♦P♥ ♣rs♥t ♥ ♥♥t ♣♣r ♦♥ t s♠ qst♦♥ ♥ ♠♥② ♦♥trt♦♥s ♦rt♦ r③ ♥r♦s ♦t♦rs ♥ sr♥ t r♥t ♣ttr♥s ♦ ♥ ①♣♦rtrs ♥ ♠♥trrs ♥ r♥t②s r③ ♥ ♥ts r③ r③ ♥ rs♣ r③ ♥ ♦♣③ r③♥ ör r③ rq ♥ ♦♣③ r③ ♦ ①♣♦rs t rt♦♥ ♦rt♦♥s♣s t♥ ♥ ♥rs ♥ ♦r♥ ②rs

❱r♦s ♣♣rs ♦s ♦♥ t ♦rts ♦ t s♦♥ t♦ ♥tr♥t♦♥③ t ♣r♦t♦♥ ♦ r♠ ♦r

r♠♥r ♦ t ♣♣r s ♦r♥③ s ♦♦s t♦♥ ♦rs s♠♣ t♦rt r♠♦r

t♦ r② t♥♥ ♦t ①♣r♠♥tt♦♥ ♥ ♥tr② ♥t♦ ♥ ①♣♦rts t s ♠♣♦rt♥t t♦ r♠r

tt t ♣rt♦♥s t rs r ♥♦t ♥q t♦ ts ♠♦ t r sr t r♦r st

♦ ①♣♥t♦♥s tt ♥♦ ①tr♥ ♦♥♦♠s r♦ss r♠s ♥ ♣r♦t ❲ r r tt t

♠♦ s ♥♦t ♦♠♣t② ♥r t♦ ♥tr♣rt t ♥ ♣♦♥t s tt ♥ ♥ rt♦♥

ss ♠rts tr r ♠♥② ♣♦t♥t ②s ♥ r♥♥ ♥ ♣♣♥ ❲ ♦ ♥♦t ♦♣ t♦

♥♦♠♣ss ♦ ts ♣♦ss ♥♥s ♥st s♠♣② ♦s ♦♥ s♥ ♣rs♠♦♥s ♠♦

s ♥ ♥str♠♥t ♥s t♦ r t ♥ t♦♥ ①♣♥s ♥ srs ♦r tst ♦

♥ ①♣♦rt ♣r♦ts s♦ sss♥ ♥♦♥ ①♠♣s s ② t♦ ① s t♦♥

♠♣r② ①♣♦rs t ♣rt♦♥s ♦ ♦r ♦r♠ r♠♦r t♦♥ rs ♥st tr♥t

♥tr♣rtt♦♥s t♦ ♦r st②③ ts s♣② ♦s♥ ♦♥ sr♥ ①♣♥t♦♥s tt ♦ ♥♦t

♥♦ r♥♥ t♦♥ ♦♥s t s♦♠ r♠rs

♠♦ ♦ strt t♥ ② r ①♣♦rtr

s st♦♥ ♦rs s♠♣ ♠♦ t ♥♦ ♠♥s♠ tt ♥s rr ①♣♦rtrs t♦ ②

♥tr② s tt t t ♠r♥ rr r♠s ♠♦r ♦s ♦♥ r t♦ ♦t tr

♠t ♣t② t♦ ♦♣ ♥ ♣r♦ts ② ♥tr♥ t ♥t♦ rsr ♥♦rs r r♠s

t ♥t ♦ r♥♥ ♦t t rt ♣r♦tt② ♦ r♥t ♥ tts s tts

t ♦t♦♥ ♦ ♠♥r t♥t t♦ t st ♣♦ss ♣r♦t ❲ ♣♣ t♦ t♦ ss♠♣t♦♥s

t♦ r ts rst rst s tt rr r♠s t♥ s♦ t♦ r s♦♣ ♥ t s♥s tt

t② ♠♦r r ♦♣t♦♥s ♦ t ♥ ♣r♦ts t♦ ♥rt s ♦rrt♦♥ t♥ s③ ♦

s♣♠♥ts ♥ s♦♣ s ♥ ♥♦♥ t st s♥ P♥r♦s ♥ r♥t② ♦♠♥t

② r♥r ♥ ♥ ♦tt ♥ ②r t③ ♥ tt♥♦ ♦r♦r ♥

st♦♥ s♦ ♠♣r② tt tr ♥tr♥ts ♥t♦ ①♣♦rt♥ ♣r♦t ♦♥ r ♠♦r

♦♥♦♠ tts ♠sr ② ♥str② sst♦♥ s♦♥ ♦r ss♠♣t♦♥ s tt

s③ ♥ s♦♣ ♦ ♥♦t ♦♣ ♦r♥t ♥ r♠s ② r♦ ♦♥ st♣ t t♠ ❲ s♦ ss♠

t ♦t♦♥ ♦ rs♦rs t♦ ♥ tt② s ♣rt② rrrs ♥rts ♥ ♥♦♥♦s

s♥ ♦st ♦r r r♠s

♥ s♦rt s♠ r♠ s s♥ s♥ ♦st ♦ ♣r♦t s♦r② r r♠ ♥tr♥ r②

r s ♥rs♥ ♦r r♥t② ts trtr s ♠ st♥t♦♥ t♥ ♦r♥ ♦s tt♥tr♥t♦♥③ ♠♠t② r♦♠ ♦tr r ♦s tt ♥tr♥t♦♥③ tr s♦♠ ②rs ♥ t ♦♠st♠rt ♦♥ ♥ rs ♦r ♥ r♦♥ ♠rts ♦♣③ ♥ ♥ r♥ r r♥t tts trtr s t r♦ ♦r ♦ ♣r♦ts ♥ t sq♥ ♦ ♥tr② tr ♣♣rs ♥ ♥tr♥t♦♥ ♠rt♥♠♣r② ①♣♦r t ♦rr ♦ ♥tr② sq♥♥ s tr♠♥♥t ♦ ♣r♦tt② ♥ ♥ ♠rt ♦r ①♠♣ ♥ ♦♦ t ♦ r② ♥tr♥t ♠t♥t♦♥s ♥ ♥ ♦ ss t ♥tr♥ts ♥ t s♠ ♠rt♥ss♦♥ ❲st♦♥ ♥ ♦s ♦♦ t ♦ sq♥ ♦ ♥tr② t ♣r♦tt② ♥ ♠♥② st♥t♦♥♠rts t ♦♥② ♦r ♠t♥t♦♥s ♥ t rts♠♥t ♥str② r ♥②ss s r♥t r♦♠ ts trtrs ♦s ♦♥ ♠♥② ♥strs ♥ ♠♦st② ♦♥ t s♦r ♦♥tr② rtr t♥ ♦♥ t st♥t♦♥ ♦♥tr②

♥t♦ ♥ ♣r♦t s t♦ t②♣s ♦ s♥ ♦sts rst s st♥r ①♦♥♦s s♥ ♦st

s q ♦r r♠s s♦♥ s ♥ ♥♦♥♦s ♦st ①s② ② r ①♣♦rtrs

s ♥tr♥ r② r♥s t r ♦♣t♦♥ t♦ ♦t t ♠♥r ♥t♦ ♥♦tr tt② rt

t♦ t r♠♥ts ♥ ①t ♥ P♥

t♣

r ♣rt qr♠ st♣ ♥♦s tr rs ♥tr strt ♣②rs ♥t t♦ ♠①♠③

t ♥t ♣rs♥t ♦ ♥t s ♦s ♦ ♦ t r♠s r s♠ ♥ ♥rr♦ s♦♣ ♥ t

tr r♠ s rr ♥ s r s♦♣

♥ t ♦♥ ♥ tr r t♦ s♠ r♠s t ♥rr♦s♦♣ A ♥ B

♦ t♥ ♦♥ s♥ss s s ♦r strt♥ ♥ ♥♣♥♥t rs② ♣r♦t r♠ A s

♥ rtr r♠ ♥ r② ①♣♦rts s♦♠ rtr ♣r♦ts ♥ t ♠s ♣r♦ts

♥♦r♠③ t♦ ③r♦ r♠ A ♥ ♦♥② ♠ ♦♥ rs② ♥ ①♣♦rt ♥♥♦t♦♥ ♦s t♦ ts ♦r

♦♠♣t♥ s♣rs ♥♦♦s② r♠ B s ♥ t t ♣♣rs ♥str② ♥

♥ tr t♦ ①♣♦rt ♥ ♣r♦t tts ♦r ♥♦t ♦t s②♠♠tr ♥rr♦ s♦♣

r♠s ①♣♦rt s♠ q♥tt② q ♥ ①♦♥♦s② ♥ t r♠s t②♣ s ♥♦t s

♥♦tt♦♥ ② s♥ t s♠ ttr t♦ ♥♦t ♦t t ♣r♦t s♣rs ♥ t s♠ r♠

tt s t ♦♣t♦♥ t♦ ①♣♦rt t r♠

♥ t ♦tr ♥ s♥ r r♠ tt ♥ ①♣♦rt r q♥tt② q > q t♦

ts r♠ s s♦ ♦♥str♥ t♦ s♥ ♥ tt② s ♦trs t ts ts s♦♥♦♠s

♦ s♦♣ ts s♦♥ ♣r♦♠ s r♥t t♥ ♦r s♠ r♠s ♥ ♣rtr t r r♠ ♥

♦♦s t♦ strt tr As♣rs ♦r Btts t ♥♦t ♦t s sss ♦ t ss♠♣t♦♥

s tt t r r♠ ♥♥♦t ② rs② ♦r♥t s ♦♥sst♥t t ♥♥ ♥ ❨

② r tt rs r♠s r♦ ♦♥ st♣ t t♠ s t② ♥ t♦ ♠t

s♦♠ ♥ ♦ ♦r♥③t♦♥ ♣t tt ♦s t♠ t♦ ♥rs t s♦♣ t♦t t♥ t

♦tr ♥r♠r♥ s♥ss ♥s

♠ s tr ♣r♦s ♦♣s♥ tr ♣r♦ts ♥ t st ♣r♦ tr♥

ts ♦r r♠s r ♥tr s ♣♦♥r ♥ t ♥ ♣r♦t tr ♣②♥ s♥ ♦st F ♣r ♥t ♦

♣t② ♥tr s ♦♦r ♥ t ♥ ♣r♦t s♦ ♣②♥ t s♥ ♦st ♥r ♥tr ♥

r♠♥ t tt② ♥♦r♠③ t♦ ③r♦ ♦s ♦ ♥tr t ♥ ♣r♦t ♥ tr t♦ r

♠♥ ♥ t♠ ♦r ♥♦t ♦♥② ♥rt♥t② ② ♣♦t♥t ♥tr♥ts ♥ ♣r♦t i = A,B

♥ rr ♠♦ t rstrt♦♥ ♦♥ s♥ ♥ tt② t t ♠r♥ ♥ t♦ s t rst ♦ ♥♦♥♦s♥st♠♥t ♥ s♦♣ t ♦♥① ♦sts ♦ st♠♥t ♦r ts ♠♦ ♦r t s♠♣ ♣♣r♦ ♥ ss♠tt t s♦♣ N s ♠t t ♥ ①♦♥♦s rt ♦ ♦♥ r② ♦r s♦ ♦r♥ t♦ Nt+k = Nt + 1r ts s t N s t t♦t ♥♠r ♦ tts ♣r♦t st♥t♦♥ ♣r♦sss tt r♠ ♥ ♥♦r tt♥ t ♥ ♦ s♦♥♦♠s ♦ s♦♣ ♥ k ♦ ♥ ♠② r♠s ♦r ①♠♣ tst♦♥ ♠♥r ♣t② ♥ t♦t s ♥ s♦♥tr t♦ ♠♥r

s t ♣r♦tt② ♦ t ♣r♦t ♥ t ♥tr♥t♦♥ ♠rt xi s r♦ss ♣r♦ts t♦t

♥st♠♥t ♦st s max 0, xi − c r c s t r ♦st ♦ ♣r♦t♦♥ s ss♠

♦♠♦♥♦s r♦ss r♠s ♥ ♣r♦ts ❲ trt xi s ♣r t♦ ♦♥♣t② t ♥

r♣rs♥t ♦tr ♣r♦t ♥rt♥t② t r♠s tt ♦♥sr ♥tr♥ ♥ ♣r♦t i

t s♠ ♣r♦t② strt♦♥ ♦r t ♥t r♥ ♦ tr ♥ ♣r♦t xi ♦ rs♦♥s ♠

ts ss♠♣t♦♥ ♦ ♦♥st♥t ♣rs r♦ss r♠s ♥ ♣r♦t ♣s rst s s♠ ♦♣♥

♦♥♦♠② ♠s t ss ② tt r♠s ♥ ♠♣t t ♥tr♥t♦♥ ♣rs ♦ ♣r♦ts

♦♥ ♥ st♦♥ ♠♣r② s♦ tt t ♣rs r ② r♠s ♥ ♣r♦t ♦ ♥♦t

sttst② r t♥ t ♥tr② ♦ ♣♦♥rs ♥ tt ♦ ♦♦rs ♥ t ♠♦ t r③t♦♥

♦ xi rs r♦ss ♣r♦ts ♥ s strt i.i.d. ♦r♥ t♦ G (xi) ♦r trtt② s

ss♠ t♦ st♥r ♥♦r♠ strt♦♥ t♥ ③r♦ ♥ ♦♥ ①♦♥♦s s♥ ♦st

F s ss♠ s♠ ♥♦ t rs♣t t♦ Emax 0, xi − c s♦ t ♦ ♣r♦♠ s ♥♦t tr

①t♥s ♦r♠ ♦ t ♠ ♦r r♠ s s♦♥ ♥ r t st 1 r♠ s

tr t♦ ♥tr ♠♠t② ♣②♥ s♥ ♦st F ♣r ♥t ♦ ♣t② ♦r t♦ t ♠♠t②

tr t = 1 t ♣rs♥ ♦ t st ♦♥ ♣♦♥r r♠ ♥ ♣r♦t i rs t♦ r②♦② t

xi ♥ tt ♥♦r♠t♦♥ t ♣♦♥r ♥ t♦ ♦♥t♥ ♥t ♣r♦ 2 ♥ ♦t ♣r♦ts

♣♣♥ xi > c tr♥t② t ♣♦♥r ♥ ①t t ♥ ①♣♦rt ♣r♦t ♦r t♦s

r♠s tt t t rt♦♥ ♦ xi ♥ tr ♥ t♠ t♦ ♥tr s ♦♦r ♥ ♣r♦ 2

♥ ♦t ♣r♦ts ♥ ♣r♦ 3 tr♥t② r♠ tt t t t = 1 ♥ ♦♦s t t = 2 t♦

♥r ♥tr ♦r ♣♦♥r r♠ ♥ ♣r♦ 3 tr s ♥♦t♥ ♥trst♥ s ♣r♦ s s ♦♥②

♦r t♥ r♠s ♥ ♦rr t♦ ♣ t s♠ P❱ t ♥tr② s♥ t s♦♥t t♦r β ∈ (0, 1)

❬r ♦t r❪

♦ ♦ r♠s ♦♦s

❲ ♥②③ t s♦♥ ♣r♦♠ ♦r ♦t s♠ ♥ r r♠s

♠ ♥rr♦s♦♣ r♠

♦s r s②♠♠tr ♦r s♠ r♠ i ∈ A,B ♦r t♠ ♥ ♣♦♥r ♥ts t

♥t ♦ ♦♥ ①tr ♣r♦ ♦ ♣r♦ts t ♣r♦t s sss t t② s♦ ♥r ♥ ♥ ①♦♥♦s

s♥ ♦st ♦ ①♣♦rt♥ Fq tt ♠② ♥♦t ♣② tr♥t② t r♠ ♥ t ♥t ♥①t

♣r♦ ♦s♥ ♦♥ ♣r♦ ♦ ♣♦t♥t r♦ss ♣r♦ts t ♥ sr ♦t t ♠♥t ♦ t♠

❲ ♠ t ♥♦♥♥t♦♥ ss♠♣t♦♥ tt s♥ ♦st r ♣r♦♣♦rt♦♥ t♦ t s③ ♦ t ♦♣rt♦♥ s♣trs t ♥tt♦♥ tt r r♠s ♠② r ♦♣♣♦rt♥t② ♦st ♦ rs♦rs t② s♥ tr♦♣rt♦♥s t♥ t♦ rr ♥ tr t② ♦ ② ①t ♣r♦♣♦rt♦♥t② s s ss♠♣t♦♥ t♦ r t♠t♠t r♥ ♥ ♣ t ♠♦ t s♥ ♠♦♥ ♣rt rsts ♥ ♥r③ ♦r t♦♥sr♦♠ ts ♣r♦♣♦rt♦♥t② ss♠♣t♦♥ ♥ t ① ♦st

max 0, xi − c q s rt♥t② tt ♥♦tr r♠ ♥tr ♥ ♣② rs xi s ♥ ①tr♠

r♣rs♥t♥ t ♠♦st t♠♣t♥ stt♦♥ ♥ t s♠ r♠ ♦ ♣rr t♦ t ♥

t ♣♣♥① s♦ tt ts ss♠ ①tr♠ s s♥s s♠♣t♦♥ t♦t ♦ss

♦ ♥rt② ♦r ♦r ♣r♠trs ♦ ♥trst ② r ♥t♦♥ t t♦ ♥t♦♥s ♥

♣r♦ 1 r

V small ipioneer = −Fq + βEmax

0,[

xi − c]

q

V small iwait = βEmax

0,−Fq + β[

xi − c]

q

♥ t qr♠ ♦ ♥trst s♠ r♠s ♣rr t♦ ♥tr s tr r ♥♦ ♦tr r♠s

s③s t r r♠ ♥ t ttr ♣rr t♦ ② s t ♦♠ r ♥

r s♦♣ r♠

♦r t r r♠ t ②♥♠ ♣r♦♠ s t s♠ s ♥ t ♥trs s ♣♦♥r t r♥t

t ts t♦ t ♥ ♥tr♦ ♦♥② ♦♥ t♦♥ ♣r♦t t t♠ t s s♦ r r♥

♦ tr♥ts t♥ A ♥ B argmaxi∈A,B xi ② ss♠♣t♦♥ strt♥ ♦t ♣r♦ts

s r ♦t s ♥♣r♦t s t♦ ♥ ♣r♦ts ♦ ♥t t ♦♥ t t♦t

♣r♦ts s sss ♦r s s s♦rtt t♦ ♦ ♥st♠♥t ♥ s♦♣ ♥ t

♠♦ ♥ ♥ ♣♦♥r ♥ tr A ♦r B s ♠t♠t② q♥t ♥ ♦r stt♥

♣t t♠ t♦tr ♥ s♥ ♦ i ♥t♦♥s ♦r ♥ ♣♦♥r ♥ ♣r♦t ♥

t♥ r

Vlarge iP ioneer = −F q + βEmax

0,[

xi − c]

q

VlargeWait = βEmax

0,max

−F q + β[

xA − c]

q,−F q + β[

xB − c]

q

♦t tt t ♦ ♣♦♥r♥ ♥ q s s♠♣② ♣r♦♣♦rt♦♥ t♦ t ♦♥ ♦r ♥rr♦s♦♣ r♠s

♥ q ♥ ♦♥trst t ♦ t♥ ♦r t s♦♣ r♠ s ♦♥ ①tr r♠♥t ♥ t

♠①♠③t♦♥ q ♥ s ♣trs t tt t r r♠ rs ♦t t st ♣r♦t

t♥ A ♥ B s s t ② ♠♦♥ ♣rt ♦ ♦r ♠♦ ♦t tt ♥ t ①♦♥♦s

s♥ ♦st F ♣r ♥t ♦ ♣t② s t s♠ ♦r r ♥ s♠ r♠s t r r♠ s ♥ ①tr

♥♦♥♦s s♥ ♦st ♠rs r♦♠ ts rr ♣♦t♥t s♦♣

qr♠ rtr③t♦♥ ♥ ♣rt♦♥s

♥ t ♣♣♥① s♦ ts ♠♦ s♦♥ tt ♥r s♦♠ ♦♥t♦♥s strt t♥ s

♦♠♥♥t strt② ♦r r r♠s t ♥♦t ♦r t s♠ ♦♥s ♥trst♥② s s ♦

ts strt t♥ ② rr r♠s s ♥ qr♠ ♥ r♠s ♣t♥ ♥ ♥

t ①♦♥♦s ① ♦st s ♥♦t r② r s ♣r♦♣♦rt♦♥ ♦ ♥t r♥s ❲ ts s

s♥s ♣r♠tr s♣ ♦r ♦r ♣r♦♠ s♥ s♥♥ ♥ ①♣♦rt ♠♥r t♦ ♦s s♠

t ♥ ♠♣♦rtr ♦rss s ♥② t♦ r rt ♦sts r ♦♣t♦♥ r♠♦r s

♥ t♦♥ s♥ ♦st t♦ r r♠s ♠r♥ r♦♠ t ♣r♦♠ ♦ st♥ ♥ tt②

♠r② s♦♥ t ♥qts ♦r t ♣r♠tr s♣ ②s tr r♥t r♦♥s ♣t

♥ r ♥ t r♦♥ Ω1 t ♦ s ♦ ♦t β ♥ F r♠s r r② ♠♣t♥t

s ♥ t r r♠ ♥ ♦t ts ♦rt ♥ t st ♣r♦t ② t♥ t ♥ ♦s ♥♦t

♦♠♣♥st t ♦♣♦rt♥t② ♦st ♦ t♠ s rst ♦t t r ♥ t s♠ r♠ ♣♦♥r

t ♣r♦t ♥ t ♦tr ①tr♠ t t r♦♥ Ω3 r r♠s ♠② ♥tr ♦r ♥♦t

♦♦♥ s♦♠ ♣♦t♥t② ♦♠♣① strts ♥ t ♣r♦r ②s t♦ st ♥ qr♠

s s ♥ ♦♦r♥t♦♥ ♣r♦♠s ❲ ♦ ♥♦t ♦s ♦♥ ts r♦♥ s ♥♦t♥ ♥ t♦

♦r ♥ tr♠s ♦ ♦ ♥ qr♠ s st ♥ ♦♥trst ♦s ♦♥ t r② r♦♥ Ω2

♥ Vlarge ipioneer < V

largewait s♦ tt t s ♦♣t♠ ♦r t ♥rr♦ s♦♣ r♠ t♦ ♥tr s ♣♦♥r ♥

♦r t r♠ t♦ t ♥trst♥② ts qr♠ tr♥s ♦t t♦ ♥ t r♦♥ t ♥♦

♣t♥ β ♥ ♠t s♥ ♦sts F s qtt② ♣♣r♦♣rt ♦r ①♣♦rt♥

♦ ♦♦ tt r♠s r② ♣r♦ ❲ ♦r♠③ ts rsts ♥ t ♦♦♥ ♣r♦♣♦st♦♥

Pr♦♣♦st♦♥ ①st♥ ♥ ♥q♥ss ❲t ♥♦ ♣t♥ ♥ ♦ ①♦♥♦s s♥ ♦sts

s tt F, β ∈ Ω2 tr s ♥q ♠ Prt s qr♠ P ♥ ♣r

strts s tt

t s♠ ♥rr♦ s♦♣ r♠ ♥trs s ♣♦♥r

t r s♦♣ r♠ ts ♦r♦r t r r♠ ♦♥② ♦♦ t st ♣r♦t ♦t

♦ t♦s strt ② s♠ r♠s ♥ ♦♥② ♦r t st ♣r♦t x > θ ≡ Fβ+ c

Pr♦♦ ♣♣♥①

❬r ♦t r❪

♦♦♥ Pr♦♣♦st♦♥ ♥ ♥ t t♦ ♠♥ ♣rt♦♥s ♦ t ♠♦ tt r♥ t♦

t t rst s tt rr ♦♦rs ♦ ♥tr ♦♥② t② ♦sr tt x > θ ≡ Fβ+ c

s ♦♦r♥tr② t♦ θ s ♦ ♦rs rr t♥ t t♦ c ♦r ♦♥t♥t♦♥ ♦ t ♣♦♥r

s s s♠r t♦ t ♥t ♦t♦♥ ♣r♦♠s ② r♥ ♦r s tt ♥ ♦r ♠♦ r♥♥♦s ♥♦t ♦♠s r♦♠ ♣r t♥ t r♦♠ t♥ ♦♣ t t ♦tr r♠s s♦♥ t♦ ♣♦♥r t ♣r♦t

♥ t ♣♦♥r s r② ♣ t s♥ ♦st F ♣r ♥t ♦ ①♦♥♦s ♣t② t ♦♥② t♥

tt ♠ttrs ♦r ♦♥t♥t♦♥ s tr r ♣r♦ts r ♣♦st xi > c ♥ t♦ t

♦♦r ♦s ♥♦t ②s ♥t t♦ ♥tr s ♠② c ≤ xi ≤ θ tr s ♦♥ r r

♦♦ tt t ♥tr ♦♠♣r t♦ t s ♥ tr s ♥♦ sr ② t s♠ r♠

s♥ ts ♦ ♠♥ tt xi < c s s s ♦r rst rst tst ♣rt♦♥s ♦r ♠♦r

♦r♠ rt♦♥ s ♣♣♥①

Prt♦♥ ♥tr② ♦ ♦♦rs s ♣♦st② rt t♦ t sr ♦ ♣♦♥rs ♥ t ♣r♦tPr♦♦ ♣♣♥①

r s♦♥ ♣rt♦♥ ♦♦s r♦♠ ss♠♥ tt t ①♣♦rts ♦sr ♦rrs♣♦♥ t♦ t r②

r ♥ r ♥♦♥♦s② ♥ sF, β ∈ Ω2 ♥ tt r♦♥ ♣t♥ β s r

♥♦ ♥ t ①♦♥♦s s♥ ♦st F s ♦ ♥♦ s♦ VlargeWait > V

largepioneer s ♠s t r

r♠ ♣rr t♦ ② t s♠ r♠ ♥trs s ♣♦♥r s q♥t t♦ t ♦♦♥

stt♠♥t

Prt♦♥ rst ♠♦r s♥t r②t♥ s ♦♥st♥t ①♣♦rt q♥tts ♥r♥s ♥ ♣r♦t r rr ♦r ♦♦rs t♥ ♦r ♣♦♥rs Pr♦♦ ♣♣♥①

t s ♠♣♦rt♥t t♦ r♠r tt t strt ② ♦♠s ② r♦♠ r r♥ t r r♠

♥♦s tt tr s ♥♦tr ♠♦r ♦s r♠ ①♣♦r♥ tt ♥tr s ♦♠♥♥t strt②

t s ♥♦t s♥t t♦ ♠♦r tr♥ts r♦♠ t♦ ♦♦s ♥ ♦rr t♦ r t q

r♠ ♦ Pr♦♣♦st♦♥ rr r♠s ♥ts ② t♥ s ♥♦r♠t♦♥ ♦t xi

r ♦♥ t r♠ t♦ ♦♦s t st ♣r♦t ♥ ♦tr ♦rs t ♥rt♦♥ ♦

♥♦r♠t♦♥ ①tr♥t② s t ♥rts t♥ ♥ t t s♥ ♦ ♦tr s♠ r♠ ♥

st♦r st♦♣s r r♥ ② t r r♠ s ♦ t s ♦r ①♠♣ t r r♠

♥♦s ♥ ♥ tt t t ♦♥② ♣r♦r ♥ t ♦♥tr② t st ♥ t ♠♠ tr♠

s s♠s ② s♥r♦ ♥ r♠s r rst ♠♦r ♥t ♥ r s

♣r♦ts tt t ♦r t ♦ ♦ ♠rt ♥ ♣r♥t ♦tr ♣②rs r♦♠ ①♣♦rt♥

♦ ♥s t s ♠♣♦rt♥t t♦ r♠r s♦♠ st♥t ♣r♦♣rts ♦ ♦r ♠♦ rst s tt t

♣r♦♣♦s ♠♥s♠ ♦rs ♥ t ♥♦ ①♦♥♦s s♣r♦♣♦rt♦♥ s♥ ♦st ♦r t ♣♦♥r

r♠ ♥♦ ♠ttr r♠ s t s ss♠ F s ♦♥st♥t r♦ss r♠s s s r♥t

r♦♠ ♠♦s s♠♥♥ ♥ ♦r ss♠ t ♣♦♥r ♣②s ♥ t♦♥ ♦st

♦ ①♣r♠♥tt♦♥ ♦♥ s t♦ r② t s♦r ♦ t ①tr♥t② ❯♥r s♦♠ ♣r♠trs

s s♦ ♣♥♥r ♦ s♦ ♥t t ♠♦r ♦s r♠ t♦ ♣♦♥r ♦t s t s

♣r ♦r s♦t② t♦ s♣♥ Fq rtr t♥ F q ♥ s t ♦s r♠ s r r ♦♣t♦♥s

♦ t♥ ♥ ♦♠♣rs♦♥ t t ♦♠♣tt qr♠ ♦ Pr♦♣♦st♦♥ t r♥ s tt

t s♦ ♣♥♥r ♦ t t ♣♦♥r ♥tr ♥ r♥ ♦ ss ♥ t ♣♦♥r ♦ ♥♦t

t s ♥trst♥ t♦ ♥♦t tt ♥ t r♦♥ ♦ ♣r♠trs ♥ ♥ r tr s ♥♦ r♦♥ ♥ t qr♠♦r t s♦♣ ♥trs ♥ t ♥rr♦ s♦♣ ♦s ♥♦t

♣♣♥① ♦rs ♥r③t♦♥ ♦ ts ♣rt♦♥s ♦r t s r t s♦♣ r♠ s ♠♦r t♥t♦ ♥ ♣r♦ts r♦♠ t♦ ♦♦s

♣rt② ♥ t♦ ♥tr ♥ tr♠s ♦ r t s♦ ♣♥♥r ♦ t r② r t♦

♠♦r ①t♥ t♦rs t rt ♠♦r ♣♦t♥t ♥tr♥ts t r t r t♦ t rt

♥ t ♣♦♥r ♥ t♦ ♥tr t ♥ ♥tr♥③ t s♦ ♥t t♦ ♣♦t♥t

♦♦rs

❲t ts s♠♣ r♠♦r t ♥ r ♥♦ ttr q♣♣ t♦ t♦ ♦♦ t t t

r t ♦♥ ♥ ①♣♦rtrs

s st♦♥ sr ♦r t s♦rs s s ♦r ♣r♦r ♦r ♦♥strt♥ ts ♦ ♥

♣r♦ts tr ♦♥ t s♦ srs t t ♦t q♥ttt② ♥ t s♣ ①♠♣s

♦ ♣r♦ts

t ♦♥strt♦♥

♦ ♥rst♥ ♣♦♥r♦♦r ①tr♥ts ♥ ♥ ①♣♦rts ♥ t♦ tst

t r♠♣r♦t s♦ ♥ st♥s r♠ ♦r r♦♠ ♥str② ♦r ♥ ♥

♣r♦ts♣r♦sss r tr s ♦t s♦♠t♥ ♥ t♦ r♥ ♥ t s ♣♦ss t♦ ♥t② t

sq♥ ♦ ♥tr② ♥ ♦♥ t st ♣♦ss ♥rs ♦ ♣r♦ts t♦ ♦ ♥st ss ♥

① ♣♦st sss st♦rs ❲ r ♥♦t r ♦ ♥② ♦tr st② ♦ ①tr♥ts t♥ ♣r♦rs

♦ ♣r♦t tt ss tst t ts tr rtrsts

❲ t ♦r tst ♦ ♥ ①♣♦rtrs s ♠♦st② ♦♥ t ♥ ts ♦ ①♣♦rt tr♥st♦♥s

♥ st♦rs ♥ t♦t st♦♠s r♦r ♠♦r t♥ ♠♦♥ tr♥st♦♥s t♥ ♥

②♥ ♦♥ st♦♠s t ♦s s t♦ ♦sr t ♦♣♠♥t ♦ ♥ ①♣♦rt ♥strs tt

r ♦ts ♦ t ♦r ♦ ♠♥tr♥ ♥sss r ♠♦r trt♦♥ s♦r ♦ t

♦r r♠ ♠♣r tr ♣♣rs ♥ ♣rtr s♥ rst♦♥ ♥ rtr ♥ ♠♥♥

r ♠♣♦rt♥t ♦r ♦♣♥ ♦♥trs ♦r ts ♥ s ♦r ♥rst♥♥

①♣♦rt ♥tr♣r♥rs♣ ♥ ss ♦♣ ♦♥trs ♦♠♣r t♦ st s♥ ♥str t

♦r r♠s ♦sr t ♣r♦t ①♣♦rt ♥ t r♠♦♥③ ②st♠ sst♦♥ t

②r ♦ t ①♣♦rt t st♥t♦♥ ♥ t ①♣♦rt s ❯ ♦rs ♦r♦r ♦r t ♠♦rt②

♦ ♣r♦ts t ♥t ♣r ♥ t q♥tt② ♥ t ♥t ♦ ①♣♦rt ♥ r♥s t

♣r♦t s ♥♦t r② ♦♠♠♦♥ ♥ t trtr ♦♥ ♥♥♦t♦♥ s♣② ♦r ♦♥♦♠②

sts ♦r ①♠♣ t trtr ♦♥ ♣t♥ts ♥♦r♠② ♦s ♥♦t t ♣r tt r♠

ts ♦r s♥ ♣t♥t ♣r♦ts ♦r ♣r♦sss

rt♦♥ ♦ t s♦ ♣♥♥rs ♣r♦♠ s ♥ t ♣♣♥①s♦ ♠♥② ♥str sr②s ♦♥② ♦♥sr r♠s ♦ ♠♥♠♠ s③ ♥ t ♥ s r♠s t ss t♥

♦rrs r ♥♦t sr②

♦ ♦♥strt ts trs rqr t♦♥ s♦rs ♦ t rst s♦♠ r② s t① r♠

r♦rs r♦♠ t ♥tr♥ ♥ r s ♥ t ♦♥♦♠ st♦rs ♦ t

r♠ ♦r♥ t♦ ♦ ♥♦♦s t♦ t sst♦♥ s ♥♦r♠t♦♥ s r t♦

sr♠♥t t♥ r♠s tt r t② ♣r♦rs ♦ t ①♣♦rt ♦♦ ♥ r♠s tt ♦♥②

trrs ♦r♥ t♦ t ♥ t s s♦ ♠♣♦rt♥t t♦ s♥t♥ t ♥ ♦ ♥

①♣♦rt♥ s♣ ♦♥ t ♦♥ ♥ ♥ t t ♦ t r♠ ♦♥ t ♦tr s s r♥t

s s♦♠ r♠s ♠② st s♥ ♥ t ♦ ♠rt ♥ t② r ♥♦t ①♣♦rt♥ ♦♥

tr ♦t s♠ tr♥st♦♥s ♥ r①♣♦rts ts ♦ ts tr♥ ♣r♦ss ♥

♦♥ ♥ t ♣♣♥① ♠r② ♥t t♦ ♦ ♠s♥t②♥ r♦♥ ♦ ♣r♦t

s ♥ ♣r♦t ♥ ♦r s♠♣ tr r ♠♦r ♦ rsst♦♥s

♥ ♥ t♦ ♦♠♦♦t ❲ t ♦rrs♣♦♥♥ r♦ss ts tr

r♥t ♥ts ♦♦♥ t s♠ t♦rt ♣r♥♣s ♦ Pr ♥ ♦tt

❲ ♥t t♦ ♥♦t tt ♥ ♣r♦② ♠♦st ss r ♥♦t ♥②③♥ ♣r♦ts tt ♥ ♥♥t

♥ s r ♣r♦ts ♥♥t s♦♠r s s♦ ♥ ♠♦r ♦s s♦② ♦♥ t ss

♦ ①♣♦rt♥ rtr t♥ ♦♥ ♠♦r ♦♠♣① ♣r♦sss s ♦ ♥♦t t s ♦r ♥

♥ ♦♥♦♠② t ❯♥ts tts r ♦r ♠t♦ ♠t ♥♦t s t♦ st②

①tr♥ts ♥ ①♣♦rts

♥♥ ♥ ♥ ♦ ♣r♦ts ♣♦♥rs ♥ ♦♦rs

tr ♣♣②♥ t trs rst ♦r t ♣r♦ts ♥ t♦ r♦♣s ♥ ♣r♦ts

♥ ①st♥ ♦r ♦ ♣r♦ts t t♦ ♦♠♥s ♦ ❲ ♥ ♥ ♦ ♣r♦t s ♥②

♦ tt s ①♣♦rt r♥ ② r♠ ♦r t st r♥ ②r r

♥②ss ♦ ♥ ♣r♦t ts ♥s ♥ ♥ ♣r♦t s ♥ s ♥ ♥ t s ♥♦t ♥

①♣♦rt ♥ ♥ t s ①♣♦rt t♥ ② t st ♦♥ r♠ t ♠♥♠♠ ♦

② ♥ t ts ♥ t r♠s st♦♣s ♦♣rt♥♦r ts ♠r ♦r t t ♥ r♠ ♣♥ r♦♠ st♦♠s ♦♥ ♠♣♦rts ♦r t ♣r♦

♥ ♥ ♦♥ s ♣r♦♠ t♦ ♥t② ♥ ♣r♦ts s ♥ r♠r ② ♦ ♥

t♦ ♥ r♥t ♦♥t①t ② ♦♦ t t ♠♣ ♥ rts ♦ ♥ t ♣r♦ts ♥ r♦s♦♥trs r♥ t ②rs ♥ r ♣rs② t ②rs ♥ st♦♠s r♦♥ t ♦r ♠♦tr sst♦♥ t♦ t r♠♦♥③ ②st♠

♣♣♥① ①♣♥s t ts ♦ t tr♥s♦r♠t♦♥♦r t ♥t♦♥ ♥ ♥②ss ♦ t trs ♣s s t ♣♣♥①❲ ts ♣r♦ts ♦ ♥ t s♥s tt tr s s♦♠ ♠♦♥t ♦ ①♣r♥ ♥ t ♦♥tr② ♦t ♦ ♥

r t♦ ①♣♦rt t♥ tt ♥t t♦ rt ②r ♣rs♠♣ ♥♦ t ♣r♦ s ♣r♦② t rst

♦ t s ①t② ♦r tt ♣r♦ r♦♥ ♥ s t t♠ ♥ st♦♠s r♦♥ t♦r strt t♦ s t r♠♦♥③ ②st♠ s r♣♦rt ② ♦ ♥ ♦♥ ②♦♥ ts t ♦rt ♠♥② ♥ ♣r♦ts tt ♠r ♦♥② ♦r ②r t♦ t ♥ sst♦♥ ♥ t ♦tr ♥ t ②r ♥♦ s ♣♣r♦♣rt s ♦♦ t t ② t♥ t ♥tr♥ ♦ t ♣♦♥r ♥

♦♥ ss② r♠s ♦r♥ t♦ t sq♥ ♦ ♥tr② ♥ ♣r♦t s ♣♦♥rs ♦r ♦♦rs

♦r ♥ ♣r♦t ♥ ♣♦♥r s r♠ tt strts ①♣♦rt♥ t ♣r♦t ♥ t rst

②r ♦♦r s r♠ tt ♥ ①♣♦rt♥ t ♣r♦t t st ♦♥ ②r tr t ♣♦♥r

♦r t s ♦ ♦ ♣r♦ts ♦ ♥♦t ♥ ♣♦♥r s t s ② ♣♦ss tt t

♣r♦t s rst ①♣♦rt ♦r ♦r ♣rs♠♣ ♣r♦ ♦ s♦ r ♥ t♦ st♥s

r♠ s t rst t♦ ①♣♦rt t ♣r♦t ♦r ①♠♣ tr r ♠♥② ss r

rt♥t② tt ts ♣r♦ts strt ♦r ♥ s♦♠ ♦ t♠ ♦r ♥trts

♦r ♥s ♦r ♦ ♣r♦ts s♦ ♥ ♦♦r ♠♦st② ♦r ♥♠r♥ ♣r♣♦ss s

♦♦rs ♦ ♥ ♦ ♣r♦t r r♠s tt ♥ ①♣♦rt♥ ♥ ♦ ♣r♦t tr s ♠♥s

tt t ♣r♦t t♦ ♥ ♦ ♦r t ♦♥tr② s st ♥ ♦r t r♠

s♦s s♠♠r② ♦ t t①♦♥♦♠② ♥ ♦♠♥s rr t♦ ♣r♦ts t t

♦♠♥ s♦♥ ♦ ♣r♦ts ♥ t rt ♦♠♥ s♦♥ ♥ ♣r♦ts r♦s rr t♦ r♠s

♣♥♥ ♦♥ t sq♥ ♦ ♥tr② ♣♦♥r rst r♦ ♦r ♦♦r s♦♥ r♦ ♣♥♥

♦♥ tr t r♠ s t rst ①♣♦rtr r♦♠ t ♦♥tr② ♦ tt ♣rtr ♣r♦t ♦r ♥♦t

s♦ s♦s t ♥♠r ♦ r♠s ♥ t♦r② ♥trst♥② ♠♦st ♦ t r♠s♣r♦t

♣rs strt ①♣♦rt♥ s♦♠t♥ ♥ ♦r t r♠ t ♦ ♦r t ♦♥tr② N = 10, 294 ♦r

♦ t ♦srt♦♥s s ♠s r tt ♥ t st② ♦ t r② sts ♦ ♥ ①♣♦rts

r ♦r♥ t s♠ rt♦♥ ♦ t ♦r ①♣♦rt strtr ♦ ♦♥tr②

❬ ♦t r❪

Pttr♥s ♦ ♥tr②

tr ♦♥♦r♥ t ♣r♦ts ♦s ♦r t ♣r♦ ♥ tt ♦t ♦

♣♦ss ♣r♦t♦s ♥ t sst♦♥ r② ①♣♦rt ♣r♦ts r♥ ♦r ♣r

s♠♣ ♣r♦ ❲ ss② ts s ♦ ♣r♦ts r ♣rrr tr ♦s

s t♦ ♥t② ♥ ♣r♦ts ①♣♦rt r♥ t ♥♦t r♥ ♦r ②r ♣r

s♠♣ ♣r♦ s r♥ ♦r s♠♣ ♣r♦ ♦ t ②rs t ♦♥tr② ①♣♦r ♦ t

t♦rt ♣♦t♥t ♦ ♣r♦ts tt r ♥♦t ①♣♦rt ♦r t♦t ①♣♦rt ♦ ts

t ♦♦r s tt ♥ ♠♦r t♥ ♦ t ss t rst ♣♦♥r ♣♣rs ♦r ②rs ♦ ♣♦♥rs ♥tr②♥t♦ ①♣♦rt♥

r ♦ ♠♦r t♥ ♦♥ ♣♦♥r ♥ t rst ②r ♦ ♣r♦t ♦r s s tr ♥ ♠♦st ss s♥ ♣♦♥r t♦ ♦ t ①t t ♦ ♥tr② ♣rr t♦ ♣ t ②r s ♦r ♠♥♠♠♥t ♦ ♥②ss

14% t tt r♥ ①♣♦rt r♦♥ ♦ t t♦rt ♣r♦ts tt r ♥♦t ②t①♣♦rt ♦r s ♥ ts s②♠♣t♦♠ tt ♦r ♠t♦ s r♥t s t ♦♥tr② s r r♦♠ tt♥ tt♦rt ♦♥r② ♦ t ♥♠r ♦ ♣r♦ts ♦r ② t sst♦♥ ♥ r ♦♣ ♦♥♦♠s

♥ ♣r♦ts st② ♥rs r♦♠ ❯ ♠♦♥ ♥ ♣r ♣r♦t t♦ ♠♦♥

♥ ♠♦♥ ♣r ♣r♦t s ttr r♣rs♥ts ♠♦st ♦ ♥♦♥♦♣♣r

①♣♦rts r♦♠

❬ ♦t r❪

t♦t ♦ r♠s ♣rt♣t ♥ ♥ ①♣♦rt ♣r♦ts t♦t ♥♠r ♦ ♥q ♣r♦t

r♠ ♦srt♦♥s s ♥t♥ tt ♦♥ r ♦♥② r♠s ♣rt♣t ♥ ♣r♦t

♦r ts r s ♥ ♥trst♥ tr♦♥t② r♦ss ♣r♦ts ♥②③s ts

tr♦♥t② t t ♣r♦t ♦♠♣♦s♥ t ♣r♦ts ♦r♥ t♦ tr ♥♠r ♦ ♣♦♥rs

♥ ♦♦r r♠s ♦r t ♣r♦ t s♦s tt ss t♥ ♦ ♣r♦ts

♦♦rs ♦♥ ♦♥② ♦♥ tr ♦ t ♣r♦ts t ♦♦rs t♦ ♦r ♠♦r ♦♦rs s

q♥ttt② ssts tt ♦♥② ♣♦t♥t ♥tr♥ts ♥t♦ ①♣♦rt♥ ♥ ♥t r♦♠ r♥♥

♦♥trsts t t r② ♣③ ss ♦ ♥ ♣r♦t ♦♣t♦♥ ♥ rtr r ②

t strtr ♦ ♥str② tr r ♠♥② ♣♦t♥t ♥tr♥ts ♦♥ ♥ ♦ t ♥ ♣r♦ts

tr s s♥ ♣♦♥r s ♣r♠ srs t tt tr r ♠♥② r♠s t♥ ♦r

s♥ tr ①♥ rt ♥ ♦r tr rstrt♦♥ t♦ ♠♣r♦ ♥ ♦rr t♦ s♥② ♠♣

♥t♦ ①♣♦rt♥ s t ♦s ♦ ♦♦♥ ♥ ♦r t ①♥ ♠♥tr♥

tr

♦t rsts ♦ t ♦ rt♦♥ ♦ ♣r♦ts t ♦♦rs ♥ t ♣r♥ ♦ ♣r♦ts t

s♥ ♣♦♥rs r r♦st t♦ ♠♦t♦♥s t♦ t ♥t♦♥s ♦ ♥ ♣r♦ts ♥ t♦ ♦♥sr♥

♦♥② r② ♦♦rts ♦ ♣r♦ts ♦r ♦r ♦r ♣r♣♦ss t♦ ♥rst♥ ①tr♥ts t

t ❯♥t tts ♦ ♥♦t ①♣t ts t♦ t s ①♣t ♦r ♦♣ ♦r ♣r♦ts rt② s ♦♥ ♥trrs♦rs ♥♦t ♣r♦ ♥ t ❯ r ♠t♦ s ♠♦r st t♦ ♠sr ♥♥♦t tt② ♥ s♠♦♣♥ ♦♣♥ ♦♥♦♠s

♥rs s r② ♦r♠♥② t♦ t sr ♦ ♥ ♣r♦ts r ♥tr♦ ♦r ♥ s♥♥t② ♥rs tr s s♥ t ②r ♦ tr ♥tr♦t♦♥ ♥t♦ ①♣♦rt ♠rts

r♠s r ♣♦♥rs ♥ ♦♥② r♠s r ♦♦rs ♥②ss ♦♥ t t s ♦r r♥♦♠ ♣♦♥r ♥ ♦r s♠♣ ♦♥ ♦♦r ♥ tt r ♦ t st

t♦ ♦♦rs t trt♦♥ s ♦ rs ♥ ♠♦r r♥t② ♦♥② ♥ ❯r② ♦str ♥ ♦s♥③

t♦♥② tr rs♦♥s ♠t ①♣♥ ♣rt ♦ t r♥ t♥ tr st② ♥ ♦rs rst tr st②

s ♥ ①♣♦rt ♣r♦t t♦ ♥②t♥ tt s ♥♦t ①♣♦rt ♦♥ ②r ♦r tr s♠♣ ♥ ♦♥trst ♦r st②ts ②rs t♦ t ♦sr t♦ t ♥ ♣r♦ts ♦♥ ♥ st♦rs ♥♦t ♦♥② ♠♥tr♥♥② ♦♦♥ ♥ ♦r ♦s ♦♥ r② r ①♣r♠♥t ♦ tr ♥trt♦♥ s t rs♠♣ ♣r♦ s ts ①tr♠ ♥ts ♦ ♥trt♦♥

♥ ♦♥ ♠② ♦rr tt ♦r s♠♣ ♦ ♦♥t♠♥t ② s♠ tr♥st♦♥s tt ♥r ♥t♥ t♦ sst♥ ①♣♦rts ♦♦ ♦♠♣♥② r ①♣♦rt♥ s♣ ♠♥ t ♦t r♦♠ ♥♦tr r♠ r♥ t s♠ ♥②ss rstrt♥ t s♠♣ t♦ ♣r♦ts r t ♣♦♥r st t st t♦ ♦♥st ②rs①♣♦rt♥ t s tr ts ② t ♦ ♠♥t♦♥ ♥♦s t s♦ ♠♥② tr ♣♦♥r rs ♦r t♣r♦s② sr ♣ttr♥ r♠♥s ♥tr ♦r ♠♦st ♣rt ♣r♣♦ss t♦ ♥sr♣rs♥② t s♠♣♦ ♥ ♣r♦ts rs r♦♠ 270 t♦ 121 ♥ t t♦ ♦r ①♣♦rts t♦ ♠♥♠♠ ♦ ♦s ♥♦trt② ♥s t ♦ ♣r♥ts t♦ t r ♥♠r ♦ ♣r♦ts 524 P♥ ♦ s♦stt t s♠ r ♦s ♦r t ♦♦rts ♦r ♥t♥ r♦st rt♦♥s♣ tt s ♥♦t ♥ rtt ♦ ttt r♠♥♥ s♠♣ t♠ tt tr ♦♦rts ♦r t rt ♦ s♦♠ ♦♦rs

rsts ♦ ♥t tt ♥ ♦♦rs s ♥rq♥t ♥ ♥ t ♣♣♥s t t♥s t♦

♥ ♠t ♥♠rs ♦r t s♦ s♦s tt ♥♦t r♠s ♥tr ♠♠t② ♠♥ t

♣s t♦ t♥ tt ♥ t ss t ♦♦rs ts r♥ s♦♠t♥ r♦♠ t ♣♦♥r

sr♣t sttsts

s♦s t rtrsts ♦ t ①♣♦rt s♣s ♦r r♠ tt ♥②③♥

rst t♥ t♦ ♥♦t s tt r♠s tt ①♣♦rt ♥ ♦♦s r ♠ rr ①♣♦rtrs t♥ t r♠s

tt ♥tr ♦♥② ♥t♦ ♥ ♦ ♣r♦t s ①♣t ♥ ♠t♣r♦t ♠♦s ♦ ①♣♦rts ♥ t st②

stt ②r t③ ♥ tt♥♦ t r♥ s ♦♥♥trt ♥ t ①♣♦rts ♦

①st♥ ♦♦s ①♥ t ♣♦♥r ♣r♦t ❲ t ♠♥ log10 ①♣♦rts ♦ ♦tr ♦♦s

♦r ♥ r♠s s t ♦r ♦ ①♣♦rtrs s ♠♦st ♥ ♦rr ♦ ♠♥t ♥

sttst② s♥♥t ♦♥ ♥ rt♥ s♦♠t♥ s♠r ①♣♦rtrs ♦ ♥ ♦♦s ♦r t

♦♥tr② s♦ r ♠♦r ② t♦ r t①♣②rs ♦r♥ t♦ t ♥ s t♥s t♦ r

♦t t tt t r ①♣♦rtr ♦ ♥ ♣r♦ts ♠t s♠ r♠ ❲ s♦ tr

tt ♣♦♥rs ♥ ♥ ♣r♦ts t♥ t♦ s♠r t♥ ♦♦rs ♥ ts s♠ ♥ ♣r♦ts t

♦r t ①♣♦rtrs ♦ ♥ ♣r♦ts r rr t♥ t♦s s♠♣② ①♣♦rt ♦ ♣r♦ts

♥trst♥② t♦ t ♣r♦t② ♦ st♥ ♠♦r t♥ ♦♥ ss♦♥ t t ①♣♦rt ①♣r♠♥t

♦s ♥♦t s♥♥t② r t♥ ♦♦rs ♦ ♥ ♣r♦ts ♥ ♦♦rs ♦ ♦ ♣r♦ts ♦t

r r♦♥ t t r ♦r ♣♦♥rs t♥ ♥t♦ ♦♥t t♦s t ♦♦rs

♥ t♦s t♦t ♦♦rs s♦ t sr♣rs♥② s♠r

tr ts ♥r ♦♠♣rs♦♥ ♦s ♦♥ t ♠r♦ r♥s t♥ ♣♦♥rs t ♦♦rs

♥ tr ♦♦rs s s ♠♦r ♠♥♥ s♥ t② t t s♠ st ♦ ♣r♦ts r

♦♥ ♥ r♠r tt ♦♦rs ①♣♦rt rr ♠♦♥ts s s♦♠t♥ tst♥ ♠♦r

♦r♠② ♥ sst♦♥ ♠♣♦rt♥t② t r♠s ♥tr♥ s ♦♦rs s♠ ♠♦r rs ♥

tr♠s ♦ tr ♦♥♦♠ tts ♦r♥ t♦ t ♥ ♦♦rs ♠♦r

♦s ♣r r♠ t♥ t ♣♦♥rs ♦ t s♠ ♣r♦ts rss rs♣t② s

t♦ ts r ♦♥sst♥t t ♦r ♠♦ ♣rt tt ♠♦r rs r♠s ♦ ♥tr

s ♦♦rs ♦t② s♦♠ ♦ ts tr♥s r s ♥ t♦t ♦♥tr♦♥ ② ♣r♦t ♦r

st♥t♦♥ rtrsts ♦r tst♥ t ♠♣t♦♥s ♠♦r ♦r♠② ♦r r②

r s♦♠ s sts t♦ r♠r qtt② ♦r rsts

❬ ♦t r ❪

♥♦♥ s sts

♥ strt ♣r ♦ ♦r r♠♥t ♥ ♦♥ ♥ r s♦s ①♠♣s ♦

♣r♦ts ♦r♥ t♦ t sss ♦ t st ♦♥ r♠ ♥ t ♣r♦t ♥ t ♥♠r ♦ ♥tr♥ts

♦♥② ♦♥ ♥tr♥t ♦r ♠♦r t♥ ♦♥ qr♥t ♦♥t♥s t rq♥② ♦ r♠s ♥ r♦♣

s s r♣ t ♥♦♥ ①♠♣ ♦ ♣r♦t ♥ tt t♦r② ♥ r♣ t

♦r③♦♥t ①s s♦s t ②r ♥ t rt t log10 ①♣♦rts ♦ r♠ ♥ t ♣r♦t

♥ ♥ ②r ♦♥♥t ② ♥ ♦r t s♠ r♠ s♦ r♥t ♥s ♦rrs♣♦♥ t♦ r♥t

r♠s s ♣r t t♦rs tt ♦s ♦♥ ①tr♥ts r♦♠ ♣♦♥r t♦ ♦♦r ♦

♦r s♠♥♥ ♥ ♦r ♦ ♦s ♠♦st② ♦♥ s ♦ ♣♦♥rs t ♦♦rs

♥ ♦♥trst t ♠② ♦ ♠♦s ♥ ♥♥r ts t ♦♠st ♠rt ①tr♠ rst

♠♦r ♥t ♦ ♥rt ss t♦s ♥ ♣♥

❬r ♦t r❪

❲ rst ♦s ♦♥ t ①♣r♠♥ts ♦ P♥ s ② r t ♠♦st rq♥t s

♣♥♥ ♦♥ t tr s ts r♦♣s r♣rs♥ts t♥ ♥ ♦ t ♣r♦ts r

♥♦ r♠ ♠♥s t♦ sr sst♥② s s♦♥ s ❩♦t ♠♥r s♦r♥t ♣♦♥r

② t♦ r♠s ♥ t s♠ ②r t tr tr ♥ ①♣r♠♥t ♦t s♦♥t♥ t ♥♦r

❲ ♥tr ♦♥ ♦ t r♠s s ♠t♣r♦t ①♣♦rtr ♦ ♠♥r rt③rs ♥

t ♦♥rst♦♥ t ♠♥r sst tt t ♦ ♦♠♣♠♥tr② ♥♣ts ♥♠② ♣r♦♣r

tr♥s♣♦rtt♦♥ ♥ rtt♦♥ s rs♣♦♥s ♦r t r ♦ ts ♣♦t♥t② sst♥

①♣♦rt ①♣r♠♥t

♦♥ ♣r♦ts t s♥ sr♥ r♠ ①♣♦rt♥ ♥ ♥♦ ♦tr ♦♦rs s

r♦♣ ♦ ♣r♦ts t sst♥ t ♦♥② ♣♦♥r t♥ t♦ r♣rs♥t ♠♦r t♥ t ss

♥ ♣♦♥rs sr ♠♦r t♥ ss♦♥s ①♠♣ s ♣♦s♣♦rs P♥t♦① ♠

P♥ s♠♣ st② ♦ t ♥str② ♠s r ② ♥ t s s♥ ①♣♦rtr s ♥♦t

sr♣rs♥ ♦s♦q♠ ♦♥ ♥ s ♥♦t ♦♥② t s♥ ♣r♦r ♦ ts ♠ ♥

t s♦ t ♦♥② ♦♥ ♥ ♦t ♠r t t t♠ ♥ ♦♥t①t ♦ ♦♥♦♠s ♦ s

t s r t♦ r tt t ♣♦♥r s ①♣t♥ s♦♠ ♦♦rs s ♦♥ ♥ ①♣t tt ♥

ts ss tr s ♥♦ ♣ t♥ t s♦ ♥ t ♣rt ♥♥ts t♦ ①♣r♠♥t ♥ ①♣♦rt♥

ts ♣r♦t

♥② ♥ P♥ ♣t ♥♦♥ s ♦ sss ♣♦♥r t ♦♦rs st♥r ♦♠

rrt♦rs ♥ ts ♣r♦t t♦ ①♣r♥ r♠s sr t♦ t tr r③t♦♥ ♣r♦

❲ ♥ sss ♥ ♣r♦t r♠ sr ♦r ♠♦r ♦♥st ②rs ①♣♦rt♥ t ♣r♦t ♥ ts♥t♦♥ ♦♦s② ① ♣r♦ts tt ♥ ♥ ①♣♦rt tr trs ♦ ♥♦t t♠t♦ ♥ s♥ r♠ ♥sr♥ ♠♦r t♥ ②rs s♥ t s♠♣ ♥s ♥

② sst♥② ♠♥ ♠♦r t♥ ②rs ♥ ♦♥tr♦♥ ② ♦♦rt tss ♥ ♥♦♦s s ♠t t ♥♦♥ s ♦ rrts ♥ t ❯♥t tts ♦♥ ♦r r♦♣ rs

♥ t s ♥ s ♥ strt t♦ ①♣♦rt rrrt♦rs r♥ t ♠ s ♥trst♥② t

②r tt t ♣♦♥r strt t♦ ①♣♦rt rrrt♦rs ♦t r♠s r ①♣♦rtrs ♦ s♦♠ ♦tr

♣r♦t s ♥r tr♥ ♥ ♦r t s ts s tt r♠s ♠t r♥♥ ♦t

①♣♦rt♥ ts ♣r♦t rtr t♥ ♥r r♥♥ ♦t ①♣♦rt♥ s♦♥ r♠r s tt

t ♣♦♥r r♠ ♥ rrrt♦rs s s②st♠t② s♠r ♥ ss rs t♥ t ♦♦r

s s ♣rs② ♦♥sst♥t t ♦r ♠♦ ♥ s♦ ♥ t♦♥ tt ts tr♥ ♦s

♦r ♦r s♠♣ ♦ ♥ ♣r♦ts

s ♦ rrrt♦rs ♥ t ♦♥ ♦r P♦s♣t ssts t ♣♦sst② ♦ ♥ ①tr♥t②

♦♥tss rrrt♦rs r st ♣r♦t t ♣♦t♥t ♥tr♥ts ♥t♦ ①♣♦rt♥ s

tr r r♠s ♥ t ♦♥tr② ♥ t s ♥② tt t strtr ♦ t ♥str② ♦ ♥

s♦ ♠ tr strt♥ t♦ ①♣♦rt ss ♣♦♥rs r ♠♦r ♦♦rs ♥ ♦r ①♠♣ t

♠t ♣♥ ♥str② r tr r ♠♦r ♣②rs ♦r ①♠♣ r s♦s r♠s

♦♦♥ t ♣♦♥r ①♣♦rtr ♦ r♦③♥ t♦♥ ♥ r♦♥ ♠♦♥ ♦rs ♥

①♣♦rts r♦♠ ♠♦st② t♦ ♣♥

❬r ♦t r❪

♥ st♦ t sr♣t sttsts ♥ ♥rrts ♦t♥ ♦ ♥t s♦♠ rtrsts

tt ♥♦t② t t ♦r ♠♦ rst s t ♠ss rs ♦ ①♣r♠♥t tt st②

r♥♥ ♦♥ s tt st♦rs t ♦♦rs s♦ st♥t ♣ttr♥ ♥ ♣♦♥rs t♥

t♦ ①♣♦rt ss ① ♣♦st ♥ ♥ r ss rs tt ♦♦rs ♥② ♥ s♦♠ st♦rs t s

rr t♦ r tt tr s r♥♥ t♥ t s♠ ♣r♦t s♥ tr r ♥♦ ♦♦rs

♥ t ♥①t st♦♥ ♠ ♠♦r s②st♠t tst ♦ t r♥t ②♣♦tss

st♥ ♣rt♦♥s

♠♦st ♥♦♥ ♦ t r♠s ♥ ♦r s♠♣ strt ①♣♦rt♥ ♥ ♣r♦ts ♥ t s♠ ②rs r t ss ♦ s♥ ♥① ♠♦s s♠rs ♥ t ♠♥s♠ t♦ ♦♣♥②♥ ♦r t③ ①♣♦rts ♦ ts ♣r♦t ♥ ♥ ② ♣♣♦♥ t Prs s r② ♥ ♠♣♦rt♥t ①♣♦rtr ♦

r♦③♥ ♣♦r ♠t ❯♥t t s t ♦♥② ①♣♦rtr ♦ ♦♥ t♦♥s r♦③♥ r♦♠ s s ♦♠♣♥②t tt ①♣rts ♥ ♦♥ ♣r♦t♦♥ t ♦t ♦ ①♣rts ♦♥ r♦③♥ ♠ts ♥ ♥ t s♥ ♠rt s♣t♥ ♥♦ r ♥t ♥ t ♣r♦t♦♥ t s t ♣♦♥r tr ♦r ②rs ♦ ♦♥② ♣♦♥r♥ ♥ r♦r♦s ♦ ❱♦r strt t♦ ①♣♦rt t rst ②rs s♣♠♥t ♠♦r t♥ rr t♥ t ♦♥ s ②t P♦♥r ♥ ts rst ②r ♥ ♠♥② ♦tr r♠s ♥tr r♦r♦ s♦r♥♦ r♥s Pr♦s♦r♥s♥ ♥trst♥② t ♦♦rs r ♦r♠♥② ♠tr r♠s ♥ t ♦♥ ♣r♦ss♥ ♥str② ♦♦rs ♣r♦ t♦♥ t ♥♦t r③ ♦r ①♣♦rt t♠ t♦ t ♠rt r t s ♠♦r ♦r②rs tr ♥ ♦♦rs t ♣♦♥r s ♥t② sr♣ss ♦t sr♣rs♥② t ♥ r ♥ ss s trst ♠t ♣r ♦ t ♦♥tr② ❲ ♦ ♥♦t ♥tr♣rt ts sr♣ss♥ s t r ♦s ♦♦♣♦st ♠rts s ♥ t ♥str r♥③t♦♥ ♦r s♥ss trt② trtr s ♠♥② ♦tr ♦♥trs ①♣♦rt t♦♥ t♦ ♣♥ r♣rs♥ts ss t♥ ♦ ♣♥s ♠♣♦rts ♥ ts ♣r♦t r t s♠s tt t♣♦♥r ♦♠♣rt ♥t ♥ ①♣♦r♥ rtr t♥ t ①♣♦rt♥ ts ♣rtr ♣r♦t

r♥ ♣♦♥rs t ♠♦r ♦♦rs

♣♦t♥t ♦♦r ♥ ♣t ts ♣r♦rs ♦t ♣r♦t ♣r♦tt② ♥ t r ♦ t

♣♦♥r ♥trst♥② ♦t r♥♥ r♦♠ sss ♥ ♦♥ t ♦sr ♣r♦ts ♣rt

♣♦st ♦rrt♦♥ t♥ t sr ♦ ♣♦♥r ♥ ♥tr② ♥t♦ t ♣r♦t s s ①t② ♦r

Prt♦♥ ♦r ♥ r s♣♣♦rt ♥ ♦r♥ t♦ P♥ ♥ t ♣♦♥r

qts ♥ t rst ss♦♥ t♥ ♦♥② ♥ ♦ t ♣r♦ts tr s ♦♦r ♥ ♦♥trst ♥

t ♣♦♥r srs t rst ss♦♥ tr s ♠♦r t♥ ♥ ♦ ♥ ♦♦rs ♣ ♦

χ2test s rsts r r♦st ♥ ♦♥tr♦ ♦r ♦♦rt ts s s♦♥ ♥

♥ ♣r♦ts r t ♣♦♥r srs ♦r ♠♦r t♥ ♦♥ ♦r t♦ ss♦♥s t s ♣r♥t ♣♦♥ts

♠♦r ② t♦ ♥ ♦♦rs ♥tr♥ t ♣r♦t ♣t♦♥s ♥ s t ♦r

s♣♣♦rt ♦r Prt♦♥ tt ♣♦♥r sr s ♣♦st② rt t♦ ♦♦r ♥tr② t♦♥

ss ♣r ♥♦r♠t♦♥ ♥ ♣♦ tsts t♦ r ♦♥r♥s ♦t ♥ tr♥t ♥tr♣rttt♦♥

♦ ts rst ♥ ♦♦rs ♠② ♥♦t r♥ r♦♠ ♣♦♥rs t s♠♣② r♥t ♥tr②

trs♦

❬ ♦t r❪

❬ ♦t r❪

♥♥ tt sr ♦ ♣♦♥rs s ♣♦st② rt t♦ ♥tr② s ♥tr tr ♥♦r ♦♦s ♥

♦r s♠♣ tr r ♣r♦ts t ①tr♠ rst ♠♦r ♥t t P♦s♣t ①♣♦rtr

sss ♥ st♦♥ ♥ ts ss t sr ♦ ♣♦♥rs ♦ r② s♦r ♥tr②

♦ ♦tr r♠s s♥ t ♣♦♥r ts ♦r t ♦♠st ♠rt ♥ ①♣♦rts ♥ ①♥t ♥

♣rtr ♠♦s t ♥rs♥ rtr♥s t♦ s t r♠ s♠♣ ♠♦♥♦♣♦st

♦♠♣tt♦♥ ♠♥ t r♠ st♣ ♦st ♦ ♣rt tr ③r♦ ♦r ♥t ♦rrt♦♥

t♥ sss ♦ t ♣♦♥r ♥ ♥tr② ♥ ts ♠♦s ♦♦r ♠② ♥t t♦ ♥tr ♥ t

s♠ ♣r♦t ♦♥② t ♣♦♥r ①ts

♦ ①♣♦r ② s♦♠ ♣r♦ts ♦♦rs ♥ ♦trs ♦ ♥♦t r♥ t♦♥ tsts ♥

♥ s♣t♦♥s ♥ ♦sr tt sr♥ t st ss♦♥s ♦s ♥♦t ♠ sttst

r♥ ♦r ♥tr② t st ♥♦t r♦ss t ♦r ♦r r rt♦♥ ♦ t ♣♦♥rs

s♠s t♦ ♥ tr♦♥♦s t ♦♥ t ♥tr② ♦ ♦♦rs ♥ ♣rtr ♦♥ t♦s ♦♦s

tt P sss s ♦♥s♠♣t♦♥ ♦♦s ♥ sss ♥ ♦♥st♥ ♣♦♥r

♦r ①♠♣ r② ♥ ❱rr s r♦st♥ss s ♠♣♦rt♥t s tr ♦ s♦♠t♥ ♣rtr ♦t ♥ ♥tr② ②r ♦r

①♠♣ ♣r♦ts tt r strt t♦ ①♣♦rt tr ♠♥② ss t♠ t♦ ♦♦rs ♠r② ♣rtr ②r ♥ s②st♠t② ♠♦r ♦r ss ♣r♦ts ♥ ♦r♥ ♦r ①♠♣ s ♦ ①♥ rt♥s s ♥ t s t t ♥♦r♥ r♥t♥ ♥

r ♥ t♦ rstrt ♦r s♠♣ t♦ ♣r♦ts strt ♥t t♦ ♥♦ t♠ t♦ t trt ♣♦♥r st ②rs ♦ ♥♦t ♥ tr t s ♦♦rs

s♠s t♦ ♥ ♥tr② ② r ♥ s♥♥t ♣r♥t ♣♦♥ts stt= 26 ♥

♥♦ts s ② s ♦sr tt ts ♦♥s♠♣t♦♥ ♦♦s t♥ t♦ ♠♦r ♦♠st

r♠s ♦♣rt♥ ♥ ts r ♥♠r ♦ ♣♦t♥t ♥tr♥t ♥t♦ ①♣♦rt♥ s ♥

♥t♦♥ tt ♠♥② ♦♦rs ♥ ♣♦t♥t② ♥t r♦♠ ♥♥ ♦♦ ①♣♦rt ♣r♦t ♦s

t♦ tt ♥str② ♦r ♥tr♠ts ♥♦♥♦♥s♠♣t♦♥ ♦♦s t r rt♦♥ ♦ ♣♦♥r

s ♥t ♣♦♥t st♠t ♦r t t ♦♥ rt♦♥ t♦ t s ♥♦t sttst② s♥♥t

♥ t ♦♥t①t ♦ ♦r ♠♦ t♥ ♦ ♦♥s♠r ♦♦s s ♣r♦①② ♦r ♣♦t♥t ♥tr♥ts

♥t♦ ①♣♦rt♥ r♥t ♣r♦①② s s ♥ ♥① ♦ t s ♦ s♦♠ ♥strs s ②

♥tràs ♦rrs♣♦♥s t♦ t r tr♥♦r ♦ ♥ sts♠♥t ♥ t ❯ s t

sst♦♥ ♥ s♣t♦♥ rr s ♠♣s rs ♥ ♣r♥t ♣♦♥ts ♥

t ♣r♦t② ♦ ♥ ♦♦rs ❲ tt ts ♣r♦①s r ♠♣rt t s♠ ♦♥sst♥t

t t tt ♥strs s♣♣♦rt♥ rr ♥♠r ♦ r♠s ♥ s♣♣♦rt ♣♦st♣♦♥r ♥tr②

♥t♦ ①♣♦rt♥ ♥ s♦rt ♦♥ ♦r rt s♠♣ ♦ ♥ str♦♥ s♣♣♦rt ♦r ♣rt♦♥ tt

sr ♦ t ♣♦♥r ♥s ♥tr② ♦r r♦♥③ tt ♣♦♥rts ♠♦s ♦

♠♣r ②t ♥ s♦♠ st♦rs s ♥ ♠♦r t♥ ♦ t ss ♦ ♦♥st♥ ♣♦♥rs

♦ ♥♦t ♦sr ♦♦rs

P♦♥rs ①♣♦rt ss t♥ ♦♦rs

♦ tst tt tr r ①tr♥ts ♥♦t ♦♥② ♥ t♦ ♥♦ tt sr ♦ ♣♦♥rs s ss♦t

t ♥tr② ♥ t ♠② ♦t t ♣♦♥r ♥ t ♦♦r ♥ st ♦sr♥ ♣ s♥

t ♥tr♥t♦♥ ♣r ♦ ♦♠♠♦t② ♥ t ♥s♣♣rs ♥ ts ss ♦♥

r♠ ♠② rt str t♥ t ♦tr t tr s ♥♦ tr r♥♥ ❯♥r ts r♠st♥s

t st♥r ♠♦ ♥ r♠s r ♦♥② ♥ ♣r♦tt② ♦ ♣rt t rst ①♣♦st

①♣♦rtr ♦ ♦♥ r t rst r♠ ♥ t♦ ♣② s♥ ♦st ♦ ①♣♦rt♥ ♥ ts

sst♦♥ ♥ ①t② t ♦♣♣♦st tt ♣♦♥rs t♥ t♦ s♠r s ♦♥sst♥t t

♣rt♦♥ ♦ ♦r ♠♦

P♦♥rs r s♠r t ♥tr②

♥② ♣♣rs ♥♦t tt r♠s t♥ t♦ ♥tr s♠ ♥ t♥ r♦ ♥ ♦♠ ♥ ❲s

♥ ❲ts♦♥ ♦r♥♦③ ♦r♦s r♥s ♥ Pr♦ r♦s r

♥♦t ♦♥② ♥ ts ♣♦st s♦♣ t♥ r♠ ♦♥t♦♥ ♦♥ sr t t ♥ t♦♥

rst tt ♦ ♥♦t ♦♠t s ♣r♦s ♣♣rs ♦ t sq♥ ♦ ♥tr② ♥t♦

s s ♦t♥ ② ♥ t ♦♥ts ♦ t ♥trt♦♥ ❬rt♦♥ ♣♦♥r≥ 5∗♦♥s♠♣t♦♥ ♦♦❪♥ tt ♦ ❬rt♦♥ ♣♦♥r≥ 5❪ ♥ s♣t♦♥ ❲ ♦t♥ s♠r rst ♥ s♣t♦♥

♥♥ tt t ①♣♦rt s♣ st t st ss♦♥s s ♥ P♥ r♥ ♥ Pr♦ ♠♦ t ts rtrsts

①♣♦rt♥ ♣r♦t s♦s tt tr t♥ ♥t♦ ♦♥t ♣r♦t ① ts ♣♦♥rs

♥tr t ♣♣r♦①♠t② ss q♥tt② ♣ ♥ r tt② ♦s

♣ t♥ ♦♦rs ♥ ♦♥trst ♥♥♦t st♥s tt ♣♦♥rs ♥tr t r♥t

♣rs r♥t ② t♦ s♦ t s♠ ♣♥♦♠♥♦♥ s r ♣♦♥rs r ss ②

t♦ t rst ①♣♦rt ♥ t ♣r♦t t ♥tr② s rst s qtt② r♦st t♦

t ♥s♦♥ ♦ r♥t t♠ ♦♥tr♦s ♣t♦♥s t♦ ❲♥ rstrt t s♠♣ ♦♥②

t♦ t♦s ♣r♦ts tt ♦t ♦♦r t ♠♦st tr ②rs tr t ♣♦♥r s♣t♦♥ t

♦♥t ♦r ♣♦♥rs s ♠♦r ♥t t♥ ♥ ♦tr s♣t♦♥s s♦♥ tt r② ♦♦rs

r ♠♦st ♠♦r ② t♦ t rst r♠ ♥ ♦♠♣rs♦♥ t♦ ♣♦♥rs

❬ ♦t r❪

❬ ♦t r❪

♥ s♦rt ♦♥t♦♥ ♦♥ ♥tr② ♦♦rs t♥ t♦ strt ①♣♦rt♥ t ♣r♦t ♥ rr ♦♠s

t♦ t s ♥♦t t ♦♥② ♣♦sst② ts ♣ttr♥ s ♦♥sst♥t t r♥♥ ② t ♦♦r

r♦♠ t ♣♦♥r ♦t ♦r ①♠♣ s♣♠♥t s③ ♠♥ ♦r ♣r rs t ♥tr② t ♥

s♦ tt ♦♦rs t♥ t♦ rr ①♣♦rtrs ♥ ♥r s t ♥ ♥ r ♥

t Prt♦♥ ♦ ♣rt ♥ r ♦sr tt t strt♦♥ ♦ ①♣♦rts ♥ ♦tr

♣r♦ts s st t♦ t rt ♥ ♦♠♣rs♦♥ t♦ ♣♦♥rs t tt s sttst② s♥♥t t

♦♥♥ ♦r♥ t♦ t ♦♠♦♦r♦♠r♥♦ tst t♦ ♦ ♥♦t ♦sr ♦♠st

ss ts tst s rssr♥ s ② t♦ s♦ tt ♣♦♥rs t♥ t♦ s♠r t♥ ♦♦rs

♥♦♥ ♣r♠tr r♥ ♥st② ♦ r P♥ s♦ s♦s tt ♣♦♥r ♥tr♥ts r

♦♥♦♠ tt② ♦s t♥ ♦♦rs ts ♦r t ♦r ss♠♣t♦♥ ♥ t ♠♦

❬r ♦t r❪

P♦♥rs r s♦ s♠r ♦♥ r tr ♥tr②

♥ ♦ r tt t ♥t ♦r ♦♦rs s ♦♥② ♦t t s③ t ♥tr② t ♥♦t ♥

ssq♥t ♣r♦s ♥ ♠♦s r r♠s strt s♠r ♦♥② ♥ t ①♣r♠♥tt♦♥ ♣s

sts ♦ ♥♦t ♥ qtt② ♥tr♦ t♠ tr♥ s♣t♦♥ ♦r t ♥tr② ②r ②r ♦ ♥tr②① ts s♣t♦♥ ♦r t♠ ♦ ♥tr② tr♥ ♥ ♠♠② ♦r r♠s tt sr ♥t s♣t♦♥

ts r t♦ r tt tr ♠t r♥♥ r♦♠ t ♣♦♥r t ♦♦r strts tr t ♥tr② ♦t ♣♦♥r t st t t②♣ ♦ r♥♥ tt r sr♥ s♠s t♦ ♠♦r rt t♦ ♥tr♥t♦♥③♥②♦r ♣r♦ts rtr t♥ ♣r♦t♦♥ ts ♦r ts rs♦♥ ♦r s♣t♦♥s rstrt t ♥tr② ♦ ♦♦rs t♦ rt♥ ♥♠r ②rs tr t ♥tr② ♦ t ♣♦♥r s♣t♦♥ ♥ t ♦♥ tt ♦s t rst t♥♣♦♥r ♥ ♦♦r♥ ♥ tt s♣t♦♥ t t ♥ ♦sr

rsts r ♥ ♥♦♠♥ ❯ ♦rs ❯s♥ r ♦ rr♥② ♥ Ps♦s ♦rrt ② ♥t♦♥ st♠♥s t t

♦ r ts ♥s ①♣♦rts ♥ t ②r ♦ ♥tr② t t♦t ♦♥t♥ t ♦♠ ♥ t ♥ ♣r♦tt② st ♥tr ♦t s♦ tt ts s ♦♠♣r♥ r♠s ♥ t s♠ st ♦ ♥ ♣r♦ts ♣♦♥r t ♦♦rs♥ tr ♦♦rs

s ♥ ❲ts♦♥ ♦r s♦ ♥ tt ♥ r r② ♦♦r ①♣♦rts

♠♦r t♥ t ♣♦♥r ♥ ♦♠♣r t♠ ♥ ssq♥t ②rs ♥ t② ♦t ①♣♦rt strt②

♣♦st q♥tts

s♦s rrss♦♥s ♦ ♣♦st ♥tr② q♥tts tr ♦rrt♥ ② ♣r♦t②r ① ts

♠♥s r ♦♠♣r♥ ♣♦♥rs ♥ ♦♦rs t♥ ♣r♦t ♥ t♥ t s♠ ②r

rss♦♥ rstrt t♦ ♦srt♦♥s ♣♦st ♥tr② s♦s ♥t ♣♦♥t st♠ts ♦r t

♣♦♥r ♠♠② t♦ ♥♥♦t sttst② rt t ②♣♦tss tt ♣♦♥rs ♥ ♦♦rs

s t s♠ ♠♦♥ts ♥ ♦ ♥♦t ♦♥t♦♥ ♦♥ t ①♣r♥ t r♠ s ♥ ①♣♦rt♥ t

♣r♦t ♦r ♥♦ tt t ts s♦♠ t♠ t♦ st♦♠r s s♦ ♥♦r♣♦rt♥

①♣r♥ s ♥ ♠♣♦rt♥t t♦r s r ② r♦s ♥ ♥ s♣t♦♥

rstrt t♦ ♠♦r ♠tr ♣s ♦ ♣r♦t ♣♥trt♦♥ ♥ r♠s t st tr ss♦♥s

①♣♦rt♥ ♣r♦t r ♦r rst r② ♠rs ♣♦♥rs r s♠r t♥ ♦♦rs ② ♥

♦rr ♦ ♠♥t 0.1 ≈ exp −2.4) tt♥ t ①♠♣ ♦ rrrt♦rs ♦sr ♥ st♦♥

❬ ♦t r❪

❬ ♦t r❪

♣t♦♥s ♥ t r♦r s♠♣ t ♦rrt ♦r ①♣r♥ ♥ t ♣r♦t ♥♥

qtt② s♠r rsts ♥ ♥♦ tt ♣♦♥rs ② ♥t♦♥ ♠♦r ①♣r♥ t♥

♦♦r ♥ ♥ ②r t s s t♦ ♦♠♣r t ♦♥t ♦ t ♣♦♥r ♠♠② t tt

♦ ♥ t♦♥ ②r ♦ ①♣r♥ t♦ t s♥s ♦ t ♠♥ts ♦② s♣♥ t♦ ①♣♦rt

t q♥t ♦ rst ②r ♦♦r ♣♦♥r rqrs tr ♦r ♦r ②rs ♦ ①♣r♥ ①♣♦rt♥

t ♣r♦t ② ♥ t ♦♥t ♦r ♣♦♥r ② t ♦♥t ♦r ②r ♦♥ ts

♦r t ♣♦♥t st♠t ❲ r♥ s♣t♦♥s t ♠♦r ① ♣ttr♥ ♦r ①♣r♥ ♥

rrss♦♥ ♥♥ qrt tr♠s ♥ ♠♠s t st ♥ tt t ♣♦♥r ss ss

q♥tt② ♥ ♦♥trst t♦ t r♥s ♥ q♥tts ♥♥♦t st♥s ♥② ♣♦♥r t

♦♥ ♣rs s s♦♥ ♥ t r♥t s♣t♦♥s ♦ s rst t t♦t tr ♦♠

r♥s t♥ ♣♦♥rs ♥ ♦♦rs s♣② t s♠ ♣ttr♥ s t q♥tt②

t s♥t s ①♣♥ ② q♥tts rtr t♥ ♣rs

❬ ♦t r❪

s s t t ♣r♦♠ r♣♦rt ② r♠♥ ♥ ♦♥t♦♠r② ♦ s♦ tt ② ♥ ③r♦sr ♥ s♦♠ ②rs ♦♥ ♥ s② t rst r t rst ♠♦r s ♥ ♥t rtr t♥ s♥t

s♠♣ t tr ♦♠ ♣r t♠s q♥tt② s st② rr t♥ t s♠♣ t s♣rt t ♦♥♣rs ♥ q♥tts r rst ♦ rst♠♦r s♥t ♦♥ t♦t tr ♦♠ r ♥♦t s♥st t♦ ♦ tt♦ s♠♣s s

❬r ♦t r❪

♦ ♠ t rst ♠♦r s♥t rr r r♣s t s♠t ss ♠♣ ②

rrss♦♥ ♦♠♣t♥ ♦♥♥ ♥trs s♥ t t ♠t♦ ♦r ♣r♦t tt s

s♦r s♥ ②rs ♦ s ♦s s t♦ s♦ ♦ ①♣t ss r② t♥ ♣r♦t s

t t♠♥ t ♥tr② ♥s ♦r③♦♥t ♥ts t ♥♦r♠③ ②r ♦ t ♣r♦t ♥

t② ♥tr s t♦s t t = 0 r t ♣♦♥rs ♦ t ♣r♦t t♦s t t = 12

6 r ♦♦rs ♥tr♥ ♦♥ t♦ ♥ ♣ t♦ s① ②rs tr t ♣♦♥r ❲ ♦sr tt ①♣r♥

♥ st♦♥ r ♠♣♦rt♥t s t rr ②♦ ♥tr t ♠♦r ②♦ s ♦r tt s ♥♦t

♦r t ♣♦♥rs ♦r r ①♣♦rt ss t♥ r② ♦♦rs s sss

♦r t ♣♦♥t st♠t ♦ ss ♦r ♣♦♥rs s t ♦♥♥ ♦♥sst♥t② ♦r t♥

♦r r② ♦♦rs r♥ s ♦♥② q♥t t♦ t t r♥s ♦r r♠ ♥tr♥ ♥ tr

♦r ♦rs ②rs tr s ♣rssts ♥ ♦♥tr♦♥ ♦r ① rtrsts ♥ ♣r♦t②r

♦♠♥t♦♥ tst s♦ ♥tr♥t♦♥ ♠♥ st ♣r ♦ tr ♥♣ts ①♥ rt

♥ ♥② s s♣t♦♥ ♥ s♦s tt tr tr ②rs ♥ ♣r♦t ♥ r ♦♦r

s ♥♦♥t♦♥② rr s♣t ♥ ss ①♣r♥ ♥ ♥ ②r

♥② t s ♠♣♦rt♥t t♦ r♠r tt ts t ♦ t ♣♦♥r ♥ s♠r srs ♥ ♥

♦s ♦♥ s♣ st♥t♦♥ t ♥♦ s♠♣ s③ ♣t♦♥ ♦ r♣ts

s♣t♦♥ t rstrt♥ ♦r tt♥t♦♥ t♦ ①♣♦rtrs t♦ r♥t♥ r rsts ♦♦ r②

s♠r ♥ sttst② s♥♥t s♣t ♥ ss t♥ qrtr ♦ t s♠♣ s③

♥ st♦ ♦r rsts ♦♥t♦♥ ♦♥ ♠t♣ ♥tr♥ts ♥t tt t ♣♦♥r ♠t ♥♦t

t r♠ tt ♥ts t ♠♦st r♦♠ t s♦r② ♦ ♥ ♣r♦t ♥trst♥② ts s ♥♦t ♦♥②

♦♥trt t♦ t ♦♥ ♦ ①♣t r♦♠ ①tr♣♦t♥ rr♥t tr ♠♦s ♦ t st②

stt t③ t t s s♦ ♦♥trr② t♦ t ss♠♣t♦♥ ♦ r♦ss♠♥ ♥ ♦ss♥sr

tt ♣♦♥rs r♦② ♦♥st♥t rtr♥s t♦ s t♥♦♦② ♥ r ♣♦♥rs ♥

♦r s♠♣ ♦ ♥♦t ①♣♦rt t rst ♠♦♥ts ♥ ♣r♦t ♦♦rs ♦

tr♥t ①♣♥t♦♥s tt ♦ ♥♦t ♠♣② ①tr♥ts

r ♥♥s ♥ t♦ t② sst st♦r② ♦♥sst♥t t ①tr♥ts ♦ st r♥

② tr♥t ①♣♥t♦♥s ♦ ♥②③ tr ♣♦t♥t tr♥ts ♦ ♥♦t ♦♥sr

①tr♥ ♦♥♦♠s ♥ tt ♦ ♥rt s♠r ♣ttr♥s ♥ t t ♦r s ♣r♦

♥ tt t♥s t♦ ♥r♠♥ t♠ s ♣♦t♥t ♥ t♦ ♦r ♥tr♣rtt♦♥

rs♥ s♦♣ ♥ ♦♥sq♥ ♦ ♦t ①♣r♥ ♠t♦♥ s s t t ♥tr② ♦ s♠rr♠s s ♥ t ♥♦ st♥r t③ st♦♥ t

♦t ♣♦♥rs ♥ ♦♦rs rt t♦ ♣② s♥

♣♦st t♠ tr♥ ♥ t ♥tr♥t♦♥ ♣r ♦ ♣r♦t ♦r ♥ ♥② ♦tr ♣②

s♥ ♦ ①♣♦rt ♣r♦tt② ♥ ♠ t s♠r r♠s ♥tr rst ♥t♦ ♣r♦t ♦♥ ss♠s

tt ts s♠r ♣♦♥rs ♥ ①♦♥♦s② ♦r s♥ ♦st ♦ ①♣♦rt♦♥ ss t r

①♣♦rtrs s st♦r② ♦ ♦♥sst♥t t ♦r st②③ ts s♦ r t ♦ ♥♦t ♥②

r♥♥ ♦♥ r♦♠ ♣♦♥rs t♦ ♦♦rs ♥ ts s♥r♦ t r r♠s ♦ rt tr ♦♥②

s t② rr ①♦♥♦s s♥ ♦st s♦ t② ♥ rr trs♦ ♣r♦tt② t♦

♥tr ♥t♦ ①♣♦rt♥ ts ♣r♦t s ♥ ♥② st♥r ②♥♠ ♥st♠♥t ♣r♦♠ r s♦

♦r tt ♦tr st②③ ts r♥r ts s♥r♦ ss ② rst s♦s tt ♣rs

r t ♥tr② ♥t♦ ①♣♦rt♥ r ♥♦t sttst② r♥t t♥ ♣♦♥rs ♥ ♦♦rs s

♥♥♦t st♥s t ♣r tr♥ ♥ ♣rs ②♣♦ts③ ② t tr♥t ①♣♥t♦♥

s♦♥ ♦♥trr♠♥t ♦♠s r♦♠ st♦♥ ①rs t r② ♠ttrs ♦r ♥tr② s ♥♦t

t sr ♦ t ♣♦♥r t s♠♣② ♣ s♥ t♥ ♥tr② ♥t♦ ♦r ♥ ♣r♦ts ♦

♦rrt t t sr ♦ ♥② r♠ rtr t♥ ♥ s♣r♦♣♦rt♦♥② ♦rrt t♦ t

sr ♦ t ♣♦♥r ❲♥ ♠♣♠♥t ts tst ♥ s♣t♦♥ t sr ♦

t ♣♦♥r ♣s ♥ sttst② s♥♥t t rt♦♥ ♦ r♥♦♠② ♦s♥ r♠ ♥ t

♣r♦t s ♥♦t s ssts tt t sr ♦ t ♣♦♥r s ♠♦r ♥♦r♠t t♦ ①♣♥ ♥tr②

♥ ♦♥trr♠♥t s tt ♠♥② ♦ ♦r r♠s s♠s t♦ r② ♣r♦♥ t ♣r♦t ♦r

t ♦♠st ♠rt s ♠s ♥② tt t ①♦♥♦s s♥ ♦sts r② s♣r♦♣♦rt♦♥②

r♦ss r♠s t t ♥ ♦ t ② t rt ♦sts r s♠♣② ♦t s♥♥ ♥ ①♣♦rt ♠♥r

t♦ ♦r♥ ♠rt t♦ ♦s ♥ ①♣♦rt ♥ ♦r r♥s ♥ s♥ ♦st ♦ ♥♦t ♦♠

r♦♠ ①♦♥♦s r♥s t♥ s♠ ♥ r r♠s t r♦♠ t t tt r r♠s

ts r♥ ♦t t ♣r♦t t♦ ♦s ♦♥ ♥ ♦♥s♦♥ ts tr r♠♥ts r

♦♥r♥s ♦r ♦r rsts ♥ r♥ ② ♣ s♥ t♦ ♥②♦♥ rtr t♥ ②

s♦♠ ①tr♥ ♦♥♦♠s

Pr♦t ②

♥♦tr ♣♦ss tr♥t r♠♥t s tt t r s♥ r ♥♦t s♦r② ①tr♥ts

t s♠♣② r♥t ♠♦rtt② ♦ r♠♣r♦t ♥s r r♥t ♦r t ② ♦ t

♣r♦t r② ♣r♦rs r ttr t t♥ t s♦r♥ r q♥tts ♥ st♥r③

♠rts ♦r ♦r s♠♣ ♦ss ♦♥ ♣r♦ts tt r ♥ ♦r t ♦♥tr② s ♦♠

♣t② r♥t r♦♠ strt♥ ♣r♦ts tt r ♥ t♦ t ♦r s ♥ t sts ♦ r

♥ ♦rt r ♥ ♣♣r ♦r♥ t♦ ❱r♥♦♥ ss ♦♣

♦♥trs strt ①♣♦rt♥ ♣r♦t ♦♥ ts r ♠♦r ♥ ♥ t ♣r♦t ② s♦

tr s ♠ ss ♥rt♥t② ♦t ♦ t♦ ♣r♦ t ♦♦ ♥tt② r♦③♥ t♦♥ ♦r

♣♦s♣t ♠ r r② ♥ ♣r♦ts ♥ t ♦r ♥ t st ②rs ②♦♥ ts ♥

♦t r♠♥t ♥ ♣♦♥t ♦t tt ♥ ♥♦ sttst r♥ t♥ t ♣rs

② ♣♦♥rs ♥ ♦♦rs ♥ t② ♥tr ♥t♦ ①♣♦rt♥ ♣r♦ts r ♦♥

q② r♥ ♦r t♠ r♠ ts sttst② t ♣r ♦ ①tr♠② ♥②

P♦♥r s ♥ ♣s ② r♦♠ t ♦♠st ♠rt

♥ ♥ r tt ♣♦♥rs r s♠r ♥♦t s t② t♦ ♥♥♦t t s t②

r ♣s ② rr ♦♠st ♣②rs ♥t♦ ♦ ♣r♦t ①♣♦rt ♠rt s ♦ rt♦♥③ ♦r

ts ♦t s♠r ♣♦♥rs t ♥ ② tt ♦s ♥♦t rqr ♥ ①tr♥t② ❲ ♦ ♥♦t t

♦♥ ♦♠st ♣rs ♥ q♥tts r r② ♥② t♦ ①st t t ♦ srt♦♥

r ♦r♥ t ①♣♦rts ♥ t♠ ♥ ♠t♣r♦ts r♠s tr s ②s t rts♠

tt ♦♥ ♦s ♥♦t ♦sr ♣r♦ts ♦ ♣r♦t ♥s s♣t ts ♣r♦♠ ♦r s♦♠ r♠♥ts

tt ♥ r ♦r ♦♥r♥s ♦t t s♥r♦ ♦ ♣s ♣♦♥rs rst ♦♥trr♠♥t

s t ♣♦st ♦r♥ t♥ t sr ♦ ♣♦♥r ♥ t ♥tr② ♦ ♦♦rs sss ♥

st♦♥ r r♠ ♦♦ss t♦ ② ts ♥tr♥t♦♥③t♦♥ ♥ t ♣r♦t s t

♦♠st r♥♥ s r♥r t s r t♦ ♥rst♥ ② t ♦ t♦ s②st♠t②

♥tr tr ♦♥ t s ♥ ss ② ♦♥ t♥s tt t ♣r r ② ①♣♦rtrs ♥♦t

sttst② ♥ t♥ t t♠ t ♣♦♥r ♥ t ♦♦r t♦ ♥tr

s♦♥ ♦♥trr♠♥t s tt ♥ r♠s r ♦s♥ ♦♠st ♠rt sr t② ♠② s♣ t♦

♠rts t ♦r qt② rqr♠♥ts ♦ tst ts ♣♦sst② r♣t t ♣r♦r ♥

t ①♥ ①♣♦rts t♦ ♥♦r♥ ♦♥trs t ♦r P t♥ ♦

♥ Pr ❲ ♥♦t ♥ qtt ♥s ♥ ♦r rsts rs ♦r ♣r♦rs ♦t ts

♣♦t♥t ♦♥r♥

t♦♥ ♥ ♥tt♦♥

♥ ♥ ♥② r tt rr ①♣♦rtrs ♠② ①♦♥♦s② ♥ ♥tr♥s② s♦r t♦ rt

rtr t♥ ♥♦♥♦s② s♦r t♦ s♥ ♦st st♦♥ s ① ♦ ②♣♦tss ♥

♥rt ♦r st②③ ts t♦t ♥② r♥♥ ♥ t ts r①♣♦rtrssts♦ ♦♥

trr♠♥t s s♠♣② stt♠♥t ♦ ♥ss rt♦♥ ♣r♦♠ ♥ ♥ ♥♦♥♦s

s♦ t r♥♥ t♥ r♠s ♥♥♦t s♣rt② ♥t ♥ t r♦ss st♦♥ r♦♠

♣r r♠ rtrsts tt r ♦♥r t t s♦ t ❲ ♣rt② s♣ r♦♠ ts

rt♦♥ ♣r♦♠ ② s♥ t♠srs rt♦♥ t♥ ♣r♦t rtr t♥ st r♦ssst♦♥

♦ r ♦t rtr ♦ ②♣♦tss ♥ ♥ ♥tt♦♥ ss♠♣t♦♥ tt t t② t♦ r

tr ♣♦sst② t♦ tst t ♣s ♣♦♥rs ♦ t♦ tr ♠♦rtt② ♦ ♣♦♥r r♠s s rs ♦♥ ♦ ①♣t t② r ♦s♥ ♠rt sr ❲ r rr♥t② ♦r♥ ♦♥ ts ♣♦sst② s♥ t♦♥ r♠ ts

s♣♦♥ st t♦ s♥s ♦s ♥♦t s②st♠t② r t♥ r ♥ s♠ ①♣♦rtrs ♦ ♣r♦t

♦r ♥tt♦♥ ♥ t s♣ ♦ rt♦♥ t♦ ♦

♥ tr♥t ♣♦sst② ♥♥♦t ② t ♣rt ♥ ♦r ♣♣r s s ♦♦s ♠♠♥ tt t rst①♣♦rt ♥t s s♠♣② t rst ♦ ♥ ①♦♥♦s ♣♦♥ r r♦♠ ♣♦t♥t st♦♠r ♦rss ♥rts ♣♦♥r ♥t ② r♥♦♠ r♠ ♥ t ♦♥tr② tr ts rst ①♣♦rt ♦r r♠s r♥ ♦tts ♥ ①♣♦rt ♣♦sst② t ♥♦♥♦s② ♦♥② t rr ♥ ♠♦st ♣r♦t t♦ ♥tr t ♣♦♥rr♠♥s ①♣♦rt♥ s♠♣② s ♦ ②strss s ♥ ♥rt s②st♠t rst ♠♦r s♥t s ♥ ♥ t t ♦ st♦r② s ♥ r♥♥ s t ♥t t♦ ①♣♦r s♥ t tt ♦ ♦r♣♣r ♦r ♥ ts st♦r② t ♥♥♦t♦♥ s ①♦♥♦s ♥ ♦rtss s♦ tr s ♥♦ s♦ st ♥ ♥♦ r♦ ♦r♣♦② r s tt tr s ♥ ♦rt ♥ s♦r♥ ♥ ①♣♦rt ♣r♦t s ♥ t t♠ ♦ ♠♥②①♣♦rt ♣r♦♠♦t♦♥ ♣r♦r♠s

♦♥♥ r♠rs

❯s♥ t st♦♠s tr♥st♦♥s r♦♠ ♦r ♣♣r ♣rs♥ts ts ♦♥sst♥t

t ♣♦♥rt♦♦♦r ①tr♥ts ♥ ♥ ①♣♦rt ♣r♦ts rst ♥ tt ♣r♦ts t

sr♥ ♣♦♥rs ♠♦r ♦♦rs s ♦♥sst♥t t tr r♥♥ r♦♠ t ssss

♦r ♦♥ t rs ♦ ♣♦♥rs ♦♥ ♥ tt ♣♦♥rs ♦t ♥tr ♥ r♠♥ s♠r

t♥ ♦♦rs sst♥ tt t rst ①♣♦rr ♠② ♥♦t t s♠ r♠ tt ♥ts t ♠♦st

r♦♠ t s♦r②

❲ rt♦♥③ ts ts ♥ s♠♣ ♠♦ ♥ rr r♠s r st ♦ ♣♦t♥t

♥ ♣r♦ts t♦ ♣rs ♥ t② ♥♥♦t ♦♣ ♦ t♠ s ♦ rs♥ rtr♥s t♦

s♦♣ tr ♣r♦♠ s t♦ ♦t ♥ ♥s sr rs♦r t♦ t st ♣♦ss s

①tr ♣♦t♥t s♦♣ ss s♠r ♥ ♠♦r ♦s r♠s ♥rts ♥ ♥♥t ♦r rr

r♠s t♦ strt② ② ♥tr② ♥ ♦♥trst s♠r ①♣♦rtrs t r ♦♣t♦♥s t♥ t♦ ♥tr

s♦♦♥r ♥ ♥♦r♠t♦♥ t♦ ♦♦rs s ♠♥s♠ t♦ s♠♣ s ♥♦ ♥ r ♥♦

t♦ ①♣♥ t ♣♦t♥t ♦r ①tr♥ ♦♥♦♠s ♦♦rs ♠② rr ♦♥ t ♣♦♥rs ①♣r♠♥t

r ♦ ♥ ts ♣♣r s t♦ ♣t ①st♥ ♣r♦rs ♦t t ①st♥ ♦ ♣♦♥r♦♦r ①tr

♥ts ♥ ♥ ①♣♦rts r♦♠ ♠r♥ ♠rts t rr ♠ r♦♠ ♠♦r ♥♦st ♣♦st♦♥

♦r rsr ♦rs st ♦ ts tt ♦ ♥♦t ② ♣r♦ t sr♦s② sst ♥str② r♥♥

♥ ♦♥trst t rr s ♥ ♣r♦s② ①♣♦s t♦ t st ssss ♦ r♠♥ts ♥

♥s ♦rs ♥ ♥② ♦r ♠♦♥ ♥ ♦r ♣♣r ♦♠s t♦♥r② ♥♦t r ♥♦♥

st s♠♣ ♦ ♣r♦ts s♦s ♦r t rst t♠ t r② rs ♦ ♥ ①♣♦rts ♥

♠♦r t♥ ♦ ♥ ♣r♦ts ♦ ♥♦t sr ②♦♥ ss♦♥s s rs ♦t t♦ ♦♥sr

② ♥② sr♦s ①♣♦rt ♣r♦♠♦t♦♥ ♣r♦r♠ s s ② ♥② strt② ♦ ♥tr♥t♦♥ ♥tr♣r♥r

s♣ ♥ ♠♦♥ ts sst♥ ①♣♦rts ♥♦t ♣r♦ts sst ①tr♥ts ♥ t st

t ♣r♦ts ♦♥② ♣♦♥rs t ♣♦♥r s r② sss ♥ ♥♦♦② s ♦♣②♥

♠② t ♠rt ♦rs ♥♦ rr t♦ ♥tr♥③ ♥② r♥♥ tt t ♣♦♥r s rt♥

r♦♠ ♣♦② ♣rs♣t st♦rs r t ♣♦♥r s ♥tr rst♠♦r♥t t

P♦s♣t s ♠② ♥♦t t ♠♦st ② s ♦ t♥ ♣r♦t ①tr♥ts

❲ ♦♥ t ♦♣♣♦rt♥ts ♦r rtr rsr rst s t♦ r♥ ♠♦r ♦t ♦ ♥

♣r♦ts strt ♥ ♣r♦ rtr t♥ ①♣♦rt ❲ ♦r ♦r♥ ♦ r♠s ♦t ♣r♦t♦♥

♥ ①♣♦rt♥ ♣♣♥ t t s♠ t♠ ♦tr r♠s r ♠ ♠♦r ♣♥♥t ♦♥ ♦♠st ♠♥

♦r tr r② r♦t s♦♥ ①t♥s♦♥ s t♦ ♥rst♥ ttr t tr♠♥s t ①♣♦rt♦♥

♦ ♣r♦ts ♦r r♥t st♥s r♦♠ t r♠s rr♥t ♣ts ♥② t s ♠♣♦rt♥t t♦

tr ♦r rsts ♥ r♣t ♦r rrs ♥ ♦tr ♦♥trs s r rr♥t②

♦♥ t ♦♦♠♥ ①♣♦rtrs

r♥s

r r ♦ r♠s ♦r t Pr♦t ② ♦tr♥ ♦♥♦♠ ♦r

♥

r ♥ ♦rt ♦t♦♥ ♦ rts ♥ ♥tr② ①t ♥ r ♦

r♠s ♦ ♦♥♦♠s ♥ ttsts

♦♥ P ♥ r♦ ♥♠♥t ♦ ♥♥♦t♦♥ rtr② ♦r♥ ♦

♦♥♦♠s

♦s♥ ♥ r♦rt ♠r♥ ♦ ss ①♣♦rt t

ts ♥ t♥ ♠r s ♦ ♥tr ♠r♥ ♦♣♠♥t ♥ ❲♦r♥

P♣rs

♦r♥♦③ ♦r♦s r♥s ♥ Pr♦ q♥t ①♣♦rt♥

♥tr ♦r ♦♥♦♠ Pr♦r♠♥ sss♦♥ P♣r ♦

r③ ♦rs ♦ ①♣♦rt sss ♥ s♠♥ ♠♠s③ ♥tr♣rss t ♠♣t

♦ ♣ ♣r♦r♠s ♥tr♥t♦♥ s♥ss

①♣♥♥ ①♣♦rt sss r♠ rtrsts ♥ s♣♦r ts ❲♦r

♦♣♠♥t

r③ ♥ rs♣ ①♣♦rtr ♣r♦r♠♥ ♥ ♣r♦♠♦t♦♥ ♥str♠♥ts ♥

♠♣r ♥ st♦s ♦♥♦♠

r③ rq ♥ ♦♣③ Pr♦ts ♥ ①♣♦rt rts r♥♥

r♦♠ ①♣r♥ ♥ r♥♥ r♦♠ trs ♥♥ ❯♥rst②

r③ ♥ ♥ts ♥tr② ♥t♦ ①♣♦rt rts ♥ Pr♦t t② r

♥s ♥♦ ♥tr ♦r♥ ♣♣r

r③ ♥ ör t♥t♦♥s ♥ P♥t ①t ♥ r♦♠

♥tr♥t♦♥ ♦ ♦♥♦♠s ♥ ♥♥

r③ ♥ ♦♣③ ①♣♦rt♥ ♥ ♣r♦r♠♥ ♥ r♦♠ ♥

♣♥ts ♥♥ ♦r♥ ♦ ♦♥♦♠s ♣♣

♠s♥ ss ♥①t ♥t ♦t ♦r ♥ t ♥str③t♦♥ ①♦r ❯♥

rst② Prss ❯

♥rs♥ ♥ t ♥tr♥t♦♥③t♦♥ Pr♦ss ♦ r♠s rt ♥②ss

♦r♥ ♦ ♥tr♥t♦♥ s♥ss ts

♥tràs P r♠s ♦♥trts ♥ r trtr rtr② ♦r♥ ♦ ♦

♥♦♠s ♣♣

r♦s rt P♥trt♦♥ ♦sts ♥ t ♦♥s♠rs r♥ ♥ ♥tr♥

t♦♥ r ♦r♥ ♣♣r ♦

r♦♥ ♥ ③r ♥tr♦t♦♥ ♦ ♥ ♣r♦ts ♠r♥ ♦♥♦♠

r♥r ♥ ♥s♥ ①♣t♦♥ ①♣♦rtr ♣r♦r♠♥ s t

♦r ♦t ♦r♥ ♦ ♥tr♥t♦♥ ♦♥♦♠s

r♥r ♥ ♥ P ♦tt t♣r♦t r♠s ♥ ♣r♦t

st♥ ♦r♥ ♣♣r

ss ♥ Prs ♥s ♦ts ♥ t rt♦♥ ♦ tr ♥♥ ♦r♥

♦ ♦♥♦♠s

Pr♦t r♥tt♦♥ ♥ rt♦♥ ♦ ❯ ♠♣♦rt tr ♦r♥ ♦ ♥tr♥

t♦♥ ♦♥♦♠s

t t ♥r③ t♦r② ♦ st♦rt♦♥s ♥ r r ♥

♦ P②♠♥ts ♥ r♦t ♣♣

rs♥♥ r♥st♥ ♥ ♥rs♦♥ ♠♣tr♥ ♦♠♣tt♦♥ ♥

s♦♥♦♠s ♦ s♦♣ strt♦♥s r♦♠ t st♦rs ♦ r♦s♦t ♥ ②rs

P ♥ tr tss

♥r ❱ ♥♦♦② ♣tt♦♥ ♥ ①♣♦rts ♦ s♦♠ ♦♣♥ ♦♥trs

♦t t rt ❲♦r ♥

rs ♥ ②♦t s r♥♥ ② ①♣♦rt♥ ♠♣♦rt♥t r♦

②♥♠s r♦♠ ♦♦♠ ①♦ ♥ ♦r♦♦ rtr② ♦r♥ ♦ ♦♥♦♠s ♣♣

♦♠♥ ♥ ♦♥ r♦ss♦♥tr② t♥♦♦② ♦♣t♦♥ ♠♥ t t♦rs

t ts ♦r♥ ♦ ♦♥tr② ♦♥♦♠s

♦♥② ♥ ❯r② r♥♥ ♦t ♥♦♦② P♥♣♣ ♥ ♥

♠r♥ ♦♥♦♠

♥ rr ♦ ♥tr② ♥ ♣r♦r♠♥ ♦ ♠t♥t♦♥ ♦r♣♦rt♦♥s ♥

♥ ♠r♥ ♠rt ♦♥t♥♥t rs♦r ♣rs♣t ♦r♥ ♦ ♥tr♥t♦♥ rt♥

♦ ♦♥tr♦ r② ♥ r③é ♠r♥ ♦

♥ ss ①♣♦rt tts ♥ r③ ♦r s ts r♦♠ t ♥tr♥ ♥ t

rtr t♦r ❲♦r♥ P♣rs

♦ r♠r ♥ ♦♥s♦♥ ♥ r♠rs t♦ ❯s rt③r ♦r②

♥ ①♣r♠♥t ♥ r♦♠ ♥② ❲♦r♥ P♣r

t♦♥ s r③♥ r ♥ ②♦t r ♥

r♥♥ ♦ ♦ ①♣♦rt ②♥♠s

t♦♥ s r ♥ ②♦t ①♣♦rt ②♥♠s ♥ ♦♦♠

r♥st♦♥s ♥ r♥③t♦♥ ♦ r♠s ♥ ♦ ♦♥♦♠②

t♦♥ s r ♥ ②♦t ①♣♦rt ②♥♠s ♥ ♦♦♠

r♠ ♥ ❲♦r♥ P♣r

t♦♥ ♦rt♠ ♥ r♠r③ sst♥ tr r♠s ♥strs ♥

①♣♦rt st♥t♦♥s ♠r♥ ♦♥♦♠

♥ P r② t♣r♦t r♠s ♥ ① ♠♥tr♥ ♥ t

♦ ♦♥♦♠② ♦ ♦♥♦♠ ts

♦str ♥ ♦s♥③ r♦♦♥♦♠s ♦ ♥♦♦② ♦♣t♦♥

♦♥♦♠ r♦t ♥tr ❨ ❯♥rst② ♥tr sss♦♥ P♣r

r♥ ♥ Pr♦ ①♣♦rt ♥tr♣r♥rs ♥ r♦♠ Pr ss

s♦♥ ♣♣r ❲♦r ♥ sr ❲♦r♥ P♣r

rt ♥ r② Pr♠♣t ♣t♥t♥ ♥ t ♣rsst♥ ♦

♠♦♥♦♣♦② ♠r♥ ♦♥♦♠

rs ❩ ②r ♦r♥ ♥ ①♣♦rt♦♥ ♥ t ♦♥♦♠s ♦ t♥♦♦ ♥

♦♥♦♠tr ♦r♥ ♦ t ♦♥♦♠tr ♦t② ♣♣

r♦ss♠♥ ♥ ♦ss♥sr ①tr♥ ♦♥♦♠s ♥ ♥tr♥t♦♥

r ① rtr② ♦r♥ ♦ ♦♥♦♠s

rrs♦♥ ♥ ♦r③r r ♦r♥ ♥st♠♥t ♥ ♥str

P♦② ♦r ♦♣♥ ♦♥trs ♥ ♥♦♦ ♦ ♦♣♠♥t ♦♥♦♠s ② ♦r

♥ ♦s♥③ ♦ ♣ ♣♣ sr

s♠♥♥ ♥ ♦r ♦♥♦♠ ♦♣♠♥t s s♦r② ♦r♥ ♦

♦♣♠♥t ♦♥♦♠s

♣♠♥ ♥ P r♠♥ rt trtr ♥ ♦r♥ r ♥rs♥

tr♥s ♠♣rt ♦♠♣tt♦♥ ♥ t ♥tr♥t♦♥ ♦♥♦♠② Prss ♠r

♥rs♦♥ ❯♥r♥st♠♥t ♥ ♥♦♠♣t♥ s s♣♦♥ss t♦ ♥♥♦t♦♥

♥ r♦♠ t P♦t♦t♦r♣ ♥♠♥t q♣♠♥t ♥str② ♦r♥ ♦

♦♥♦♠s ♣♣

♦ ♥r rs ♥ s♠♥♥ ♣r♦t

s♣ ♦♥t♦♥s t ♦♣♠♥t ♦ ♥t♦♥s ♥

♦ ②s♥ r♥♥ ♥ ♥ ♥♥t ♥str② ♠♦ ♦r♥ ♦ ♥tr♥t♦♥ ♦

♥♦♠s

♦♣♥②♥ ♥tr② ①t ♥ r♠ ②♥♠s ♥ ♦♥ ♥ qr♠ ♦♥♦

♠tr ♣♣

♦♦♥ ♥ ♦r t♣r♦t ①♣♦rtrs Pr♦t r♥♥ ❯♥r

t♥t② ♥ ①♣♦rt s♦rs ♦♥♦♠ ♦r♥ ♦rt♦♠♥

rt♥r ♥ ♥rs♦♥ ♦r♣ ♦③t♦♥ ♦ ♥♦

s♣♦rs s ♥ ② ♣t♥t tt♦♥s rtr② ♦r♥ ♦ ♦♥♦♠s

♦ ♥ ♦ ♠♣♦rt♥t s t ♦♦s r♥ ♥ ♥tr♥t♦♥

r r sr ♥ ♦ ♥♥♣♦s sr ♣rt♠♥t t ♣♦rt

♥♥ ♥ ❨ ❨ s♥ss r♦♣s ♥ ♠r♥ ♠rts Pr♦♥s ♦r ♣r

sts ♦r♥ ♦ ♦♥♦♠ trtr

♣♣r ♥tr② ①t r♦t ♥ ♥♥♦t♦♥ ♦r t Pr♦t ②

♠r♥ ♦♥♦♠

♥r ♥ r♠♥ s♦r② ♥ ♦♣♠♥t ♥ ♠♣r ①♣♦rt♦♥

♦ ♥ ♣r♦ts ❲♦r ♥ ♦r♥ ♣♣r

r♠♥ ♥ ♦♥t♦♠r② rst♠♦r ♥ts trt ♥

♠♥t ♦r♥

rst♠♦r s ♥ts tr♦s♣t ♥ ♥ t t rs♦rs

trt ♥♠♥t ♦r♥

♦♣③ ♥ ♥ r♥ ♦r♥ ♦ ♦r ♦r♥ r♦♥

♥ r♦♠ ♥ ①♣♦rt♦r② st② ♥ t ♦st ♥ s♦tr ♥str② ♦r♥ ♦ ♥tr♥t♦♥

s♥ss ts

s ♥ ♠r ♦♥♦♠tr

♦ ♦♣♠♥t ❯♥♦r ♣tt♦♥ qst♦♥ ♥ t rt

♦r ♥ ❲♥s ♥ t ❯ ❲♦r♥ P♣r

♥ss♦♥ P ❲st♦♥ ♥ ♦s rr♦♥tr② ts ♦r r

r♠s ♥ ♦♣♥ rts ♥ ①♠♥t♦♥ ♦ t♥t♦♥ rts♥ ♥s ♦r♥

♦ ♥tr♥t♦♥ rt♥

♥s ♥tt♦♥ ♦ ♥♦♥♦s s♦ ts rt♦♥ ♣r♦♠

♦ ♦♥♦♠ ts

rs ♥ P r♦s st s♦♥ ♦ s♠rt ♦♠♣♥s ②♣ss r

♥♥♦t♦♥ t♦ ♥tr ♥ ♦♠♥t ♥ ♠rts ♦ss②ss ♥ P

rs r r③t♦♥ ♥ P♦ts ♥ ♠♣t ♦♥ ♥str ♥②

P tss rr ❯♥rst②

②r t③ ♥ tt♥♦ rt s③ ♦♠♣tt♦♥ ♥ t Pr♦t

① ♦ ①♣♦rtrs ♠♦ rr ❯♥rst②

t③ ♠♣t ♦ tr ♦♥ ♥tr♥str② r♦t♦♥s ♥ rt ♥str②

♣r♦tt② ♦♥♦♠tr ♣♣

♦♥ Ø ♥ P rs ♦r♥ ♦ ♦r r ♦ ①♠♥♥ t ①♣♦rt

♦r ♦ s♠ ♥ ♠♠s③ ♥tr♣rss ♦r♥ ♦ ♥tr♥t♦♥ rt♥

♦st ♥ ♣♣r ♥str ♦♣♠♥t tr♦ t ♥♦

♥ ♥ r♦♠ t ♥s r♠♥t ♥str② ♠♦

♦ ❱ ♥ ❨♣ ♦③t♦♥ ♥ ♥♦♥♦s r♠ s♦♣

❲♦r♥ P♣r

P♥ r r③t♦♥ ①t ♥ ♣r♦tt② ♠♣r♦♠♥ts ♥ r♦♠

♥ ♣♥ts ♦ ♦♥♦♠ ts

P♥r♦s ♦r② ♦ t r♦t ♦ t r♠ ①♦r ❯♥rst② Prss ❯

Pr ♥ P ♦tt ♦♥♦r♥ ❯ r♠♦♥③ s②st♠ t♦rs ♦r

t♠ ❲♦r♥ P♣r

P♦rtr ♦♠♣tt ♥t ♦ t♦♥s rr s♥ss

strs ♥ t ♦♥♦♠s ♦ ♦♠♣tt♦♥ rr s♥ss

Prs ♥ ♠t③ ♥ ♦♠♣♥s ♥t♥ r ♥t ♥♥♦t

rst t② ♦ t P ♦tr ♥str② ♦ ♦♥♦♠s ♥ ttsts

♥ ❲ts♦♥ trt♥ s♠ ♥ ♥ ♥♠r ♥r♦♥♠♥t ♥tr♥

t♦♥ ♦r♥ ♦ ♥str r♥③t♦♥

♦♠r P ♥♦♥♦s t♥♦♦ ♥ ♦r♥ ♦ P♦t ♦♥♦♠②

♦s♥t ♥ ❲ tr♥ ♠r♦♠♣rs ♦ ♦♠rt♦♥ ♦♥♦♠s

♥ ♦♠♣♥♦♥ t♦ ❯r♥ ♦♥♦♠s ② r♥♦tt ♥ ♥ ♣ ♣♣

Ps♥

♥ ❲s ①♣♦rtr ②♥♠s ♠♠♦

♠♣tr t♦r② ♦ ♦♥♦♠ ♦♣♠♥t ♥ ♥qr② ♥t♦ ♣r♦ts ♣t

rt ♥trst ♥ t s♥ss ② r♥st♦♥ Psrs t♦♥

r② ♥ ❱rr ❯♥rt♥t② ♥ ♥tr② ♥t♦ ①♣♦rt

♠rts ♦♠♥t♦s r♦ ♥♦ s♣♥

r ♦ ♦♥♦♠rts st ♥♥♦t♦♥ ❯♥♣s ❲♦r♥ P♣r ❯♥rst②

♦ ♦

❱r♥♦♥ ♥tr♥t♦♥ ♥st♠♥t ♥ ♥tr♥t♦♥ r ♥ t Pr♦t ②

rtr② ♦r♥ ♦ ♦♥♦♠s ♣♣

rs

r r♠ s♦♥ t ①t♥s ♦r♠ ♦ t ♠ ♦r r♠ ♣♥♥ ♦♥ t②♣

F

β

0 0.05 0.15 0.200.5

0.6

0.8

0.9

1.0

F, β ∈ Ω3

F, β ∈ Ω2

small firm pioneersand large firm waits

F, β ∈ Ω1

both firms pioneer

r qr ♣♥♥ ♦♥ t s ♦ ♣t♥β ♥ ①♦♥♦s s♥ ♦st F ♦♥ Ω1

♥ s ♥q qr♠ ♥ ♦♠♥♥t strts ♥ ♦t r♠s ♥tr ♠♠t② s♣♦♥rs ♦♥ Ω2 ♥ r② s t ♥q qr♠ ♦ ♥trst ♥ ts ♣♣r ♥ ♥♣♦♥r s t ♦♠♥♥t strt② ♦r t s♠ r♠ ♥ t♥ s t ♦♠♥♥t strt② ♦r t rr♠ ♦♥ Ω3 ♥ ♣♦t♥t② ♠t♣ qr♠ t t ♦t♦♠ ♣♥♥ ♦♥ ♠♦rs♦♣stt qr♠ ♦♥♣ts ❱s ♣♦tt t c = 0.1

r r♣s s♦♥ t ①♣♦rt ss ♥ log10 ❯ ♦rs ♦ r♠s ①♣♦rt♥ ♥♣r♦t r♠ s ♦♥♥t ② ♥ ♦ t s♠ ♦♦r ♥ t♦♥ ♦♥ r♠ ♦s ♥♦t sttr ♣♦♥t ♥ ♥ ②r t ♠♥s tt t ♥♦t ①♣♦rt

rt♦♥ ♦ t ①♣♦rt s♣sst♥ ①♣r♠♥t

Nfirms=

1

ss t ♦♥② ♣♦♥r t♦ ♦ ♣r♦ts r t♦ ♦ ss

Nfirms>

1

P♦♥r t ♦♦r ts ♣ ≤ ♦ ss

♣♦♥r ♥ sts s t ♦rrs♣♦♥s t♦ t ♥ tt strts ♦sr t♦ t t ♦ r♣

r s t ♠♥② ♣♦t♥t ♥tr♥ts ♥t♦ ①♣♦rt♥

♦t ①♣♦rts ♥ ♦tr ♣r♦ts t ♥tr② ♦ ❯ ♠r ♦ st♥t♦♥s sr ② t r♠ ♦

r♠ s♦♣ ♠r ♦ tt② ♦s

r ♠♣r strt♦♥ r♥ ♥st② ♦ t ♦♠ ♦ ♦tr ①♣♦rts t ♥♠r♦ st♥t♦♥s sr t s♦♣ ♦ r♠s ♠sr ♥ tr♠s ♦ ♥♠rs ♦ ❯ tts♦rt♠ s ♦r ♥ ♦r ss t strt♦♥ ♦r ♦♦rs s ♠♦r ♠ss t♦ trt ♦ t strt♦♥ t s♥♥ ♦r♥ t♦ t ♦♠♦♦r♦♠r♥♦ tst ♦ strt♦♥qt② ♣ ♦r ①♣♦rt ♦♠ ♣ ♦r st♥t♦♥s ♣ ♦r s♦♣

r ♠t♦♥ ♦ t rrss♦♥ ♦♥ts s♦♥ ♥♦ rst ♠♦r ♥t ♦♥♥♥trs t

s

①♦♥♦♠② ♦ r♥t ♥ts ♦ r♠ ①♣♦rt♥ ♣r♦t

s ♥② r♠ ①♣♦rt ts ♣r♦t r♦♠ t ♦♥tr② ♦r

❨

♦ ♣r♦t ♥ ♣r♦t

❨ Pioneernew product

N = 0 N = 136

s t t rst r♠ ①♣♦rt♥ t

♣r♦t r♦♠ t ♦♥tr②

Followerold product Followernew product

N = 10, 294 N = 308

①♣♦rt ♣r♦ts ♦r ss ♦r♥ t♦ ♥♠r ♦ ♣♦♥rs ♥ ♦♦rs♦♦rts ♦ ♣r♦ts strt ② s♦♠ r♠ ♥ ♥

♥② ♣r♦t ♦♦rts ♦r ♥② ♣r♦t ♦♦rts ♦r

♦ P♦♥rs ♦ P♦♥rs

♦t ♦t

♦♦rs

♦♦rs

t♦ t♦

♦t

N = 270∗

♦t N = 175∗∗

t♦ t♦ ♥ ♥ ♣r♦t s ♠♥♠♠ ♦ ①♣♦rts ♥ ♥ ②r ② r♠ ♦♦rt ♦ ♣r♦ts

♦r♥ ♥ s ① r♦♠ t t♦♥ ♥ P♥ s tr r ♥♦ ♦♦rs ② ♥t♦♥ t rs

t t♦t s♠♣ r♦♠ ♣r♦ts t♦ s r♦st♥ss P♥ ♥s ♦♥② t ♦♦rts ♦ ♣r♦ts

strt② ♦r t♦ tt t ♣ttr♥ sr ♦r s r♦st r♦ss ♦♦rts

sr♣t sttsts ♦ ♣r♦tr♠ ♣rs

②♣ ♦ ♣r♦tr♠♣r ♥ t s♠♣

log10①♣♦rts

♦♣r♦t

t pf=

0

N♦

tt②♦s

r

t①♣②r

♠♠②

log10①♣♦rts

♦tr

♣r♦tst p

f=

0

♣tr♥t♥

♠♠②

rt♦♥

≥1ss♦♥

♠♠②

♦♦r ♥ ♥ ♣r♦ts ♠♥

♠♥

♠♥

P♦♥r t ♦♦r ♠♥

♠♥

♠♥

P♦♥r ♦ ♦♦rs ♠♥

♠♥

♠♥

♦t ♣r♦ts ♠♥

♠♥

♠♥

♦♦r ♦ ♦ ♣r♦ts ♠♥

♠♥

♠♥

①♣♦rt s r ♥ ❯ ①♣rss♦♥ tpf = 0 rrs t♦ t ②r ♦ ♥tr② ♦ r♠ ♥t♦ ts ♥ ♣r♦t tt t r♠

♥♦t ①♣♦rt ♦r rt♦♥ ≥ 1 ss♦♥ ♠♠② ♥ts tt t ①♣♦rt s♣ ♦r tt r♠ ♥ tt ♣r♦t sr

♠♦r t♥ ♦♥ ss♦♥ ①♣♦rt♥ r ①♣②r s sst♦♥ ♦ t ♥ ♥tr♥ ♥ rs ♥♠r

♦ t♦rs ♥ t r♠ ♣rt♣ts s t② ♥ ♣tt♦♥ ♦ t s②st♠ t ♠♦r r♥rt② s

② t ♥tr♥ ♥ r ♥

Pr♥t ♦ ♣r♦ts ss ♦r♥ t♦ t sr ♦ ♣♦♥rs ♥ ♥tr② ♦ ♦♦rs

②r rt♦♥ ♦ ♣♦♥r ♥ ②r rt♦♥ ♦ ♣♦♥r

Pr♦t s ♦♦rs Pr♦t s ♦♦rs

♦ ❨s ♦t ♦ ❨s ♦t

P♦♥r

rt♦♥ < 5

P♦♥r

rt♦♥ ≤ 1

P♦♥r

rt♦♥ ≥ 5

P♦♥r

rt♦♥ > 1

♦t ♦t

N = 75∗ N = 239

Pr(

Prs♦♥s χ2(1) > 8.72)

= 0.03 Pr(

Prs♦♥s χ2 ≥ 5.67)

= 0.018

♠♣ ♥s ♦♥② ♣r♦ts strt ②

s♦♠♦♥ ♥t ♦trs ♦r ♥t♦♥ ♦

sss ♦ tt♦♦② ③r♦ ♥ tr

♦♦rts s♦ t s♠♣ s rstrt t♦ ♣r♦ts

♥ t st ♦♥ ♦♦r st♥ ♠♦r t♥ ♦♥

ss♦♥ t s♦rt tr♠ ♦♦rs r ♥

t r♥ s ♥ rr ♥st t ♥

②♣♦tss

srt♦♥s ♦♥② ♦ ♣r♦ts strt ♥t

t♦ ♥♦ t♠ t♦ ♦♦rs

♥r ♣r♦t② rrss♦♥s ♦ ♦♦rs ♥tr② ♦♥ ♣♦♥r ♣r♦r♠♥ ♥ ♣r♦trtrsts

♣♥♥t r 1 [♥tr② ♦ ♦♦rs > 0]

rt♦♥ ♣♦♥r ≥ 1

rt♦♥ ♣♦♥r ≥ 2

rt♦♥ ♣♦♥r≥ 5

♦♥s♠♣t♦♥ ♦♦

rt♦♥ ♣♦♥r ≥ 5 ♦♥s♠♣t♦♥ ♦♦

log ♦ ♣r♦t♦♥

rt♦♥ ♣♦ ♣♦♥r ≥ 1

❨r ♥ ♣r♦strt

yearyear2

yearyear2

srt♦♥s sqr ♦st st♥r rr♦rs ♥ ♣r♥tss ♣ ♣ ♣ rt♦♥ ♦ ♣♦♥r rs ♦rrs♣♦♥ t♦ t rt♦♥ ♥ ②rs ♦ t ①♣♦rt s♣ ♦ t ♣♦♥r ♥

tt ♣r♦t rt♦♥ ②♦♥ ②rs ♣ts t ♠♦st ♦♥ ②r ♦ ♥trr♣t ①♣♦rts t♥

s♣ ♦♥s♠♣t♦♥ ♦♦ s ♠♠② ♦r Ps sst♦♥ ♦ ♦s s ♦♥s♠r s ♦♣♣♦s t♦

r♥t t♦rs ♦ ♥tr♠t ♦♦s t ♦ s ♦ ♣r♦t♦♥ s ♣r♦t rtrst

tt ♦rrs♣♦♥s t♦ t r sts♠♥t ss ♦ t ♥strs ♣r♦♥ ts ♣r♦ts ♥ t ❯

s t ♠♣ s③s ♥ s♣t♦♥s t♦ r s♠r s t s♠♣ s rstrt t♦

♣r♦ts strt ♥t s♦ t s ♣♦ss t♦ ♦sr ♣♦♥r ♦r t st ②rs ♥ ♦♦rs

rss♦♥ s r ♦srt♦♥s s ♥♦t st♦rs st♦rs ♥ ♠t t♦ t

♦s t♦ ♠r t r ♦ ♣r♦t♦♥ rt♦♥ ♣♦ ♣♦♥r s t rt♦♥ ♦

r♥♦♠② ♦s♥ r♠ ♥ t ♣r♦t ♥ t ss ♦ ♣r♦ts t s♥ r♠ t ♦♥s t t

tr ♣♦♥r t ♥ ♣r♦ts t ♦♦rs t ♦s ♥♦t ♥ssr② ♦♥ t rrss♦♥s

♦♥st♥t ♥ ②r ♦♥ts ♥♦t r♣♦rt s ♦ s♣ ♦♥str♥ts

rss♦♥s ♦ r♥t ♦r ♦ ♣♦♥rs t ♥tr②

♦♠♠♦t② ♥r st② ② ♥tr②

❱ ln(N

codes+1)

ln(P

Q♦tr

♣r♦)

ln(P

Q)

ln(P

)

ln(

)

❬rt♦♥

≥2❪

1 ∗ [pioneer]

♦♥st♥t

Pr♦t

R2

♦st st♥r rr♦rs ♥ ♣r♥tss ♣ ♣ ♣

♥r Pr♦t② rss♦♥s ♦♥ ♠♠② ♦r ♥ t rst ①♣♦rtr ♥ t ♣r♦tt ♥tr② r② ♦srt♦♥ s s♥ r♠ ♥ ♣r♦t ♠♥ ② t ♣r♦t ① ts

♥tr② t♥ ②rs tr t ♣♦♥r ♥tr②

t♥

②rs

♥tr②

t♥

②rs

1 [P♦♥r ♥ ♣r♦t]

②r ♦ ♥tr② FE

1 ∗ [sts ♥t ♥ ♦ s♠♣]

♦♥st♥t

srt♦♥s

sqr

② ♥t♦♥ ♦♥② ♣r♦ts t ♦♦rs r ♥ ♥ t ♥②ss ♦st st♥r rr♦rs ♥ ♣r♥tss

♣ ♣ ♣ t s♣t♦♥s ♦♥t♥ ♣r♦t ① ts♥ ♥ ♦♥

♣r

rss♥ q♥tts ①♣♦rt ♦♥ ♣♦♥r ♠♠s ♦♥tr♦♥ ② ♣r♦t②r s♦s

log q♥tt② ①♣♦rt ② r♠ ♥ ♣r♦t ♥ ②r st♥t♦♥s ♥②

♣♦♥r ♥♣r♦t

tpf ①♣r♥ ①♣♦rt♥ t ♣r♦t

t2pf

♠r ♦ ♣r♦ts ①♣♦rt ② r♠

r ♦ ♣r♦t ♥ ①♣♦rts ♦ r♠

♦♥st♥t

srt♦♥s sqr

♦st st♥r rr♦rs ♥ ♣r♥tss ♣ ♣ ♣

♥tts r ♠sr ♥ t ♥ts ♥ t st♦♠s tr♥st♦♥ sr♦r tpf ♦rrs♣♦♥s t♦ t ①♣r♥ ①♣♦rt♥ ♥ ♣r♦t♣t♦♥ rstrts t♦ ♣♦st ♥tr② ♥ts ♣t♦♥ ♦s t ♦rsrrs ♦ t st tr ss♦♥s ♣t♦♥ s s♣t♦♥ t ♦♥tr♦♥ ♦r ①♣r♥ ♣t♦♥ ♥s r♦s t♦♥♦♥tr♦s ♣r♦t rst♦♥ ♥ t sr ♦ t ①♣♦rt ♥t ♣r♦t s rt♦♥ ♦ ①♣♦rts t♦ ♠sr t ♠♣♦rt♥ ♦r t♣r♦t ♦r t r♠

rss♥ ♣rs ♦♥ ♣♦♥r ♠♠s ♦♥tr♦♥ ② ♣r♦t②r s♦s

♦ ♠♥ ①♣♦rt ♣r ♦ r♠ ♥ ♣r♦t ♥ ②r

strt♦♥ tpf ≥ 1 tpf ≥ 2 tpf ≥ 3

♣♦♥r ♥ ♣r♦t

♦♥st♥t

srt♦♥s sqr

♦st st♥r rr♦rs ♥ ♣r♥tss ♣ ♣ ♣ tpf ♦rrs♣♦♥s t♦ t ①♣r♥ ①♣♦rt♥ ♥ ♣r♦t ♣t♦♥ rstrts t♦ ♣♦st ♥tr② ♥ts ♣t♦♥ ♦s t ♦r srrs ♦ t stt♦ ss♦♥s ♥ s♣t♦♥ ♦r srrs ♦ tr ss♦♥s s stst ♦r s♠♣ s③ s ♠♦ t♦ t rt ♥ r♥t s♣t♦♥ t♦t♥♥ t ♣♦♥r ♠♠② s tt ♠♦st ♦ t rt♦♥ ② R2 st♥ ♣ ② t ① t tr s tt r♠ rt♦♥ ♥ ♣rs

♥r rrss♦♥ ♦ r♠s ①♣♦rt ❬♦ ❯❪ t♥ ♣r♦t ♥ ②r ① ts

♣♥♥t r r♠s ①♣♦rt ❬♦ ❯❪

♣♦♥r ♥ t ♣r♦t

♦ ①♣♦rt t ♥tr② ♥

♣r♦

①♣r♥ ♥ ♣r♦t ②rs

①♣r♥ ♥ ♣r♦t sqr

♦ ♣r♦ts ①♣♦rt ②

r♠

r ♦ ♣r♦ ♥ r♠s ♥

♦♥st♥t

Pr♦t ❨r

srt♦♥s

R2

♦st st♥r rr♦rs ♥ ♣r♥tss ♣< ♣< ♣<

♣♣♥① ♦rrs♣♦♥♥ ♦r ♦♠♠♦t② ♦s

♦ ♠sr t s♦♥ t♦ ①♣♦rt ♥ ♣r♦t ♦r t ♦♥tr② t s ♥ssr② t♦ ♦♠♦♦t

♣r♦t ♦s tr♦ t♠ r♠♦♥③ ②st♠ ♦♥ssts ♥ ♦s t♦ ♣r♦t ♦s

♦r ♦♥ r② ②rs t sst♦♥ s ♥tr♥t♦♥② ♣t s ♠♣s tt sr

♦s r ①♣♥ ♥t♦ ♥ ♦s t ♦r ♦ ♥ ♣♦rt ♠s ♣②rs ♥

♦ ♥ ①♣♥ ♥t♦ ♣♦rt sstt ♠s ♣②rs ♥ ♣♦rt ♠s

♣②rs ♥ tr ♦♥ ♥t♦ P ♣②rs tr ♦s r ♦♣s ♥t♦ s♥ ♦

♣r♦ts tt r s♦♠ ①♣♦rt ♦r r t♥ ♦t ♦ t sst♦♥ ♦♠ ♦s r st

r ♥ tr r ♦♠♥t♦♥s ♦ t ♦ ♦ tt ♦♠s ♣rt ♦ t♦ r♥t

♦s ♥♦♠♣ss ♦tr ♦s tt r s♦r ② ♥ ♦ s t s ♣♦ss tt

t ♦sr s ♥ ♦s r ♥♦t ♥ ♣r♦ts ♥ ①♣♦rt t s♠♣② ♥ ♦t♦♥

♦ ♣r♦t tt ♦ ♥ ①♣♦rt ♦r ♥r r♥t ♦

♥ t ♦ ♣r♦♠ t ♥ s ♦♠♠♦♥ st♦♥ r♦ss t♠ s s ♥

♥ ①st♥ ♦rrs♣♦♥♥s ♦r sst♦♥s t ts ♦rrs♣♦♥♥s ♥ ♦

t♥ t r♥t ss s r♦♠ ❲ ❲♦r st♦♠s r♥③t♦♥ ❯

♥ t ❲♦r ♥ ♦♥② ♦ t♦ ♦♥♥t r♥t sst♦♥s t ♦ ♥♦t ♣r♦ ♥q

♦♠♠♦♥ ♣r♦t ♦s r♦ss t♠ s t ♥ ♦r ♦r ♣♣r ♥ ♦tr ♦rs t

t② ♣r♦ s ♦ ② ♦ ♦rrs♣♦♥♥ t♥ r♥t sst♦♥s ❲t ♥

♦r s t♦ ♥rt ♦♠♠♦♥ ♦s r♦ss sst♦♥s ♦ t st ♦ ♦r ♥♦ t ♦♥②

♦r tt r♥t② ♣r♦s ts s Pr ♥ ♦tt ♥ tr t♥ ♣♣r t② ♣r♦

♦♠♦♦t♦♥ ♣r♦r r♦ss t♠ ♥ ♦rr t♦ ♦♥sst♥t ♦s ♦r ❯ t ①♣♦rt

♥ ♠♣♦rt ♦s t♦ ♥ ♦r♥ ♦♥ ts ♦♠♦♦t♦♥ ♦r t② ♣s tr

♦r♥ ♣♣r s♠r ♣r♦r♠ tt srs t s♠ ♣r♥♣s ♦ tr ♣r♦t ♦

♦♠♦♦t♦♥ rt♥ ♦♠♠♦♥ ♥q ♦s ♦r ♣r♦t ♦s tt ①♣♥ ♦r ♦♥trt tr♦

t♠ ❲ ♣rr ♦r ♦rt♠ ♥ ♣r♦r♠ t♦ trs s ♦ t stt② ♦ t t ♥♣t

s t sst♦♥s ♥ t ♦t♣t tt ♥ s♥ ♦♠♦♦t

sst♦♥

sst♦♥s ♦♥sr

r t ♦♥ssts ♦ st♦♠s ts ♦r t ♣r♦ ♦♠♣♠♥t s♥

t s♥ t t s ss ♥r t r♠♦♥③ ②st♠

♦t♦♥ ♦r t ♣r♦ ♦♥srs r♥t sst♦♥s ♥

s r ♠♦r rsst♦♥s ♦ ♦s tr t ♦s ♥ t ② ①♣♥ ♦

s ♠♣s ♥ ♣rt tt ♥ t♦ ♦♠♦♦t ♦s tt ♥ r♦♠ ♦♥ sst♦♥ t♦

t ♦tr r r t♦ ♠♦r ♥s r♦♠ t♦ ♥ r♦♠ t♦

❲ ♥ ♣r♦r tt ♦♥srs ♦♠♣t sst♦♥s ♥ tr ♦rrs♣♦♥♥s t♦ ♥ t♦ ♥ tt ♦ ♣r♦ s t ♥q ♥ sst♦♥ tt ♦ ♦rrs♣♦♥ t♦ ♥ rt② t♦ s♥ t s♠ ♣r♥♣ t♦ ♦♥♦r sst♦♥s tr♦ t♠Pr ♥ ♦tt s♣ ♣r♦r♠ s ♥♦t ② st ♦r t ♥ s t ♥♣t t t② s s t ❯ t ♦ ♥s s ♥r♠♥t ♣r♦♥ st ♦ ♦s ♦s tt ♥ ♥ ♠♥② r♥tts ♥ t② ♥ r t ♦♥ssts ♦ ♦rrs♣♦♥♥s t♥ sst♦♥s r ttr♥ t r♥t ♦ ♥ t♠ t ♦ ♦s ♦ ♥ ♦ sst♦♥ ♥ t ♦rrs♣♦♥♥♦s ♦r t ♥ sst♦♥ s ♥ ♦s tt ♥♦t ♥ tr♦ t♠ s♦ t ♦t♣t tt ♥ s ♦rrs♣♦♥♥ ♦ ♦r♥ sst♦♥ t ♥ ♦♠♦♦t sst♦♥ ♦ ♦ s t♦ ♦r rt② t t t t ♦♠♦♦t ♦s ♥ ♦r ♣♣r ♥ t ♣r♦r ♦Pr ♥ ♦tt ♥♦t ♣r♦ rt②

♦♥② ①♣t♦♥ s s ♣rt② t s♠ s t sst♦♥ tt ①st s♥

♣r♦♠ ♥ ♥ ①♠♣

❲t ♥ t♦ ♦ s t♦ ♦ ♦♥t♥ ♥ ♦s t② r ♦s tt ♣♣r t♦

rsst♦♥ ❲ s♦ ♥ t♦ t ♥t♦ ♦♥t ss ♦ ♣r♦ts tt r ♦♣s ♥t♦

s♥ ♦ s♥ ♦ ♥♦t ♥♦ t ♥ ♦ ①sts t♦ ♦ ♣r♦t s ♠♣s

tt ♥r tr s ♥ ①♣♥s♦♥ ♦ ♦s ♥ t♦ ♦♥sr t ♦r♥ ♦ s t ♦rrt

♦ ♥ ♥ tr s ♦♣s ♦ ♦s ♥ t♦ ♦♥sr t ♥ ♦ s t ♦rrt ♥

♥q ♦ ♥ tr ♦ ♦♠♥t♦♥s ♦ ♦t ♥ ♠t♣ ♦♣ss ♥t♦ ♦♥ ♣r♦t

t ♠♦st ♦♥srt ② ♦ ♦♥ rsst♦♥ s ♥ trt ♦♣s♥ ♦ ♦s ♥t♦

♠♥♠♠ ♦♠♠♦♥ ♦ tt ss♠s ♦s tt ♦ rss ♥ ♦♥ ♦r ♥♦tr ♦

t♦r②

♦r ①♠♣ s♦s t t ♣r♦r ♦ ♦ t♦ t ♦♦♥ ♦s

①♠♣ ♦ ♣r♦t ♦♠♦♦t♦♥ ♣r♦r

♥ ♦

♥ ♦

♥ ♦

♥ t rst st ♦ ♦s t♦ ♦s tt ♦♣s ♥t♦ ♦♥ ♥ ♦ t♥ ♠st t

♠r ♦ s♥ ♥♥♦t ♥♦ t ♠ r♦♠ t rst ♦r s♦♥ ♦ s♦♥ st s♦s

s♣t ♥ ♥♥♦t ♥♦ t ♦ ♥ s ♦r t♦ ♦♥sr t

♠♦st rt ♦♥ tr s s tt ♠♦r ♦♠♣t s s♣t s ♥♦t

t s ♥♦r♣♦rt ♥t♦ ♥ ♠♥♠♠ ♦♠♠♦♥ ♦ ♥ ts s s

♣r♦ss ♦ ♥rt♥ ♠♥♠♠ ♦♠♠♦♥ ♦ ♠st trt ♥ ♠st ♦♥

s♦ r♦ss ♠♦r t♥ ♦♥ sst♦♥ ♠st ♦♥ s♦ ♦♥sr♥ ♦s

♣r♦r ♦♦♥ ♥♦♦s ♣r♥♣s t♦ Pr ♥ ♦tt t ♦r t②

♣s tr ♦r t ♦ tt rst ts t♦ sst♦♥s ♦r ①♠♣

♥ ♥ ♦♣ss ♥t♦ s♥ ♦ ♥② ♦r♥ ♦s tt ①♣♥ ♦r ♦♥trt

♦r ①♠♣ ts ss♠ tt r♠ strts ①♣♦rt♥ ♦ ♥ ♥r ♦ ♥ ♥♦ tt ①♣♦rt ♦rrs♣♦♥s t♦ t② ♥ ♣r♦t ♦r ♥ ♦ ♦ ♥ t s ♠♣♦ss ♥ t♦ ♦♣st ♦ t♦ ♦ t ♥ ♦ r♦♥ sst♦♥ ♦ ♥ ♦s s ♥ ♣r♦ts

❲ r t♥ t♦ ① ♦ ♥② ♣r♦ t ♥tr ♣♦rt♦♥s ♦ ts ♦ ❲ ♦♥♣ t♦ ①♣♥ t ♦ r s♦ t rr ttr ♥rst♥♥ ♦ t s s♦ ♦♥t ♣♣♥①

t♥ ♦t sst♦♥s ♥ t ①♠♣ ♦ t t ♦ts tr ♥q ♦s t♦ ♦

t tr ①♠♣s ♣t ♥ t t s♠ s t♥ ♦♥ ♦r t ♥①t t♦ sst♦♥s

♥ ❲ ts ♥ ♣ t t♦ ♥ ②r ♣r♦t sst♦♥s ♦♥ tt ♥s

ss ♥ ♥♦tr ♦r ss ❲ ♦♥ ♦t ♥ ♦t♦♥s s♥ t ♦s s

♦♥♥t♦rs r ♦♠♠♦♥ ♥ ♦t ♥ sst♦♥s ♦♥ s t♦ ♦rrs♣♦♥♥

t♥ t t♦ ♥ r♣t t ♣r♦ss ♦♥ ♠♦r t♠ s ♦s s t♦ ♥ ♥q

♦ tr♦♦t t ♣r♦

ts ♥ ♠tt♦♥s ♠♥ ♠tt♦♥ ♦ ts ♣r♦r s tt t rqrs ♦♣s♥

♠♥② r♥t ♦s ♥t♦ s♥ ♦♥s s♥♥t② r♥ t ♥♠r ♦ ♦s ♦r

♥②ss s♥ t ♦♣ss ♥② ♦s tt r ①♣♥ ♦r ♦♥trt r♦ss sst♦♥s

♦♥sq♥ s tt ♦s sr ♥ ♣♦t♥t r♥t srt ♥♦r♠t♦♥

♦♥♦♥ t t ♦rrs♣♦♥♥ s r ♦♥ t t♦rs st ♥r

t ♥♠ tr♥s♦❴❳❳t r ❳❳ s t ②r ♦ t ♦r♥

❲ s t ♦s s ♠♥♠♠ ♦♠♠♦♥ ♦ ♥ ss ♦ s♠♣ ①♣♥s♦♥ ♦r ♦♥trt♦♥ ♦ ♦s ♦rss ♦ ♦♠♣① ♦ r♦♣♥ t ♦s♥ ♦ s t ♦ t t st ①♣♦rt ♥ t r♦♣ ♦r t♦ s♠♣ ♣r♦

♣♣♥① trs s t♦ ♥ ♥ ①♣♦rt ♣r♦ts

♠♣r② ♥rst♥♥ t s ♥ ①♣♦rt s ♥♦t tr ♥ t ♦♥ ♥ ♥

♥ ♣r♦t t♦♦ ♦♦s② t♥ t ♦ r② t t♦ ♥ ♥② r♥♥ s♥ ♦

♥ ♦ sr ♦ tr ♥ ♣r♦ts ♥ ♦r s♠♣ s ①♣t r♥♥ t♦ t ♣

s♣r♦♣♦rt♦♥② ♥ tr② ♥ ♣r♦ts s ♦♥ ♦ ♥r r♦♠ ♦str ♥ ♦s♥③

♥ t ♦tr ♥ r t♦♦ t♦ t t ♥t♦♥ ♦ ♥ ♣r♦t t♥ t ♥♠r ♦

ss ♦ r♠t② sr♥ ♥ ts tr ♦ t♥ stt♦♥ ♦ ♥ ♣r♦ts ♦r t

♦♥tr② ♥ t q♥tt② ♦ ♣r♦ts tr t♦ ♥ t♦rs stt♦♥ s ♠ s ♣♦ss

t st ♣♥ ♥♦ ♦srt♦♥s t♦ ♠ t rsts sttst② s♥♥t ♦♦♥

t ts t trs tr t ♦♥ r② tr ♥ ♣r♦ts ♥ ♥ t s♠♣ s③

♦ ♦ t trs ♠♣t t ♥ r♠s ♥ t ♥♠r ♦ ♣r♦ts♦♠♣t♥ ♦s

trs t♦ ♥ ♣r♦t s ♥

♦r t ♦♥tr②

sr

♦ tr ♥

♣r♦ts ♥ s♠♣

s♠♣ ♦

♣r♦ts s r s

♣♦ss

♦♠♠♥ts

♦r ∑

f xpf ≤ X ♦r ♦♥②

rt t ♥♦ r♠ t

X =

US$1, 000

+ − rs ♦ r①♣♦rts

♥② ♦♥sr♥ ①♣♦rts ♣♦st ②

♣r♦r r♠s trrs ♦ ♥♦t ♦♥t

④r t ♦s r♠s ♦ t①

tt② ♦ ⑥

+ − rrs r ♠♣♦rt♥t t ♦t

♦ s♦♣ ♦ ♣♣r

①♣♦rts r ♥♦t ♦♥t s ①♣♦rt

xpfy > θmpfy r θ

θ = 2 + θ♥♦t t♦♦ r −

r♦♣ ♣r♦ts t sr♣t♦♥

♦♥t♥♥ ♦trs ♥

+

t♦ xpfy >≥ X ♥ ♣rs♠♣

t♦

X =

US$1, 000

X r t♥ ♠♦st ♥♦

♣r♦ts r t

t♦ xpfy ≥ X ♥ s♠♣ t♦

X =?

♠♣s ♠♣ tr ♦r ♠♥r② + s s♦♠ ♦ ♦♠♣♦♥♥t ♥

ts ♥t♦♥

①♣♦rt tr♥st♦♥s ♣r ②r t♦

♦♥sr

xpfy ≥ 2 +

♦ ♦ rtr♥

s♣② ♠♥s

−

♥ ♦s ♣r♦ts t

s♥ tr♥st♦♥

s t♦rs ss r

Pr♦♦s

s ♣♣♥① ♦rs ♦t t ♣r♦♦s ♦r ①st♥ ♥ ♥q♥ss ♦ ♥ qr♠ ♦ t t②♣ r ♥trst

t rt♦♥s ♦ t st♣

❱ ♦ ♥ ♣♦♥r

❱ ♦ ♥tr♥ ♠♠t② ♦r ♥② r♠ s ♣r♦♣♦rt♦♥ t♦ q ♠② V ipioneer = −Fq +

βEmax 0, [x− c] q ♥ t s ♦ ❯♥♦r♠ strt♦♥ ♦♠s

1

qV ipioneer = −F + β

1

2(1− c)2

❱ ♦ ♥ ♦♦r

♦ t♥ s ♦♥ t♦ r♥t ♦r r♥t r♠s

1

qV small iwait = βEmax 0,−F + β [x− c]

♥ ♠♥♣t ♥♥ ♠♥ ♦r s♠♣t② θ ≡ Fβ+ c t

1

qV small iwait = β2 [Emax θ, x − θ]

①♣t ♦ ♥ ♦♠♣♦s ♥ t

1

qV small iwait = β2 [θ × Pr (x ≤ θ) + E [x|x > θ]× Pr (x > θ) − θ]

❯s♥ t Uniform(0, 1) strt♦♥ ♦r x ♥ r♦s r ♠♥♣t♦♥s t

1

qV small iwait = β2

[

1

2(1 + θ)2

]

♦t tt qt♦♥ s s s♠r t♦ qt♦♥ t t t♦ ♠♥ r♥s rst t t♦♦r ♥tr② tr ♥rt♥t② s r θ ≡ F

β+ c > c s rr t♥ t t♦ ♦r ♦♥t♥t♦♥

♥ t ♣r♦t ♥ t ♥tr② ♦st s r② s♥ tr t ♥♦r♠t♦♥ s r t s♦♥t♦ ♥tr s♠♣② ss t st♥r P❱ rtr t♦ ♥tr s♥ tr s ♥♦ ♦♣t♦♥ ♦ t♥tr xi s r s♦♥ r♥ s tt t ♣r♦t s ♣s ♦♥ ♣r♦ ♥t♦ t trs♦ tr s t♦♥ s♦♥t♥

s s st② ♠♦r ♦♠♣① s t strt♦♥ ♦ ♦rr sttst x ≡ max

xA, xB

s ♥♦t♥♦r♠ ❲ ♥ strt t t s♠ q t ♥♦ ♣t♥ t♦ t t tt r ♦t t♣r♦t② strt♦♥ ♦ x

1

qV

largewait = β2 [Emax θ, x − θ]

♦ ♠♦ ♦rr ♥ t ①♣tt♦♥ ♦ t ♠①♠♠ ♥ ♦♠♣t ♥②t② ss♠ tt t iid. strt♦♥ ♦ xi s st♥r ♥♦r♠ t♦ t ♠♦ s ♦r ♣♦t♥t s♦♣ s = 2 t t rsts ♦r ♥② ♣♦st ♥tr ♣♦t♥t s♦♣ s♦ t t ①♣tt♦♥ ♥ s t t tt t kt ♦rr sttst ♦ N iid rsr♦♠ Uniform(0, 1) s strt ♦r♥ t♦ t Betapdf (k, [N + 1− k]) ♣r♦t② ♥st②♥t♦♥ ♥ ♦r s r ♥trst ♥ t ♠①♠♠ N ≡ s t st ♦rr sttsts x (s) ∼ Betapdf (s, 1) ♥ ♣rtr t ①♣t ♦ ♥trst s

E (max θ; x (s)) = Betacdf (θ, s, 1) θ + (1− Betacdf (θ, s, 1))E [x (s) |x (s) > θ]

r Betacdf (y, s, 1)s t ♠t ♥st② ♥t♦♥ ♦ r y strt Betapdf (N, 1)♥ ♣rt ts ♠t ♥st② ♦ t t strt♦♥ s ♥ ② t r③ ♥♦♠♣tt ♥t♦♥ ♥ ts s s

Betacdf (θ, s, 1) = Iθ(s, 1) = θs

❲t ts s♦ ♦r t ♣r♦t② ts ♥ qt♦♥ Pr (x (s) ≤ θ) = θs s♦ Pr (x (s) > θ) =1 − θs ♦♥② ♥s♦ ♣♦rt♦♥ ♥ qt♦♥ s t ①♣tt♦♥ E [x (s) |x (s) > θ] st ①♣t ♦ t t strt♦♥ ♦ xmax (s) ♥ t ttr♥t t θ ♦♦♥ t♥t♦♥ ts ①♣tt♦♥ ♦♠s

E [x (s) |x (s) > θ] =

∫ 1

θx (s)Betapdf (x

max (s) , s, 1)dxmax (s)∫ 1

θBetapdf (xmax (s) , s, 1)dxmax (s)

r t ♥st② ♥t♦♥ s ♥ ② Betapdf (x; s, 1) =xs−1

∫1

0us−1du

= xs−1

[ 1sus]|10= xs−1

s−1 = sxs−1

♣♥ ts t

❲ r st s♥ t ♦ t♦t ♣r♦t② t♦ ①♣rss

E (max θ; x (s)) = Pr (x (s) ≤ θ) θ + Pr (x (s) > θ)E [x (s) |x (s) > c]

r③ ♥♦♠♣t t ♥t♦♥ t ♣r♠trs y a ♥ b s Iy(a, b) =∑a+b−1

j=a(a+b−1)!

j!(a+b−1−j)!yj(1−

y)a+b−1−j s♦ Iy(a, b) = B(y;a,b)B(a,b) =

∫y

0ta−1(1−t)b−1dt

∫1

0ta−1(1−t)b−1dt

❲r B(y; a, b) s t ♥♦♠♣t t ♥t♦♥

B(y; a, b) =∫ y

0ta−1(1 − t)b−1dt ♥ B(a, b) s t t ♥t♦♥ B(a, b) =

∫ 1

0ta−1(1 − t)b−1dt s ♥♦t t

s♠ s t t ♣r♦t② ♥st② ♥t♦♥ ♥② ♣♣②♥ t ♥t♦♥ t♦ ts ♣r♦♠ ②s

Ic(s, 1) =

s∑

j=s

s!

j!(s− j)!cj(1− c)s−j =

s!

s!0!cs(1− c)0

♥ ♥r t t strt♦♥ t ♣r♠trs a ♥ b ♦r r♥♦♠ r y s Betapdf (y;α, β) =yα−1(1−y)β−1

∫1

0uα−1(1−u)β−1dus ♦♥ s♦ ①♣t t ♥♦♠♥t♦r ♦ qt♦♥ ♦♥ t♥ ③r♦ ♥ ♦♥ t ♥♠rt♦r s

s♠r t♥ t ♥♦♠♥t♦r s xmax (s) < s s♥ x (s) ∈ [0, 1] s ≥ 1 s s s♥t② ttt ①♣tt♦♥ s s♠r t♥ ♦♥ ♦t t♦ t s s♥ x ∼ Uniform(0, 1).

E [x (s) |x (s) > θ] =

∫ 1

θx (s) s [x (s)]s−1

dx (s)∫ 1

θs [x (s)]s−1

dx (s)

♠♣s

Emax θ, x (s) =θs+1 + s

s+ 1

♦t tt ♦r θ = 0 ♥ ts ♦rrs♣♦♥s t♦ t st♥r ♠①♠♠ ♦ s ♥♦r♠ r♥♦♠ rss

s+1 ♥ ♥ θ = 1 t ①♣t s ♦♥ ♦t ①tr♠ ♦♥t♦♥s r rssr♥ ♦ ♦r

t♦♥s

♦ ♥♦ ♥r♥ts t♦ r rt qt♦♥

1

qV

largewait = β2

[

θs+1 + s

s+ 1− θ

]

①st♥ ♦ qr♠

r s♦ t ①st♥ ♦ ♥ qr♠ ♦r ♦r ♠♦ ♥ t♦♥ ♥ t♦ r♠s tt ♣♦t♥t s♦♣ ♥ ♥ ♣r♦ts s = 1 ♥ ♦♥ r r♠ s ♣♦t♥t s♦♣ s = 2 ♥ s♦♠ss s♦ t ♠♦r ♥r t♦♥s ♦r s > 2 ♥t♦♥s t♦ ♦r r♠ ♦♣♦t♥t s♦♣ s ♥ ♥ tts s ♣r♦♣♦rt♦♥ t♦

Vpioneer =− F + β

1

2(1− c)2

Vwait(s) =β2

[

θs+1 + s

s+ 1− θ

]

s♦♥ t♦ ♣♦♥r ♦r t ② t s♠ r♠

s♠ r♠ ♥tr β2[

12(1− θ)2

]

< −F + β[

12(1− c)2

]

tr s♦♠ ♠♥♣t♦♥s

♦♠s

1 <(1− β)

(

1− 2(

Fβ+ c

)

+ c2)

F(

Fβ+ c

)

E [xmax (s) |xmax (s) > θ] =

(

1

1− θs

)

s

∫ 1

θ

x (s)sdx (s) =

(

1

1− θs

)

s

s+ 1

[

x (s)s+1

]∣

∣

∣

1

θ=

(

1

1− θs

)

s

s+ 1

[

1− θs+1]

♦r t s♣ s ♦ t c = 0 ♥qt② ♦♠s

F < (1− β)

(

β

F− 2

)

s♥ F s rstrt t♦ ♣♦st ♥ β

F> 2 ♥ ♦t♥ t β ♦s t♦ ♦♥

♣t♥ t ♥♦t ♥♥t ♥ F ♦s t♦ ③r♦ ♦r ①♠♣ F = 0.1 ♥ β = 0.9 ②s ♣♦ss s sr ♦r t ss ♦r ts s tr s ♦♥ r

s♦♥ t♦ ♣♦♥r ♦r t ② t r r♠

s♦♥ t♦ ♥tr ♣♥ ♦♥

Vlargewait < V i

pioneer

β2

[

θs+1 + s

s+ 1− θ

]

< −F + β

1

2(1− c)2

♦r s = 2 ts ♦♠s[

2

3β +

2

3β

(

F

β+ c

)3

− F − βc−1

2+ c− c2

]

< −F

β

r ♣r♦r♠s rsr t♦ ♥ t t r♦♥ ♦ ♣r♠trs ♦r ts t s

Pr♦♦ ♦ ♥q♥ss ♦ qr♠

♥ t s♣t♦♥ ♦ ♦s ♦♥ r♠s strts t② ♥♦ ♦r sr tt ♥♦tr r♠ ♥tr ♥ t ♥①t ♣r♦ r r① ts ss♠♣t♦♥ t♦ s♦ tt ♦r t r♦♥ ♦ ♣r♠trsΩ = Ω1 ∪ Ω2 ♥ ♥ Pr♦♣♦st♦♥ ♥ r t ss♠♣t♦♥ tt t st ♦♥ r♠ ♥trss ♣♦♥r s t♦t ♦ss ♦ ♥rt② ♥trst♥② s♦ tt t qr♠ ♥ ♥Pr♦♣♦st♦♥ s ♥q ♦r t ♥♦♥♦s r♦♥ Ω2

♦ ♥r③ t st♣ ♦ st♦♥ ts ♥♦t ② pj s t ♥♦♥♦s ♣r♦t② tt r♠j ♥trs s ♣♦♥r p−j ♥♦ts t tt t ♦tr r♠ ♥trs s ♣♦♥r ♥ t ♥t♦♥s ♦r r♠ ♦ t②♣ ϕ ♦♠

1

q (ϕ)V ipioneer = −F + βEmax 0, [x− c] q

1

q (ϕ)Vwait (ϕ) = p−j × β2

[

θs(ϕ)+1 + s (ϕ)

s (ϕ) + 1− θ

]

+ (1− p−j) β1

q (ϕ)max

V ipioneer, 0

r♥ t t ♣r♦s st♣ s tt t ①♣t ♦ t♥ ♣♥s ♦♥ t stt ♥ r♠ ♠② t rs♣t ♦ t t ♦tr r♠ ♦ ❲ ♦♥♥trt ♥t s r β, F ∈ Ω2 s ♥ ♥ Pr♦♣♦st♦♥ ♦ ♣r♦ t r♠♥t ② ♦♥trt♦♥ s♦ ss♠ ♦♥trr② t♦ Pr♦♣♦st♦♥ tt t r r♠ s t s♠ r♠ ♠② ♥♦t♥tr s ♣♦♥r ♦r sr 0 ≤ psmall < 1 r psmall r♣rs♥ts t tt t r r♠ s♦t t ♥tr② ♦ t s♠ r♠

r♦♠ st♦♥ ♥♦ tt ♥ r♦♥ Ω = Ω1 ∪ Ω2 t s ♦♠♥♥t strt② ♦r t s♠r♠ t♦ ♥tr ♠♠t② ♥ t ♥♦s ♦r sr tt s♦♠♦② s ♥tr♥ s ♣♦♥rt ♠♥s ♥ t t plarge = 1 t s♠ r♠ st ♣rrs t♦ ♥tr ♠♠t② ♦rs ♥ t s t plarge = 0 t s♦ ♥t t♦ ♥tr s tr s ♥♦ rs♦♥ t♦ t ♥② ♣♦t♥t ♣r♦ts t♦t ♥t r♦♠ ttr ♥♦r♠t♦♥ ② ♦♥t♥t② ♦ t ①♣t♣r♦t ♥t♦♥ ♥ qt♦♥ t♥ ♦r ♥② plarge ∈ [0, 1] t s♠ r♠ ♣② strt②psmall = 1 s ♦♠♥♥t strt② β, F ∈ Ω s rst t ♦ ♥ ♥♦♥sst♥t ♦rt r r♠ t♦ ①♣t psmall < 1 s ♦♥s ♦r ♣r♦♦ ② ♦♥trt♦♥ ♦ t ♥q♥ss ♦qr♠ ♥ r♦♥ Ω t psmall = psmall = 1 s t ♥q rt♦♥ ♦t t s♠ r♠♥tr② ♣ttr♥ ♥trst♥② ts ♠s t ss♠♣t♦♥ tt t st ♦♥ r♠ ♥trs s ♣♦♥r♠ ♥ st♦♥ t♦ t♦t ♦ss ♦ ♥rt② ♥ qr♠ ♥ psmall = 1 t ♥q♦♠♥♥t strt② ♦ t r r♠ ♥ r♦♥ Ω2 s t♦ t plarge = 0 s♥ ② ♥t♦♥ ♦ Ω2

Vlargewait > V i

pioneer qr♠ s t♥ ♥q q

Pr♦♦s ♦ ♣rt♦♥s

Pr♦♦ ♦ ♣rt♦♥

r♦ss ♣r♦ts t ♥♦♥t♦♥ ♣r♦t② ♦ ♦♦r ♥tr② ♥ t ♠♦st sss st♦rs Pr [x > θ]= 1 − F

βq− c t ♣r♦t② ♦ ♥tr② ♥ tt s♠ st♦r ♦♥t♦♥ ♦♥

♣♦♥r sr s Pr[

x > θ∣

∣

∣x > c

]

= 1c

(

1− Fβ− c

)

> Pr [x > θ] s t ♣r♦t② ♦ ♥

♦♦r s ♣♦st② rt t♦ t sss ♦ t ♣♦♥r

Pr♦♦ ♦ ♣rt♦♥

t ♦♦s rt② r♦♠ Pr♦♣♦st♦♥ s s♠ r♠s ♣♦♥rs ①♣♦rt♥ q rr r♠s ♥tr s ♦♦rs ①♣♦rt♥ q