5i^i?|@* U|L?t | 5TT*) N?Uih|@?|) @* i3@?tht|L w@MLh@|Lh) uLh , Tih4i?|@* ,UL?L4Ut N?iht|) Lu L?? _i?@ih@**ii 2ee2 #D  L??c Bih4@?) i4@*G T@*9*@MiUL??ML??_i At ihtL?G a*) bb.

Devwudfw Wkh sxusrvh ri wklv sdshu lv wr dqdo|vh wkh lpsdfw ri vxsso| xqfhuwdlqw| rq wkh irupdwlrq ri sulfhv dqg rq wkh vhoohu*v h{shfwhg uhyhqxh lq vhtxhqwldo uvw0 dqg vhfrqg0 sulfh vhdohg elg dxfwlrqv1 Dwwhqwlrq lv sdlg wr wkh vhoohu*v rswlpdo srolf| uhjduglqj wkh uhohdvh ru zlwkkroglqj ri lqirupdwlrq derxw wkh dydlodeoh vxsso|/ wr wkh ex|huv* vwudwhjlf lqihuhqfhv derxw wkh vhoohu*v frqfhdolqj srolf| dqg wr wkh uhvxowlqj vhtxhqfh ri h{shfwhg sulfhv1 D fdvh zkhuh wkh vhoohu frpplwv klpvhoi wr eh xqdzduh ri wkh dydlodeoh vxsso| iru vdoh lv dovr frqvlghuhg1 Lw lv vkrzq wkdw vxfk d frpplwphqw/ zklfk kdv ehhq hpslulfdoo| revhuyhg/ pd| ohdg wkh vhoohu wr lqfuhdvh/ ghfuhdvh ru wr pdlqwdlq klv orqj uxq h{shfwhg uhyhqxh htxdo wr wkh rqh rewdlqhg li wkh dydlodeoh vxsso| zdv dozd|v uhsruwhg1

MHO Fodvvlfdwlrq Qxpehuv= G77/ G;4/ G;5 Nh|zrugv= Pxowl0xqlw Dxfwlrqv/ Sulydwh0Lqghshqghqw Ydoxhv/ Xqfhuwdlqw|1 L

dp wr judwhixo Urqdog Kduvwdg dqg Dodq Nlupdq iru khosixo frpphqwv rq dq hduolhu gudiw1 Uhpdlqlqj

huuruv duh p| rzq1





W?|hL_U|L?

W? t thi) Lu @hLt hi@*Lh*_ @U|L? 4@h!i|tc @tt@_) EbS. hiTLh|t |i i t|i?Ui Lu @U|L?t ihi ti**iht |L*_ uhL4 M)iht @?) ?uLh4@|L? UL?Uih??} |i @4L?| Lu tTT*) @@*@M*i uLh t@*i 5U Th@U|Ui @t Mii? LMtihi_ ? €t 4@h!i|t tU @t |Lti Lu OL?! kL?}c Ai* c O@u@c @?*@ @?_ Lu |i 6hi?U 4i_|ihh@?i@? UL@t|*?i ? |i 4@h!i| Lu 5 i|i uLh i @4T*ic |i @U|L? t|@h|t @t |i €ht| |h@*ih _ti4M@h!tc |i 4ihU@?_ti t Lgihi_ ? *L|t Lu @ Uih|@? ?4Mih Lu !*Lt Lu @ }i? tTiUit ,@U Lu |iti *L|t t |i? U@hhi_ L? @ 4L?} Mi*| uhL4 |i t|LhihLL4 |L |i M)iht @?_ @__|L?@* tTT*) t _tT*@)i_c ? |i t@4i @)c @UULh_?} |L |i ML@|t< Lh_ih Lu @hh@* )iht U@? |t L?*) tii |i Lgih?}t @t |i @U|L?iih t|@h|t |i @U|L?c |L| uh|ih ?uLh4@|L? @ML| |i _@)
Thiti?Ui Lu ?Uih|@?|) @ML| |i @U|@* tTT*) |L Mi @U|L?i_ ? ti^i?|@* @U|L?t Ai ThTLti Lu |i Thiti?| T@Tih t |L @?@*)ti |i 4T@U| Lu tTT*) ?Uih|@?|) L? |i uLh4@|L? Lu ThUit @?_ L? |i ti**ih
doldwhg ydoxhv frqfhsw zdv lqwurgxfhg e| Plojurp dqg Zhehu ^4<;5d`/ lwv ihdwxuh ehlqj wr surylgh

d pruh jhqhudo iudphzrun doorzlqj iru qrq0qhjdwlyh fruuhodwlrqv dprqj elgghuv* ydoxhv1



@U|L?t @?_ |@| | |i @tt4T|L? Lu _iUhi@t?} @MtL*|i ht! @ihtL?c M)iht L*_ |i? h@?_L43i |ih M_t tL |@| |i @**LU@|L? Lu }LL_t L*_ ?L| ?iUitt@h*) Mi iUi?| @?_ i TiU|i_ ThUit L*_ ?L| ?iUitt@h*) _iU*?i *@U! @?_ #i i3@ Ebb2 _ii*LTi_ @ |L TihL_ 5 @U|L? 4L_i* ihi ? i@U TihL_ L?i |i4 @t Lgihi_ uLh t@*i @?_ ihi i@U M)ihc UL?_|L?@* L? ???} |i €ht| TihL_ @U|L?c @t }i? |i LT|L? |L M) |i hi4@??} |i4 @| |i €ht| TihL_ ThUi 5U Th@U|Ui @t ?_ii_ Mii? LMtihi_ @| tL4i ?i @U|L?t Ai) tLi_ |@| u M)iht @*i |i €ht| |i4 4Lhi |@? |i tiUL?_c tU @? LT|L? L*_ h@ti |i ti**ih
^4<;<` uhsruwv krzhyhu wkdw wklv ex|hu*v rswlrq kdv ehhq dgrswhg e| ydulrxv dxfwlrq krxvhv

suhflvho| wr dwwhqxdwh wklv ghfolqlqj sulfh skhqrphqrq dqg wkdw revhuyhg sulfhv dsshdu wr ghfuhdvh pruh vhyhuho| lq dxfwlrqv zkhuh vxfk dq rswlrq lv devhqw1 6 Wkh

frqfhsw ri cpruh glvshuvhg rughu vwdwlvwlfv* pd| ru pd| qrw eh ghshqgdqw ri fkdqjhv lq wkh phdq1

e

W? B@*i @?_ O@tU Ebbec |L M)iht UL4Ti|i uLh |i ThU@ti Lu L?i Lu |L t|LU@t |U@**) i^@*i?| |i4t tL*_ ? @ ti^i?Ui Lu 5 @U|L?t Bi? |@| Th@|i @*it uLh ML| |i4t @hi !?L? @| |i L|ti| Lu |i @U|L? tittL?c |i @|Lht _ihi_ UL?_|L?t ?_ih U | 4@) Mi LT|4@* uLh @ TL|i?|@* M__ih |L tM4| |i 4?44 @UUiT|@M*i M_ ? |i €ht| @U|L? Lh ii? |L ?L| i?|ih ? UL4Ti||L? uLh |i €ht| |i4 t |i L|UL4i 4}| |i? *i@_ |L @? ?iUi?| @**LU@|L?c | t tL? |@| M) *i||?} |i ??ih Lu |i €ht| @U|L? ULLti t Thiuihhi_ |i4 E@ h}||LULLti< 5 @U|L?c |t L*_ ?iUitt@h*) )i*_ iUi?U) @?_ _iU*??} i TiU|i_ ThUit 6h|ih4Lhic |i |hi?_ Lu ThUit ? ti^i? |@* 5 @U|L?t @?_ |i _gihi?Ui Mi|ii? i TiU|i_ hii?it uLh |i ti**ih uhL4 5 @?_ h}||LULLti< 5 @U|L?t @i |i t@4i t}? W? @| uL**Ltc W t@** hiuih |L *}hL4 @?_ `iMih
D

|i M)iht< T_@|i_ M__?} t|h@|i}it 4@)  )i*_ 4 @ *Lih i TiU|i_ hii?i |@? @| i ?|@**) i TiU|i_ @?_  ThL_Ui @ ti^i?Ui Lu i TiU|i_ ThUit U t !?!i_< Ei €ht| UL?t|@?| @?_ |i? _iU*??} Aiti hit*|t i |i?_ |L U@tit ihi M)iht @i hL?} Mi*iut @ML| |i @U|@* h@?_L4?itt Lu tTT*) Ei |i) @hi i|ih |LL LT|4t|U< Lh |LL Titt4t|U< 6h|ih4Lhic @ ?4ihU@* i @4T*i tLt |@| ? |i *L?} h? Ei L? @ih@}ic tU @ 4)LTU _iUtL? uLh |i ti**ih L*_ )i*_ 4 @ }ih i TiU|i_ hii?i i? M)iht @hi Titt4t|U @ML| |i @U|@* h@?_L4?itt Lu tTT*)c @ *Lih L?i u |iti @hi t*}|*) LT|4t|U @ML| | @?_ |i t@4i i TiU|i_ hii?i @t |i L?i LM|@?i_ ? |i tTT*) Uih|@?|) uh@4iLh! u M)iht @i i|ih @ ULhhiU| Lh @ ih) LT|4t|U Mi*iu Ai tiUL?_ ti||?} hiuiht |L @ U@ti ihi |i ti**ih t ?@@hi Lu |i @@*@M*i tTT*) |L Mi T| T uLh t@*i 5U @ t|@|L? @t Mii? i4ThU@**) LMtihi_ ? |i @MLi 4i?|L?i_ 6hi?U €t 4@h!i|t ?i hi@tL? uLh |t |L @TTi? t |i i t|i?Ui Lu |4i @?_%Lh Lh}@?3@|L?@* UL?t|h@?|t ?_ih U |i ti**?} @t |L LUUh W? |iti €t 4@h!i|tc U @hi Lh}@?3i_ L? @ ti^i?|@* #|U @U|L? M@ttc |ihi U*i@h*) @hi |4i UL?t|h@?|t uLh M)iht L Lu|i? ?ii_ |L |h@?tTLh| |ih 4ihU@?_ti i*tiihi M) @ Uih|@? |4ic @?_ _LU!?} *4|@|L?t uLh |h@*iht EU @hi LM*}i_ |L _ti4M@h! ? ti^i?Ui ?L|ih U@h@U|iht|U Lu |iti 4@h!i|t t |@| |i @U|L?iih Thii?|t M)iht uhL4 _h@?} @?) Lu |i ThiLt t|h@|i}U ?uihi?Uit M) UL44||?} 4ti*u |L Mi ?@@hi Lu |i ^@?||it Lu €t |L Mi tL*_ W| ** Mi tL? ihi |@| i? |i M)iht< Mi*iu t |@!i? ?|L @UUL?|c tU @ UL44|4i?| uLh |i ti**ih 4@) *i@_ 4 |L i|ih ?Uhi@tic _iUhi@ti Lh 4@?|@? t *L?} h? i TiU|i_ hii?i i^@* |L |i L?i LM|@?i_ i? |i @@*@M*i tTT*) t @*@)t hiTLh|i_ Ai uL**L?} tiU|L? Thiti?|t |i 4L_i* 5)44i|hU i^*Mh4 M__?} t|h@|i}it @?_ |hi?_t Lu ThUit @hi _i|ih4?i_ ? 5iU|L?  5iU|L? e i T*Lhit |L t|@|L?t ihi |i ti**ih Mi@it t|h@|i}U@**) | hitTiU| |L |i hi*i@ti Lh |L*_?} Lu ?uLh4@|L? @ML| |i @U|@* tTT*) |L Mi @U|L?i_ @?_ 5iU|L? D UL?U*_it |i T@Tih

S

2

AiLhi|U@* uh@4iLh!

tt4i |@| ? : 2 ht!?i|h@* M)iht @||i?_ @ 4@h!i| ihi & ? L4L}i?iLt |i4t @hi |L Mi tL*_ ? @ ti^i?Ui Lu @U|L?t | |i i?_ Lu i@U @U|L?c L?i ?| ** Mi @@h_i_ |L |i M)ih L tM4||i_ |i }it| M_ ,@U M)ih  @t Th@|i ?uLh4@|L? UL?Uih??} t L? @*i % uLh |i |i4 |L Mi tL*_ ** @*it @hi h@?_L4*) @?_ ?_iTi?_i?|*) _h@? uhL4 @ }i? ThLM@M*|) _t|hM|L? u?U|L? 8 c U @t @ UL?|?Lt _i?t|) s _i€?i_ L? df( n4 )iht @i ?| _i4@?_tG i@U Lu |i4 _ithit L?*) L?i ?| Lu |i |i4t Lgihi_ uLh t@*i N?Uih|@?|) @ML| |L|@* tTT*) t ?|hL_Ui_ M) @tt4?} |@| |ihi t @ 4@ 44 ?4Mih & Lu |i4t |L Mi @U|L?i_ @?_ |@| @| |i i?_ Lu i@U @U|L? hL?_ | &c L?i 4Lhi t@*i 4@) LUUh | ThLM@M*|) B 5 Ef(  W| t @*tL @tt4i_ |@| ?c &c B @?_ 8 @hi UL44L? !?L*i_}i |L @** M)iht @?_ |@| L?*) |i ???} M_ t hii@*i_ @| |i i?_ Lu i@U @U|L? hL?_ t 4Lt| hit*|t hiuih |L Lh_ih t|@|t|Utc |i h@?_L4 @h@M*i fE E@?_ |t hi@*3@|L? %E  t|@?_ uLh |i | }it| Lu ? _ _h@t uhL4 8 c tL |@| fE  fE2    fE? 



,^*Mh4 M__?} t|h@|i}it @?_ |hi?_ Lu ThUit

W? @ 6 @U|L?c |i |i4 t @@h_i_ |L |i }it| M__ih uLh @ ThUi i^@* |L t M_ 5L*_ |ihi Mi L?*) L?i |i4 |L Mi tL*_c VU!hi) EbS tLi_ |@| @ t)44i|hU i^*Mh4 t|h@|i}) L*_ Mi uLh @ M)ih |L tM4| @ M_ i^@* |L |i i TiU|@|L? Lu |i tiUL?_ }it| @*i }i? |@| i t tTTLti_ |L @i |i }it| L?i A@| t KE% ' .ifE2 mfE ' %j W? @ 5 @U|L?c t?Ui |i }it| M__ih t @@h_i_ |i |i4 uLh @ ThUi i^@* |L |i tiUL?_ }it| M_c | t @ _L4?@?| t|h@|i}) uLh @ M__ih |L tM4| @ M_ i^@* |L t @*i | i^*Mh4c |i ThUi T@_ M) |i ??ih t |t i^@* |L %E2  6Lh & :  @?_ B ' c `iMih EbH  tLi_ |@| ? @ ti^i?Ui Lu & @U|L?t @ M__ih
.

}it| @*i }i? |@| t @*@|L? t |i || }it| ? 6 @U|L?t Ei .ifE&n mfE| ' %jc Lh |i E| n | }it| L?i ? 5 @U|L?t Ei .ifE&n mfE|n ' %j Ai uL**L?} ThLTLt|L? }i?ih@*3it |iti hit*|t |L U@tit ihi B 5 Ef(  hLTLt|L? G wi| & Mi |i 4@ 44 TLttM*i ?4Mih Lu |i4t |L Mi tL*_c @?_ _i€?i B @t |i ThLM@M*|) |@| L?i 4Lhi @U|L? ** LUUh 6Lh i@U @U|L? uLh4@| |ihi i t| @ ?^i &|T*i EK c K2 c c K&  Lu t)44i|hU ?Uhi@t?} i^*Mh4 M__?} t|h@|i}it U UL4TL?i?|t @hi _i€?i_ @t uL**Lt  uLh ti^i?|@* 6 @U|L?tG K&3, E% ' B , .ifE&n mfE&3, ' %j n

,S 3 'f

B  E  B.ifE&3,nn mfE&3, ' %j

uLh , ' c c &  c

@?_ K& E% ' .ifE&n mfE& ' %j

uLh , ' f

2 uLh ti^i?|@* 5 @U|L?tG K&3, E% ' B , .ifE&n mfE&3,n ' %j n

,S 3 'f

B  E  B.ifE&3,nn mfE&3,n ' %j

uLh , ' c c &  c

@?_ K& E% ' .ifE&n mfE&n ' %j

uLh , ' f

hLLuG 5ii |i TTi?_  W| @TTi@ht uhL4 |i @MLi ThLTLt|L? |@| uLh B 5 Ef(  @?_ uLh | &c |i i^*Mh4 M__?} t|h@|i}it uLh ML| @U|L? uLh4@|t @hi Thi t|h@|i}it |@| ii? L| @** TLttM*i L|UL4itG @| TihL_ |c |i i^*Mh4 t|h@|i}) t @? @ih@}i Lu |i E&  | hi4@??} i^*Mh4 t|h@|i}it i? B '  i}|i_ M) |i ThLM@M*|it |@| |ihi ** Mi c 2c E&  | 4Lhi |i4t uLh t@*i H

Ai uL**L?} ThLTLt|L? t|@|it |@| uLh @hLt *ii*t Lu ?Uih|@?|)c |i hit*|?} ti ^i?Ui Lu ti**?} ThUit 4@) i|ih Mi @ 4@h|?}@*i i|ih @i @ _iU*??} |hi?_ hLTLt|L? 2G 6Lh ML| 6 @?_ 5 @U|L? uLh4@|t @?_ | B i^@* |L |i ThLM@M*|) |@| L?i 4Lhi @U|L? ** LUUhG  |i ti^i?Ui Lu i TiU|i_ ThUit t @ 4@h|?}@*i i? B 'c E`iMih EbH  .iK&3, EfE&3, j ' .iK&3,3 EfE&3,3 j 2 |i ti^i?Ui Lu i TiU|i_ ThUit t _iU*??} uLh @?) B 5 Ef( G .iK&3, EfE&3, j  .iK&3,3 EfE&3,3 j hLLuG 5ii |i TTi?_ 

e

Ai ti**ih
 UL?ti^i?Ui Lu hLTLt|L?  t |@| |i ?UL?_|L?@* i TiU|@|L? Lu K, E Ei |i i @?|i i TiU|i_ ti**?} ThUi Lu |i , | |i4 t _i?|U@* uLh ML| @U|L? uLh4@|t `i @hi |ihiuLhi @M*i |L i |i?_ `iMih
|'

At u@h | @t Mii? tL? |@| |i Thiti?Ui Lu ?Uih|@?|) @ML| |i @U|@* ?4Mih Lu |i4t ? ti@*i_ M_ @U|L? uLh4@|t h@tit |i i TiU|i_ ThUi Lu |i €ht| E&   L?it u |ihi @hi i @U|*) & |i4t T| T uLh t@*i W| @t |t 4T*U|*) @tt4i_ |@| |i @U|@* |L|@* tTT*) Ei?UiuLh| _i?L|i_ M) &W  @t i^@* |L & tL |@| |i ?Uih|@?|) ui@|hi Lu |iti b

@U|L?t ?@h@M*) Lh!i_ ? u@Lh Lu |i ti**ih
e

Ai ?L UL44|4i?|< U@ti

W| ** Mi @tt4i_ |@| |i ti**ih !?Lt |i @U|@* tTT*) &W @?_ tit |t ?uLh4@|L? ? @ 4)LTU @) |L ?Uhi@ti t i TiU|i_ hii?i W| ** |i? Mi tL? L |i ti**ih
&[ W 3 |'

+

B &3 .ifE&n j n

& 3 [ |'

, B | E  B.ifE|n j

u   &W  &  c Lh {B E&W  ' &W .ifE&W n j 

&[ W 3 '

+

B &3 .ifE&n j n

& 3 [ |'

, B | E  B.ifE|n j

.ifE&n j u &W ' & W? ML| i^@|L?tc &W .ifE&W n j t|@?_t uLh |i i TiU|i_ hii?i i? B '  *i |i uL**L?} |ih4t hiThiti?| |i i TiU|i_ hii?i i? B 5 Ef(  ? i|ih U@ti Bi? @ ti| Lu T@h@4i|iht ?c &c s E @?_ Bc | t TLttM*i |L _i€?i tL4i ?|i}ih & tU |@| {B E&W  t TLt|i uLh &W & E? U U@ti |i ti**ih Thiuiht |L hii@* |i @U|@* tTT*) Lh ?i}@|i uLh &W  & EtL |@| i Thiuiht |L UL?Ui@* | Oi?Uic TL? t _iUtL? |L UL?Ui@* &W c M__iht

f

** h@|L?@**) ?uih @ 4?44 TLttM*i ?4Mih & Lu |i4t |L Mi tL*_ @?_ ULhhitTL?_?}*) T_@|i |ih i^*Mh4 M__?} t|h@|i}it ? |i L|ih @?_c t?Ui |i ThLM@M*|) |@| L?i 4Lhi t@*i 4@) LUUh @t Mii? !iT| UL?t|@?| uLh i@U hL?_  | &c M__iht< T_@|?} ThLUitt ** L?*) @giU| |ih t|h@|i}it @?_ ?L|  Eg O@?} _i|ih4?i_ tU @ &c M)iht ** |t M_ @t u |i) ihi thi |@| |ihi ** Mi @| *i@t| & |i4t T| uLh t@*i Ai i^*Mh4 M__?} t|h@|i}it uLh |t ?i i?hL?4i?| @hi _i€?i_ @t ? hLTLt|L?  E| B '  uLh TihL_t c c & @?_ |i hit*|?} ti^i?Ui Lu i TiU|i_ ThUit t tL? |L Mi !?!i_< @| |i & | TihL_G | t UL?t|@?| uLh TihL_t  |L & @?_ | @t @ _L?@h_ _hu| uLh TihL_t E& n  |L & MLt*) u & ' &c |i ti**ih
frxog dovr dvvxph wkdw wkh vhoohu iruhvhhv elgghuv* lqihuhqfhv dqg frqvhtxhqwo| zlwkkrogv lqirupdwlrq

derxw wkh dfwxdo vxsso| iru ydoxhv ri n vpdoohu wkdq n1 Dv wklv zrxog lqyroyh ixuwkhu cfrpprq nqrzohgjh* dvvxpswlrqv/ vxfk dowhuqdwlyh kdv ehhq glvfdughg iurp wkh dqdo|vlv1 Dqrwkhu srvvlelolw| zrxog eh iru wkh vhoohu wr uhylvh klv lqlwldo ghflvlrq wr frqfhdo n lq rughu wr dyrlg orvvhv1 Wklv zrxog reylrxvo| ohdg ex|huv wr jxhvv wkh h{dfw qxpehu ri lwhpv wr eh dxfwlrqhg1



€?ih ?uLh4@|L? @ML| &W tL |@| i 4@) t|** i|ih ?Uh @ *Ltt Lh hi@*3i @ }@? At t t44@h3i_ ? |i uL**L?} ThLTLt|L? hLTLt|L? eG Ai ti**ih
? i @4T*i

tt4i |i uL**L?} ti| Lu T@h@4i|ihtG Aihi @hi 2f M__iht E? ' 2fc f _i?|U@* |i4t |L Mi @U|L?i_ E& ' f @?_ M__iht @*it @hi _h@? uhL4 @ ?uLh4 _t|hM|L? L? dfcffo LhhiU| Mi*iutG B ' BW  A@M*i  hiTLh|t |i @*it Lu {E&W  i? EBc BW  ' EfDc fDc |i i TiU|i_ ThUit i? &W ' & Ei .i j @?_ |Lti hit*|?} uhL4 |i ti**ih
A@M*i G B@?t @?_ wLttit i? B ' BW ' fD nW 4 5 6 7 8 9 : ; < 43

S +w @ nW , 318 3158 31458 313958 3136458 31348958 3133:;46 31336<39 31334<86 31334<86 4

HU+nW ,@ 78157 751;9 63169 4<138 44149 9158 616< 41:< 31<5 31<6 4941<6

HiS jK ;81:5 ;31<: :9156 :4183 991;5 95153 8:1:7 8618: 83133 7:195

fD +nW , 71:8 71:6 0313: 0<199 057143 076177 09:1;8 0<:194 0466165 04:914;

HiS jS :9156 :9156 :9156 :4183 991;5 95153 8:1:7 8618: 83133 7:195

fD +nW , 47158 4;1<: 4714: 718; 0<1;9 05<153 086194 0;616: 044<13< 04941<7

HU +nW ,_ 78157 751;9 5;18< 4;1:9 4417: 91:4 61;3 5144 4148 4158 4941<6

= Orqj uxq h{shfwhg uhyhqxh zkhq N @ n dqg wkh vhoohu uhyhdov n + @ 3=8,1 HU+n ,@n Hi[+n .4, j=S +w @n , e = H{shfwhg vhoolqj sulfh li n @n dqg  @ 3=8 f = Xsgdwhg h{shfwhg vhoolqj sulfh li wkh vhoohu frqfhdov n dqg  @ 3=8 g = Orqj uxq h{shfwhg uhyhqxh zkhq N @ n dqg wkh vhoohu uhyhdov vwudwhjlfdoo| n 1 Li 3=8 +n , A 3/ zh kdyh HUx +n ,@HU+n , Sn HiSx jl Li 3=8 +n , ? 3/ zh kdyh HUx +n ,@S +w @ n , l@4 d

T|4t|U Mi*iutG B : BW  )iht @hi @tt4i_ ihi |L Mi 4Lhi LT|4t|U |@? |i ti**ih EL @t TihuiU| ?uLh4@|L? @ML| |i h@?_L4?itt Lu tTT*) A@M*i 2 hiTLh|t |i U@ti ihi EBc BW  ' Ef.c fD *|L} {fD E&W  ? A@M*i  ?_Uit |i ti**ih |L UL?Ui@* &W u &W  2c i ** ?L| _L tL Oi ** hii@* &W u &W  D ? Lh_ih |L hi4@? UL?tt|i?| | M)iht< ?uihi?Uit U @hi M@ti_ L? B E|t t ?_Ui_ M) {f. E&W  ? A@M*i 2  W? |t ti||?}c |i M__iht< LT|4t|U Mi*iu 4i@?t |@| |i ti**ih U@??L| |@!i u** @_@?|@}i Lu t L? €?ih ?uLh4@|L? BW  A@M*i 2 uh|ih4Lhi hii@*t |@| |@| {f. E&W  f uLh &W  S @?_ {f. E&W  f uLh &W  b tL |@| M) UL?Ui@*?} &W c |i ti**ih ** ?Uh @ *Ltt u S  &W  H @?_ hi@*3i @ }@? u &W t i^@* |L b Lh f W? |i *L?} h? Liihc |t t|h@|i}U TL*U) L*_ )i*_ 4 @ *Lih i TiU|i_ hii?i |@? u i @*@)t hii@*i_ |i @@*@M*i tTT*) |L Mi @U|L?i_



A@M*i 2G B@?t @?_ wLttit i? B : BW Q EB ' f.c BW ' fD Q nW 4 5 6 7 8 9 : ; < 43 e f

S +w @ nW , 318 3158 31458 313958 3136458 31348958 3133:;46 31336<39 31334<86 31334<86 4

HU+nW , 78157 751;9 63169 4<138 44149 9158 616< 41:< 31<5 31<6 4941<6

HiS jK :<1;4 :8157 :31:9 9916< 9514; 8;155 87193 8417; 7<138 7:195

f. +nW , 43199 4916: 4:137 45189 51:9 045194 0661;; 094188 0<9164 046<14:

HiS jS 8;155 8;155 8;155 8;155 8;155 8;155 87193 8417; 7<138 7:195

f. +nW , 65158 871<; 9;14< :41;: 99136 83199 5<16< 41:5 066137 0:81<3

HU +nW , 78157 751;9 63169 4<138 44149 8179 6149 41:; 31<< 413; 494145

= H{shfwhg vhoolqj sulfh li n @n dqg  @ 3=: = Xsgdwhg h{shfwhg vhoolqj sulfh li wkh vhoohu frqfhdov n dqg  @ 3=:

A@M*i G B@?t @?_ wLttit i? B BW Q EB ' f c BW ' fD Q nW 4 5 6 7 8 9 : ; < 43 e f

S +w @ nW , 318 3158 31458 313958 3136458 31348958 3133:;46 31336<39 31334<86 31334<86 4

HU+nW , 78157 751;9 63169 4<138 44149 9158 616< 41:< 31<5 31<6 4941<6

HiS jK ;;177 ;619: :;1<4 :7148 9<16< 97197 8<1<4 8815< 831<8 7:194

f +nW , 5137 0319; 0;149 053174 06:175 08<154 0;81:< 044:15: 04861<7 04<91:<

HiS jS ;619: ;619: :;1<4 :7148 9<16< 97197 8<1<4 8815< 831<8 7:194

f +nW , 91;3 713; 06173 048198 065199 087178 0;4136 0445184 047<14: 04<5136

= H{shfwhg vhoolqj sulfh li n @n dqg  @ 3=6 = Xsgdwhg h{shfwhg vhoolqj sulfh li wkh vhoohu frqfhdov n dqg  @ 3=6

e

HU +nW , 78157 741;7 631:; 53136 451;4 :14 7135 5156 4154 4164 4981<6

itt4t|U Mi*iutG B BW  W? A@M*i c | t @tt4i_ |@| M)iht @i @ Titt4t|U Mi*iu @ML| BW G EBc BW  ' Ef c fD Ai @h}4i?| t t4*@h |L |i L?i t| }i? i UiT| |@| |i ti**ih ** ?Lc @UULh_?} |L {f E&W c UL?Ui@* &W  2 *i i L*_ @i Thiuihhi_ |L hii@* | L?*) uLh &W E@UULh_?} |L {fD E&W  ? A@M*i  ) UL4T@h?} |i hi@*3@|L?t Lu g uLh U {f E&W  @?_ {f E&W  MiUL4i ?i}@|ic i tii |@| |i ti**ih
uvw prphqwv ri wkh rughu vwdwlvwlfv iru wkh orjqrupdo glvwulexwlrqv zhuh wdnhq iurp Jxswd/ Pf0

Grqdog dqg Jdoduqhdx +4<:7,1

D

|L Mi tL*_c |i ti**ih
e2

Ai UL44|4i?|< U@ti

+@|ih |@? UL?Ui@*?} t|h@|i}U@**)|i @U|@* tTT*) T| T uLh t@*ic |i ti**ih UL*_ @*tL UL44| 4ti*u |L Mi ?@@hi Lu |i tTT*) @@*@M*i uLh t@*i Ai i TiU|i_ hii?i uhL4 @ }i? tittL? L*_ |i? _iTi?_ i U*ti*) L? |i hi@*3@|L? Lu gG {B E&W  4@) i|ih Mi ?i}@|i EuLh &W  & Lh TLt|i EuLh &W & Wu B ' BW c |i ti**ih
S

|@| t B BW EB : BW c | uL**Lt |@| |i ti**ih L*_ Mi Mi||ih Lg ELhti Lg UL44||?} 4ti*u |L Mi ?@@hi Lu |i @@*@M*i tTT*) |L Mi Lgihi_ uLh t@*i ? @ }i? tittL? At t t|@|i_ ? |i uL**L?} ThLTLt|L? hLTLt|L? DG `i? UL4T@hi_ |L |i tTT*) Uih|@?|) U@ti EB ' c |i ti**ih
D

L?U*tL?

W? |t T@Tih | @t tL? |@| i? ht!?i|h@* M__iht T@h|UT@|i ? @ ti^i?Ui Lu 6 Lh 5 @U|L?t | ?Uih|@? tTT*)c @ _iU*??} |hi?_ Lu ThUit 4@) hit*|t 5)44i|hU i^*Mh4 M__?} t|h@|i}it ihi _ihi_ uLh ML| @U|L? uLh4@|t W| @t LMtihi_ |@| uLh @?) }i? TihL_c |i LT|4@* M_ t @? @ih@}i Lu |i hi4@??} i^*Mh4 M_t |@| L*_ Mi tM4||i_ ? |i tTT*) Uih|@?|) uh@4iLh!c i}|i_ M) |i ThLM@M*|it |@| |iti hi4@??} |i4t ** ?_ii_ Mi Lgihi_ uLh t@*i W| @t @*tL tL? |@| |i ti**ih
.

i@h*ih ThL€|t @hi 4Lhi @*i_ |@? *@|ih L?itc M__iht t@_i |ih M_t *itt |@? u |i) ihi ?_gihi?| @ML| |i |4?} Lu |ih ii?|@* ThL€| *|L} ML| |i ?Uih|@? tTT*) @?_ _tUL?|?} @tt4T|L?t @hi t4*@h ? |ih4t Lu |ih 4T@U| L? |i uLh4@|L? Lu ThUit |L |i UL?t|@?| @MtL*|i ht! @ihtL? @tt4T |L?c |iti |L UL?UiT|t hi4@? u?_@4i?|@**) _gihi?| Ai *@||ih t ?_ii_ @ |*|@h@? |LL* i Thitt?} |i M)iht< hi*U|@?Uic uLh @ }i? TihL_c |L T*@) @ *L||ih) Lti Uih|@?|) i^@*i?| U@? Mi LM|@?i_ L? T@)4i?| Lu @ ht! Thi44 *i |i uLh4ih @tt4T|L?t U@h@U|ih3ic ? |t ti^i?|@* ti||?}c @ |4i u@U|Lh U Uhi@|it @ *?! Mi|ii? TihL_t 6?@**)c @t |i @MLi hit*|t L*_ L?*) u |i @U|@* ?4Mih Lu |i4t |L Mi @U|L?i_ t i^@* |L @| M__iht @tt4i |L Mi |i 4@ 44 TLttM*i ?4Mih Lu |i4t &c |L U@tit ihi |i @U|@* tTT*) UL*_ Mi *itt |@? & ihi i @4?i_ Ai €ht| U@ti @tt4i_ |i ti**ih |L !?L |i @@*@M*i tTT*) @?_ |L @_LT| @ 4)LTU t|h@| i}) |L@h_t |i hi*i@ti Lh |L*_?} Lu t ?uLh4@|L? ? Lh_ih |L ?Uhi@ti t i TiU|i_ hii?i W| @t tL? |@| TL? t _iUtL? |L UL?Ui@* |i @@*@M*i tTT*)c u M__iht @hi i?_Li_ | @ h@|L?@* ?uihi?Ui ThLUittc |ih T_@|i_ t|h@|i}it 4@) )i*_ |L |i ti**ih @ *Lih i TiU|i_ hii?i |@? |@| U i ?|@**) i TiU|i_ Aiti T_@|i_ t|h@|i}it @hi _i|ih4?i_ @?_ |i hit*|?} ti^i?Ui Lu i TiU|i_ ThUit t tL? |L Mi !?!i_G | 4@) €ht| Mi UL?t|@?| uLh @ }i? ?4Mih Lu TihL_t @?_ @i @ _iU*??} _hu| uLh |i hi4@??} L?it L?t_ih@|L? @t @*tL }i? |L t|@|L?t ihi M)iht @i @ hL?} Mi*iu @ML| |i @U|@* h@?_L4?itt Lu tTT*) @?_ |i 4T@U| Lu tU @ hL?} Mi*iu L? |i ti**ih
H

|i tTT*) Uih|@?|) uh@4iLh!c ?Uhi@tic _iUhi@ti Lh *i@i ?@giU|i_ t *L?} h? i TiU|i_ hii?i At hit*| t LM|@?i_ M) @tt4?} |@| |i t@4i ti^i?Ui Lu @U|L?t t hiTi@|i_ Lih |4i | |i t@4i ?4Mih Lu T@h|UT@?|t _h@?} |ih Th@|i?_iTi?_i?| @*it uhL4 |i t@4i _t|hM|L? At @tt4T|L? t T@h|U*@h*) hi*i@?| uLh 4@h!i|t U @hi Lh}@?3i_ L? @ hi}*@h M@tt | |i t@4i ti| Lu T@h|UT@?|tc tU @t @U|L?t uLh Tiht@M*i }LL_t 6?@**)c @t tU @ UL44|4i?| uLh |i ti**ih @t Mii? i4ThU@**) LMtihi_ ? tL4i €t @U|L?tc |t hit*| 4@) ThL_i tL4i ?t}|t ?|L |i i t|i?Ui Lu tU Th@U|Ui

b



TTi?_

hLLu Lu hLTLt|L? G Ai ThLLu U@t|t |i uL**L?} wi44@c ThLi_ ? w@gL?| @?_ AhL*i Ebb c T2 wi44@ G L?t_ih @ |Ui UL?|?Lt*) _gihi?|@M*i u?U|L? Eoc %c KEo $ ? ihi KE t @ UL?|?Lt 4L?L|L?U u?U|L? Lu o Wu Y Eoc %c KEomo'% ' f |i? tUi?| UL?_|L?t @hi @*tL t@|t€i_G o ' % hiThiti?| @ }*LM@* LT|44 uLh Ec c  AL _i|ih4?i |i t)44i|hU i^*Mh4 M__?} t|h@|i}itc | t UL?i?i?| |L UL?t_ih |i t|@?_TL?| Lu @ }i? M)ih Lti @*i t % @?_ L _i€?it t : t2 :  : t?3 @t |i Lh_ih t|@|t|Ut Lu |i E?   L|ih @*it t @** @*it @hi ?_iTi?_i?|*) @?_ _i?|U@*) _h@? uhL4 @ ?L? _i}i?ih@|i_ _t|hM|L? 8 E _i€?i_ L? ?n c |i _t|hM|L? Lu t, }i? |i hi@*3@|L? Lu t,3 ' +,3 @?_ |t _i?t|) @hi _i€?i_ @t  ?3, 8 El E?  ,8 El?3,3 s El 8t, Elm+,3  ' @?_ st, Elm+,3  ' 8 E+,3  8 E+,3 ?3, | 8t| Em+ c +2 c c +|3  ' 8t| Em+|3  t u@h @t ?L|@|L? t UL?Uih?i_c |i t)44i|hU i^*Mh4 M__?} t|h@|i}) @| TihL_ | }i? |i LMtihi_ hi@*3@|L?t Lu t c t2 c c t|3  t _i?L|i_ M) K| Ec + c c +|3  @?_ |i i ThittL? Yo Eoc %mo'% ** t|@?_ uLh |i €ht| _ih@|i Lu Eoc % | hitTiU| |L o 6Lh i@U @U|L? uLh4@|c |i ThLLu ThLUii_t ? |L t|iTt 6L**L?} *}hL4 @?_ `iMih EbH2Mc | t €ht| tL? |@| ? @?) }i? TihL_ |c @ M__ih U@? _L ?L Mi||ih |i? |L M_ K @? ?Uhi@t?} u?U|L? Lu 4?i%c +|3 j At t _L?i hiUhti*) M) t|@h|?} uhL4 |i *@t| @U|L? TihL_ @?_ M) t?} @ |)TU@* tM}@4i TihuiU|L? @h}4i?|G @| i@U TihL_ |c @ M__ih ** it|4@|i t ii?|@* }@? Lh *Ltt uhL4 _i@|?} uhL4 |i t)44i|hU i^*Mh4 t|h@|i}) }i? |@| @** L|ih M__iht @_LT| |i i^*Mh4 t|h@|i}) @?_ |@| i ** M_ @| i^*Mh4 ? @** tMti^i?| TihL_t Ai i^*Mh4 M__?} t|h@|i}it @hi |i? _i|ih4?i_ ? @ tiUL?_ t|iT 2f

 5i^i?|@* 6 @U|L?t 5L*_ |i &| @U|L? TihL_ LUUhc @ M__ih
Lh i^@*i?|*) & Eo& c %



8 Eo&  ' d%  K& Eo& c + c c +&3 o 8 E+&3 

?3&

@?_ u o& : +&3 c & Eo& c % ' d%  K& Eo& c + c c +&3 o  Ai €ht| Lh_ih UL?_|L? hi^hit |@| Yo& & Eo& c %o '% ' f 6hL4 wi44@ c t?Ui K& E t & t|hU|*) ?Uhi@t?} ? M__iht< @*itc |t ?iUitt@h) UL?_|L? t @*tL tUi?| 6Lh o&  +&3 c | |t uL**Lt |@| Yo& K& Eo& c + c c +&3 8 Eo& ?3&  nd%  K& Eo& c + c c +&3 oE?  &8 Eo& ?3&3 sEo& o '% ' f & U )i*_t Yo& K& E%c + c c +&3  ' d%  K& E%c + c c +&3 oE?  &

s E% 8 E%

u %  +&3 c

@?_ Yo& K& E%c + c c +&3  ' f

u % : +&3 

At t @ €ht|Lh_ih _gihi?|@* i^@|L? U @t uLh ML?_@h) UL?_|L? KEfc  ' f 6h |ih4Lhic t?Ui Yo& K& E%c + c c +&3  t ?_iTi?_i?| uhL4 + c c +&3 uLh %  +&3 c K& E%c + c  c +&3  t @U|@**) i^@* |L K& E% ? |i L|ih @?_c uLh % : +&3 c K& E%c + c c +&3  ' K& E+&3  Ai *@t| TihL_ i^*Mh4 t|h@|i}) t |t @ u?U|L? _i€?i_ M) K& E4?i%c +&3 j 2

6Lh TihL_t | ' c c &  c |i M__ih
&3 c %

'

] o&3 f

d%  K&3 Eo&3 c + c c +&32 ost&3 Ekm+&32 _k

nB

] +&32 o&3

d%  K& E4?i%c kjost&3 Ekm+&32 _k

u o&3  +&32 c @?_ &3 Eo&3 c % ' d%  K&3 Eo&3 c + c c +&32 o u o&3 : +&32  `i? o&3  +&32 c |i tiUL?_ *?i hiThiti?|t |i ThL€| @ M__ih i TiU|t uLh |i &| TihL_ }i? |@| i __ ?L| ? |i ThiLt @U|L? Eihi i M_ @t u t @*i @t o&3  +&32  @?_ |@| i ** ti t LT|4@* t|h@|i}) ? |i & | @U|L? ? |i L|ih @?_c M) M__?} ? |i ?i ||L*@t| TihL_ @t u t @*i @t o&3 : +&32 c |@| M__ih ** ? | ThLM@M*|) L?i t?Ui |i M__?} t|h@|i}it @hi @tt4i_ |L Mi t|hU|*) ?Uhi@t?} ? M__iht< @*it t uLh |i *@t| TihL_c |i 4@ 4t@|L? Lu |i M__ih
E &3 '%

'f

t ?L|i_ M) Uuii @?_ V?Ui?| Ebb c E t _gihi?| _iTi?_?} L? i|ih % : o&3 Lh % o&3 M| UL?ih}it |L |i t@4i @*i @t o&3 @TThL@Uit % ) ti||?} E i^@* |L f @| % ' o&3 c |i uL**L?} _gihi?|@* i^@|L? t LM|@?i_

22

Yo&3 K&3 E%c + c c +&32  ' d%  K&3 E%c + c c +&32 oE?  & n  Bd%  K& E%oE?  & n 

s E% 8 E%

s E% 8 E%

u %  +&32 c @?_ Yo&3 K&3 E%c + c c +&32  ' f u % : +&32  6hL4 ihic | uL**Lt |@| |i i^*Mh4 M__?} u?U|L? @| |i E&| @U|L? TihL_ t ?_iTi?_i?| uhL4 + c c +&3 u %  +&32 c tL |@| K&3 E%c + c c +&32  ' K&3 E% @?_ |@| K&3 E%c + c c +&32  ' K&3 E+&32  u % : +&32  Ai i^*Mh4 M__?} u?U|L? uLh |i E&  | @U|L? TihL_ t |t _i€?i_ @t K&3 E4?i%c +&32 j Ai t@4i ThLUi_hi U@? Mi ti_ |L _i€?i i^*Mh4 M__?} u?U|L?t uLh |i E&  2 hi4@??} TihL_t | |i L|ti| Lu |i ti^i?Uic +f t @tt4i_ |L Mi i^@* |L ?€?|) ELh |L |i i |hi44 Lu |i tTTLh| Lu 8 E | |i @U|L? TihL_ |c |i LT|4@* M__?} t|h@|i}) t |t _i€?i_ @t K| E4?i%c +|3 j t |i M__?} t|h@|i}it @hi @** ?Uhi@t?} ? @ M)ih
2

@?_ uLh |i ?i ||L*@t| @U|L?

+

%

?3& & ] % 8 E| K&3 E% ' B E?  & n  %  _| 8 E% f &,  ] % 8 E| ?3&n _|  E?  & %  8 E% f %

+

?3& , ] % 8 E| nE  B %  _| 8 E% f Lh i^@*i?|*) K&3 E% ' B.ifE&n mfE&3 ' %j n E  B.ifE& mfE&3 ' %j K&32 c K&3 c c K @hi LM|@?i_ ? @ t4*@h @)

 5i^i?|@* 5 @U|L?t Bi? |@| |i ThUi T@)i_ M) |i }it| M__ih t i^@* |L |i tiUL?_ }it| M_c |i _L4?@?| t|h@|i}) _i€?i_ uLh L?itL| @U|L?t Ei |L tM4| L?i
nB

+] +&32 o&3



] % f

st&3 E1m+&32 _1 

d%  1ost& E1m+&3 ' %_1

u o&3  +&32 c @?_ &3 Eo&3 c % ' d%  K&3 Eo&3 c + c c +&32 o u o&3 : +&32 

2e

`i? o&3  +&32 c |i €ht| *?i i Thittit @ M__ih
d%  K&3 Eo&3 c + c c +&32 oE?  & n 8 Eo&3 ?3& sEo&3  B E?  & n 8 Eo&3 ?3& s Eo&3  

] % f

E2

  E?  &8 E1?3&3 s E1  d%  1o _1  8 E%?3&

o&3 '%

'f

Oihi @}@?c E2 t _gihi?| i|ih % : o&3 Lh % o&3 @?_ UL?ih}it |L |i t@4i @*i @t o&3 @TThL@Uit uhL4 %c tL |@| ti||?} E2 i^@* |L f @| % ' o&3 )i*_t |i uL**L?} ti| Lu i^@|L?t %

?3& & ] % 8 E1 K&3 E%c + c c +&32  ' E  B% n B %  _1 8 E% f

u %  +&32 c

@?_ Yo&3 K&3 E%c + c c +&32  ' f

u % : +&32 

Mtihi |@| |i i^*Mh4 M__?} u?U|L? @| |i E&  | @U|L? TihL_ _iTi?_t L?*) L? % u %  +&32 c tL |@| K&3 E%c + c c +&32  ' K&3 E% @?_ |@| K&3 E%c + c c +&32  ' K&3 E+&32  u % : +&32  Ai i^*Mh4 M__?} u?U|L? uLh |i E&  | @U|L? TihL_ t |t _i€?i_ @t K&3 E4?i%c +&32 j W| U@? t4*@h*) Mi tL? |@| ? i@U TihL_ |c @ M__ih U@? _L ?L Mi||ih |@? |L M_ K| E4?i%c +|3 j U hiih|t Q M) ti Lu |i u@U| |@| M__?} t|h@|i}it @hi ?Uhi@t?} u?U|L?t Lu @*it @?_ ? UL??U|L? | _i€??} +f @t ?€?|) Lh @t |i i |hi44 Lu |i tTTLh| Lu 8 E Q |L M_ K| E% Ai *@||ih ** |t |@!i |i uL**L?} i ThittL?t

2D

K& E% ' % Lh i^@*i?|*)

K& E% ' . fE&n mfE&n ' %

@?_ K&3 E% ' B.ifE&n mfE& ' %j n E  B.ifE&n mfE&n ' %j K&32 c K&3 c c K @hi LM|@?i_ ? @ t4*@h @)  t |i uL**L?} ThLLut }L @*L?} |i t@4i *?it uLh ML| @U|L? uLh4@|tc L?*) |Lti uLh |i 6 @U|L? ti||?} @hi ThL_i_

2S

hLLu Lu hLTLt|L? 2G  6Lh B ' c  .iK&3, EfE&3, mK&3,3 EfE&3,3  ' qj / .i.ifE&n mfE&3, jmK3 &3,3 Eq ' fE&3,3 j  3 / .i.ifE&n mfE&3, jmK3 &3,3 Eq ' fE&3,3 j / .ifE&n mK&3,3 Eq ' fE&3,3 j  / K&3,3 EK3 &3,3 Eq ' q

2 6Lh f B c |@!i |i _gihi?Ui Mi|ii? |i i TiU|i_ ThUi Lu |i E&  ,| TihL_ Ei |i ?UL?_|L?@* i TiU|i_ M_ LM|@?i_ i? B 5 Efc  | |i L?i LM|@?i_ i? B '  At )i*_tc # B , .ifE&n j n Lh i^@*i?|*)c E  B

, 3 [ 'f

, [ 'f

$ B  E  B.ifE&3,nn j

 .ifE&n j

  B  .ifE&3,nn j  .ifE&n j

E 

U t TLt|i uLh @?) f , &   5?Ui |i ti^i?Ui Lu i TiU|i_ ThUit @t tL? |L Mi @ 4@h|?}@*i ? |i tTT*) Uih|@?|) U@tic | uL**Lt |@| E  t ?Uhi@t?} | , uLh @?) B 5 Efc  6Lh , ' fc E  t i^@* |L 3ihL 

hLLu Lu hLTLt|L? eG 6ht|c | tL*_ Mi ?L|i_ |@| @|iih |i ti| Lu T@h@4i|iht hi|@?i_ Ei ?c s E @?_ & : c {B E t @*@)t TLt|i @?_ {B E& t @*@)t ?i}@|i 6h|ih4Lhi t?Ui {B E&W  t t|hU|*) UL?U@i ? &W c |ihi i t| L?*) L?i hi@* ?4Mih V 5 E( & tU |@| uLh &W Vc |i ti**ih ?Uht @ *Ltt M) |L*_?} ?uLh4@|L? E{B E&W  : f @?_ uLh &W : Vc i hi@*3it @ }@? E{B E&W  f W? Lh_ih |L @L_ |i ti||?} Lu |iMhi@!?} h*it i? V @t @? ?|i}ih @*i ? E( & U L*_ )i*_ {B EV ' f uLh V ' &W c | t @tt4i_ |@| |i ti**ih hii@*t |i @U|@* tTT*) i? &W ' V  NT_@|i_ i^*Mh4 M__?} t|h@|i}it @?_ hit*|?} |hi?_ Lu ThUit 2.

O@?} _i€?i_ @? ?|i}ih & 5 E( & tU |@| {B E&   : f @?_ {B E& fc @?_ M) t?} |i ThLLu Lu hLTLt|L?  E| B '  uLh TihL_t  |L &c |i T_@|i_ i^*Mh4 M__?} t|h@|i}it uLh 6 @U|L?t U@? Mi _i€?i_ @t K&3, E% ' B &3& .ifE&n mfE&3, ' %j n

&3S & 3 'f

B  E  B.ifE&nn mfE&3, ' %j

uLh , ' fc c &  c

K&3, E% ' B , .ifE&n mfE&3, ' %j n

,S 3 'f

B  E  B.ifE&3,nn mfE&3, ' %j

uLh , ' c c &  c

@?_ K& E% ' .ifE&n mfE& ' %j ) |@!?} |i ?UL?_|L?@* i TiU|@|L?t Lu |iti i^*Mh4 M_tc | t tii? |@| uLh TihL_t  |L &c |i i TiU|i_ ti**?} ThUit ** Mi UL?t|@?| @?_ i^@* |L B

& 3&

.ifE&n j n

&3 & 3 [ 'f

B  E  B.ifE&nn j

*t| uLh TihL_t E& n  |L &W c |i) ** Mi _iUhi@t?} E|t t tii? uhL4 |i tiUL?_ U@ti Lu |i ThLLu Lu hLTLt|L? 2  Ai ti**ih
}i? |i t|hU| UL?U@|) Lu {B E&W  ? &W c |ihi t @ ?i V : V tU |@| @ ?i ?|i}ih &  & U@? Mi _i€?i_ t @ hit*|c u &  &W &  c |i ti**ih L*_ @i Thiuihhi_ ?L| |L UL?Ui@* &W t?Ui |t )i*_t 4 ?L @ t4@**ih i TiU|i_ hii?i i? UL4T@hi_ |L |i L?i i UL*_ LM|@? M) ?|@**) hii@*?} &W  A@| tc {B E&W  @t ?|@**) ?i}@|i *i {B E&W  t ?L TLt|i ? |i L|ih @?_c u &  ' &c {B E&W  hi4@?t ?i}@|ic tL |@| |i ti**ih ?Uhi@tit t i TiU|i_ hii?i uhL4 |L*_?} ?uLh4@|L? L? &W  2 uLh B BW c | t !?L? uhL4 hLTLt|L? 2 |@| |i ti**ih
2b

hLLu Lu hLTLt|L? DG  W? |i tLh| h? t ? |i ?L?UL44|4i?| uh@4iLh!c |ihi @hi |hii U@tit |L UL?t_ih _iTi?_?} L? M__iht< UL44L? Mi*iu B @ML| |i @U|@* h@?_L4?itt Lu tTT*) BW  5?Ui |ihi @hi ?L LT|L?t uLh |i ti**ih |L ULLti t Mit| ?uLh4@|L? TL*U)c L?i U@? L?*) _i|ih4?i |i L|UL4it Lu g uLh U i hi@*3it @ }@? Lh @ *Ltt Aiti @hi t4*@h |L |Lti _i€?i_ ? |i ThLLu Lu hLTLt|L? e  W? |i *L?} h? W? Lh_ih |L UL4T@hi |i *L?} h? i TiU|i_ hii?it LM|@?i_ uhL4 |i tTT*) Uih|@?|) @?_ |i tTT*) ?Uih|@?|) i?hL?4i?|tc | tUit |L UL4T@hi @** TLttM*i i TiU|i_ hii?it uLh |i ti**ih i? ML| |i ti**ih @?_ |i M)iht @hi TihuiU|*) ?uLh4i_ @ML| |i @U|@* tTT*)c |@| t & 3

BW

&.ifE&n j n

& 32 [ 'f

BW E  BW E n .ifEn2 j

Ee

| @** TLttM*i i TiU|i_ hii?it LM|@?i_ ? |i tTT*) ?Uih|@?|) U@tic |@| t # $ & 32 n &[ 3|3 [ [ BW E  BW  B &3| .ifE&n j n B  E  B.ifE|n n j |'

'f

& 3

nBW

 'f

+ &32 n # $ , &[ 3|3 [[ & 3|  B .ifE&n j n B E  B.ifE|n n j n .ifE&n j 'f |'

ED

 'f

W| t ?L ih€i_ |@| ED i^@*t Ee uLh B ' BW c |@| | t }hi@|ih uLh B BW @?_ t4@**ih uLh B : BW  

f



)LJXUHVHOOHU VORQJUXQH[SHFWHGUHYHQXH (difference between "concealing N " and "always revealing N ") 8 7 6 5 4 3 LogN(50;5)

2

LogN(50;10)

1

U[0;100] 0 -1 -2

0

0,2

0,4

0,6

0,8

1

%X\HUV %HOLHI G

+iuihi?Uit do ti?ui*|ihc h*i) c bHbc OL @U|L?t Lh! uLh ?i @?_ @h|c aLh?@* Lu ,UL?L4U ihtTiU|itc c 2  S d2o ih?@h_|c #@? @?_ #@_ 5ULL?itc bbec  ?L|i L? ti^i?|@* @U|L?tc 4ihU@? ,UL?L4U +iic Hec SD SD. d o *@U!c a@?i @?_ #@_ #i i3@c bb2c 5)t|i4@|U ThUi _gihi?Uit Mi|ii? tUUitti @U|L?t @hi ?L @?L4@*)c aLh?@* Lu ,UL?L4Ut : @?@}i4i?| 5|h@|i})c c Sf.S2H deo @tt@_)c +@*T ahc bS.c U|L?t @?_ U|L?iih?} EN?iht|) Lu @*uLh?@ hittc ih!i*i)

2

dDo ,?}i*MhiU|`}}@?tc +U@h_c bbec 5i^i?|@* @U|L?t Lu t|LU@t|U@**) i^@*i?| LMiU|tc ,UL?L4U wi||ihtc eec H.bf dSo 6h@4c #L?@*_ B @?_ wii 6 5Uh@_ihc b.fc ? i Tih4i?|@* UL4T@htL? Lu ThU?} ? |L @U|L? t)t|i4tc 4ihU@? aLh?@* Lu }hU*|h@* ,UL?L4Utc D2c D2HD e d.o B@*ic W@? w @?_ #L?@*_  O@tUc bbec L||L4€t?} @?_ _iU*??} ThUit ? ti ^i?|@* @U|L?tc B@4it @?_ ,UL?L4U i@Lhc .c H  dHo BT|@c 5@?| 5c B@h)  U#L?@*_ @?_ #@?i W B@*@h?i@c b.ec L4i?|tc ThL_U| 4L4i?|t @?_ TihUi?|@}i TL?|t Lu |i Lh_ih t|@|t|Ut uhL4 |i *L}?Lh4@* _t|hM|L? uLh t@4T*it Lu t3i |i?|) @?_ *ittc 5@?!)7@G Ai W?_@? aLh?@* Lu 5|@|t|Utc Sc 5ihit c 2 f2Sf dbo w@gL?|c ai@?a@U^it @?_ ai@? AhL*ic bb c  |iLh) Lu ThLUhi4i?| @?_ hi}*@|L? EWA hitt dfo @||itc 5|ii?c bH.c L4T@h?} @U|L?t uLh ht! @ihti M)ihtG  M)ih


dDo 5?!i*tc aihLi?c bbc *|?|c 4*|TihL_ @U|L?tc tTT*) ?Uih|@?|)c @?_ |i iUi?U) Lu t)44i|hU i^*Mh@c ?TM*ti_ 4@?tUhT|c h?Ui|L? N?iht|) dSo VU!hi)c `**@4c bSc L?|ihtTiU*@|L?c @U|L?tc @?_ UL4Ti||i ti@*i_ |i?_ihtc aLh?@* Lu 6?@?Uic Sc H . d.o `iMihc +LMih| ac bH c *|T*iLMiU| @U|L?tc ?G +U@h_ ,?}i*MhiU|`}}@?tc @h|? 5M! @?_ +LMih|  5|@h!c i_tc U|L?tc __?} @?_ L?|h@U|?}G Ntit @?_ AiLh) Ei vLh! N?iht|) hitt SDb

e

Sequential Auctions with Supply Uncertainty

Page 1 ... earlier draft. Remaining errors are my own. 1 ..... requirement for the seller will in turn make him unable to take full advantage of his own. 7One could ...

277KB Sizes 0 Downloads 432 Views

Recommend Documents

Auctions with Online Supply - Microsoft
Therefore, for any set of bidders bi such that for all bi, pbi = vbi , then any deterministic truthful mechanism that achieves an n-approximation can only sell the first ...

Auctions with Online Supply - Microsoft
Aaron L. Roth. Computer Science Department ... work in computer science on online mechanism de- .... and they require a high level of trust in the auction- eer.

Auctions with Online Supply - Microsoft
work in computer science on online mechanism de- ... online envy-free (a desirable fairness property that ... ing a truthful, online-envy-free mechanism which.

Sequential Descending-Price auctions with asymmetric ...
Nov 23, 2000 - The paper reports an analysis of price behaviour at a fish market which is or- .... they symmetrised? buyers by assuming that one large buyer (who bought ... The work of Ginsburgh (1998) on wine auction data stands as an ...

Uniform vs. Discriminatory Auctions with Variable Supply
Sep 8, 2009 - ... Str. 58, 69115 Hei& delberg, Germany, email: oechssler@uni&hd.de ..... case as a benchmark for our experimental results. 3 Experimental ...

Auctions with Variable Supply: Uniform Price versus ...
Aug 26, 2009 - 1201 West University Drive, Edinburg, Texas 78539, USA, email: ... consider a model of a perfectly divisible good in which the marginal cost of the seller is known to the ..... If 0 ≤ xi ≤ x−i/2, it is not profitable for the sell

Uniform vs. Discriminatory Auctions with Variable Supply
Sep 8, 2009 - [8] Greiner, B. (2004), sThe Online Recruitment System ORSEE 2.0 uA. Guide for the ..... phone and donrt switch it on until the end of the experiment. If you have ... After answering the questionnaire, please come to the ...

Auctions with Variable Supply: Uniform Price versus ...
Feb 4, 2008 - Drive, Edinburg, Texas 78541-2999, USA, email: [email protected]. ♢CER-ETH ... units of a good to two or more buyers in an auction. Buyers are ...... bidder i, which shifts the probability mass of an interval Zε. ∗ := [z∗,z∗ .

Auctions with Variable Supply: Uniform Price versus ...
Aug 26, 2009 - We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty, where uncertainty is caused by the interplay of t

Bidders' and Sellers' Strategies in Sequential Auctions ... - CiteSeerX
empirical problem using data on auctions of modern and contemporary art objects ... The assumption of unbiased estimates has two important consequences. .... objects sold in an auction, is fairly big and is likely to imply a negligible bias.8.

Bidders' and Sellers' Strategies in Sequential Auctions ... - CiteSeerX
Using dynamic panel data econometric techniques, we analyze the price ... and the dynamic nature of price determination, we propose an interpretation of the ...

Auctions with Intermediaries
to buy via intermediaries. Our motivation arises from ad auctions on the Internet. In sponsored search auctions, online advertisers may use in- termediaries to bid ...

Auctions with Limited Commitment
Jun 7, 2017 - ‡University of College London, [email protected]. §University of Toronto ... buyers which helps extract higher payments from high-valued buyers. If no bidder bids above .... buyers accept the posted price. 5 ..... density of th

Sequential Negotiations with Costly Information ...
Aug 1, 2013 - Sonat “stated that other parties had expressed interest in a business combination ...... No sale to a noninspecting bidder occurs before the final period, since the option to .... The item is a startup with a novel tanning technology.

With Sequential Service Taken Seriously
random times) in a discrete model." However, they did not appeal to these hints when they asserted consistency between the sequential service constraint and the policy that they identify with deposit insurance and that overcomes the difficulties asso

Asymmetric Auctions with Resale
Auctions with two asymmetric bidders. • Only the winning bid is ... revenue results are few and far between. ... Observation: the FOC for the symmetric first-price.

Sponsored Search Auctions with Markovian Users - CiteSeerX
Google, Inc. 76 Ninth Avenue, 4th Floor, New ... tisers who bid in order to have their ad shown next to search results for specific keywords. .... There are some in- tuitive user behavior models that express overall click-through probabilities in.

Equilibrium in Auctions with Entry
By the induced entry equilibrium, Bi(q*, Ω)=0,thus seller's expected revenue constitutes total social welfare: • PROPOSITION 1: Any mechanism that maximizes the seller's expected revenue also induces socially optimal entry. Such a mechanism migh

Ascending Auctions with Package Bidding
Warner Amex. 13,700,000. 4. RCTV ..... auction with two bidders in which both bidders pay their own bids but only the ...... bid (T-bill mechanism). ◇ Vickrey's ...

Efficiency in auctions with crossholdings
Nov 21, 2002 - i's valuation, i =1, 2,3, denoted by vi, is private information to i. Each valuation is drawn independently from an interval [0, 1] according to the same strictly increasing distribution function F with corresponding density f. F is co

Uncertainty Propagation with Monotonicity Preserving ...
Center for Mathematics and Computer Science (CWI), .... terms, where pj(x) is the local polynomial degree of wj(x, ξ) in Ξj. The coefficients cj,i(x) are determined.

Monetary Policy with Uncertainty Conclusions
Data uncertainty: – Certainty equivalence ... Data and model uncertainty together can explain gradual Fed policy. 2 ... Active learning computationally intensive.

Observational Learning with Position Uncertainty
Sep 15, 2014 - Keywords: social learning, complete learning, information ...... The graph on the left side of Figure 1 represents the weights wt,τ agent t place on ...

Data integration with uncertainty
Feb 17, 2008 - This section describes the requirements from a data integra- tion system that supports uncertainty and the overall archi- tecture of the system.