On Market Games When Agents Cannot be Two Places at Onces

? @h!i| B@4it `i? }i?|t @??L| Mi AL
*@Uit @| ?Ui
+L_ B@hh@|| @?_ i?}~L?} "?
#iT@h|4i?| Lu ,UL?L4Ut
N?iht|) Lu @*uLh?@
5@?|@ @hM@h@c bfS
a*) 2.c bbH
Devwudfw
Zh frqvlghu pdunhwv lq zklfk djhqwv vxsso| wkhlu wlph ru wkh vhuylfhv ri
d fdslwdo jrrg/ dqg wkh gxudwlrq ri wkh pdunhw lv olplwhg1 Zh vkrz wkdw d
frdolwlrqdo jdph fdq eh jhqhudwhg e| vxfk d pdunhw li dqg rqo| li wkh fkdudf0
whulvwlf ixqfwlrq ri wkh jdph lv vxshudgglwlyh1 Zh dovr fkdudfwhul}h wkh yhfwruv
ri edodqflqj zhljkwv wkdw duh dvvrfldwhg zlwk ihdvleoh sodqv iru iruplqj frdol0
wlrqv lq d wlph0frqvwudlqhg pdunhw1 Wkhvh duh vkrzq wr eh wkh vdph dv wkh
rqhv jhqhudwhg iurp d pdunhw zlwk lqglylvleoh djhqwv dqg orwwhulhv1
Zh
wkdqn vhplqdu sduwlflsdqwv dw XFOD/ XFVG/ wkh Xqlyhuvlw| ri Dul}rqd/ wkh 4<<; Hfrqrplf
Wkhru| Frqihuhqfh lq Yhqlfh/ dqg wkh Qlqwk Vwrq| Eurrn Vxpphu Ihvwlydo lq Jdph Wkhru| iru
khosixo frpphqwv1 Zh duh sduwlfxoduo| judwhixo wr Eloo ]zlfnhu dqg Oor|g Vkdsoh| iru wkhlu uhpdunv1


W?|hL_U|L?
W? tTiUu)?} @ 4@h!i|c |i T)tU@* ThLUitt Lu |h@_i t t@**) }?Lhi_ OLiihc
@hLt @tTiU|t Lu |i |h@_?} ThLUitt U@? Mi 4TLh|@?| ? _i|ih4??} U @**LU@
|L?t @hi ui@tM*i ? |i 4@h!i| W? T@h|U*@hc tTTLti @** i U@?}it 4t| Mi 4@_i
? TihtL?c @t L*_ Mi |i U@ti u |i UL44L_|it tTT*i_ M) ?__@*t ihi |ih
|4i hc 4@}?i |@| ?__@*t TLttitt U@T|@* }LL_t |@| ThL_i tihUit Lih
|4ic tU @t @ }i?ih@|Lh |@| ThL_it i*iU|hU|) Lh @ UL4M?i @hit|ih Ai?c |i
|4i @@*@M*i uLh |h@_it |L LUUh 4@) *4| |i ti| Lu ui@tM*i i U@?}it
AL **t|h@|i |t _i@c tTTLti |hii ?__@*t @hi t|h@?_i_ L? @ _itih| t*@?_
Ai) ** Mi L? |i t*@?_ uLh L?*) L?i _@)c @?_ @hi TL?_ih?} i|ih |L tTi?_
|i |4i tiT@h@|i_ Lh ? }hLTt L?t_ih @ T*@? ihiM) i@U ?__@* @}hiit |L
tTi?_ @*u @ _@) | i@U Lu |i L|ih |L ?__@*t Ai |4i tTT*i_ M) i@U
?__@* i^@*t ih |4i i?_L4i?|c M| |i T*@? t ?L| ui@tM*i t?Ui | hi^hit
tL4iL?i |L Mi ? |L T*@Uit @| L?Ui
Ai _itih| t*@?_ t|Lh) U@T|hit 4TLh|@?| ui@|hit Lu 4@?) t|@|L?t ihi
ULLTih@|i @U||it |@!i T*@Ui ? hi4L|i *LU@|L?t 5Ui_*?} uLh @ ThLuittL?@*
4ii|?}c ULLh_?@|?} @U||it L? @ tT@Ui t|@|L? Lh @tt}??} ?__@*t |L €h4t
@hi @** Th@U|U@* i @4T*it Ai !i) ui@|hit @hi |@| ?__@*t tTT*) |ih |4i @?_
|4i t UL?t|h@?i_ M) |i _h@|L? Lu |i ii?| |@| Mh?}t |i ?__@*t |L}i|ih
A4?} UL?t_ih@|L?t 4T@U| |i ui@tM*i @**LU@|L?t ? |i 4@h!i| @?_ ? |h?
@giU| |i U*@tt Lu }@4it |@| U@? Mi }i?ih@|i_ uhL4 tU 4@h!i|t `|L| |i
|4?} hit|hU|L?t |i _itih| t*@?_ 4@h!i| t @ _hiU| 4@h!i| @t _i€?i_ M) 5@T*i)
@?_ 5M! EbSbc @?_ |i U*@tt Lu }@4it |@| U@? Mi }i?ih@|i_ M) tU 4@h!i|t
t |i U*@tt Lu |L|@**) M@*@?Ui_ }@4it Ai 4@TT?} uhL4 @ 4@h!i| |L @ }@4i tit
?uLh4@|L? L? @** |i ui@tM*i @**LU@|L?t Lu |i 4@h!i| |L }i?ih@|i |i U@h@U|iht|U
u?U|L? Lu |i }@4i ) hit|hU|?} |i ti| Lu ui@tM*i @**LU@|L?t Lu |i 4@h!i|c |i
ThLTih|it Lu }@4it }i?ih@|i_ M) |i 4@h!i| @hi @*|ihi_
W? |t T@Tihc i UL?t_ih |4iUL?t|h@?i_ _hiU| 4@h!i|t `i tL |@| @ UL@*
|L?@* }@4i U@? Mi }i?ih@|i_ M) @ |4iUL?t|h@?i_ 4@h!i| u @?_ L?*) u |t U@h@U
|iht|U u?U|L? t tTih@__|i `i ThL_i @? i @4T*i |L **t|h@|i |i hit*|c @?_
|i 4TLh|@?Ui Lu |@!?} @UUL?| Lu |4i hit|hU|L?t `i @*tL _i?|u) |i tMti|
Lu iU|Lht Lu M@*@?U?} i}|t uLh @ }@4i |@| @hi @ttLU@|i_ | ui@tM*i UL@*|L?
uLh4@|L?t ? @ |4iUL?t|h@?i_ i?hL?4i?| At tMti| t tL? |L Mi |i t@4i
@t |i tMti| Lu iU|Lht Lu M@*@?U?} i}|t }i?ih@|i_ uhL4 @ 4L_i* | ?_t
4 E|
jdphv/ zh phdq frdolwlrqdo jdphv zlwk wudqvihudeoh xwlolw| dv ghqhg e| Vkdsoh| +4<9:,1
2
M*i UL44L_|it @?_ *L||ihit 6?@**)c i ThL_i @ t4T*i U@h@U|ih3@|L? Lu |iti
iU|Lht i? |ihi @hi *itt |@? €i @}i?|t
2
Ai 5|@?_@h_ TThL@UG @*@?Ui_?itt @?_ AL
|@* @*@?Ui_?itt
UL@*|L?@* }@4i | |h@?tuih@M*i |*|) Ei?UiuLh|c @ }@4i t @ T@h Ec c
ihi ' ic 2c c ?j t |i T*@)ih ti| @?_ t |i U@h@U|iht|U u?U|L? _i€?i_
L? |i u@4*) 2 Lu @** tMti|t Lu 6Lh 7 c E7 t |i Lh| Lu |i UL@*|L?
7c U t |i 4@ 44 |L|@* |*|) |i 4i4Miht Lu 7 U@? LM|@? Ai @*i Lu
|i i4T|) UL@*|L? t 3ihL Ai T@h Ec ?L*it |h@?tuih@M*i |*|) MiU@ti |i
U@h@U|iht|U u?U|L? t @tt4i_ |L _i|ih4?i @ ti| Lu ui@tM*i |*|) @**LU@|L?t
S
T E7 ' i 5 U m M7 E7j uLh i@U UL@*|L? 7
7
6Lh @?) UL@*|L? 7 c *i| e7 _i?L|i @ iU|Lh ? U
n tU |@| e '  u 5 7 @?_
7
A
e ' f u 5
* 7 6Lh A c *i| KEe Mi |i ti| Lu ?L? ?i}@|i iU|Lht ' E7 7 \
tU |@|
[
7 e7 ' eA E
7 \
iU|Lh 5 KEeA t !?L? @t @ iU|Lh Lu M@*@?U?} i}|t Lu |i tM}@4i EAc tM}@4i EAc t M@*@?Ui_ u
[
7 \
7 E7 EA E2
L*_t uLh iih) 5 KEeA W? |i *@|i t |itc w*L)_ 5@T*i) @?_ @h|? 5M! ?|hL_Ui_ |i ?L|L? Lu @
4@h!i| }@4i 4@h!i| }@4i t @ UL@*|L?@* }@4i |@| t }i?ih@|i_ uhL4 @ 4@h!i|
M) ti||?} |i Lh| Lu @?) UL@*|L? ? |i }@4i i^@* |L |i |L|@* |*|) 4i4Miht Lu
|i UL@*|L? U@? @Uii ? |i 4@h!i| Ai 4@h!i|t 5@T*i) @?_ 5M! UL?t_ih @hi
i U@?}i iUL?L4it ? U UL44L_|it @hi TihuiU|*) _tM*i @?_ @}i?|t< |*|)
u?U|L?t @hi UL?|?Lt @?_ UL?U@i N|*|) t 4i@thi_ ? ?|t Lu 4L?i)c @?_
@}i?|t U@? i U@?}i UL44L_|it @?_ |h@?tuih 4L?i) ? @?) @4L?| 5@T*i) @?_
5M! EbSb it|@M*t |@| @ }@4i t @ 4@h!i| }@4i u @?_ L?*) u | t |L|@**)
M@*@?Ui_G iih) tM}@4i t M@*@?Ui_
Ai ?|ihThi|@|L? Lu |i iU|Lht Lu M@*@?U?} i}|t ti_ ? |i |it| uLh M@*
@?Ui_?itt _iTi?_t L? |i |)Ti Lu ?|ih@U|L? Mi?} 4L_i*i_( T@h|U*@h*)c L? |i
4@??ih ? U @}i?|t T@h|UT@|i ? UL@*|L?t Ai ?|ihThi|@|L? i @_LT| ihi
t |@| @}i?|t T@h|UT@|i ? UL@*|L?t M) tTT*)?} |ih |4i2 Ai?c iU|Lht Lu
5 Wklv
lqwhusuhwdwlrq lv rhuhg dv d _qdwxudo% rqh e| Dxpdqq +4<;</ s1 75,1 Zh zrxog olnh wr
M@*@?U?} i}|t tTiUu) _h@|L?t uLh @** |i TLttM*i UL@*|L?t |@| @hi ui@tM*i
}i? |i |4i i?_L4i?|t Lu |i @}i?|t
6L**L?} |hL} L? |t ?|ihThi|@|L? | MiUL4it @TT@hi?| |@| uLh |i |it| Lu
M@*@?Ui_?itt _itUhMi_ ? E2 |L Mi @TThLTh@|ic |i |4i @@*@M*i uLh uLh4?} UL@*
|L?t 4t| Mi ?*4|i_ |ihtic i UL*_ @UU_i?|@**)< h*i L| tL4i }@4it @t
U@?__@|it uLh 4@h!i| }@4it L? |i M@tt Lu UL@*|L? uLh4@|L?t |@| @hi ?L| TLttM*i
Ai _i@ t **t|h@|i_ ? |i uL**L?} i @4T*i
Ai iU!iht B@4i G L?t_ih @ }hLT Lu ? @}i?|t L @hhi @| @ UL44?|)
@** |L T*@) UiU!iht Ai @** t LTi? uLh L?i Lh @?_ i@U @}i?| t|@)t uLh |i
L*i Lh }i?|t hiUii |*|) i^@* |L L?i@*u |i @4L?| Lu |4i |i) tTi?_
4@|Ui_ | @?L|ih ?__@* T*@)?} UiU!iht Ai ?_ih*)?} UL@*|L?@* }@4i
@t @ U@h@U|iht|U u?U|L?
%
&
m7m
E7 '
c 7 c
2
ihi m7m _i?L|it |i U@h_?@*|) Lu 7c @?_ d@o _i?L|it |i }hi@|it| ?|i}ih *itt |@?
Lh i^@* |L @
5TTLti ? t }hi@|ih |@? |hii @?_ ii? Ai?c |t }@4i t M@*@?Ui_c M| @?)
tM}@4i | @? L__ ?4Mih E}hi@|ih |@? L?i Lu @}i?|t t ?L| M@*@?Ui_ 6Lh
?t|@?Uic UL?t_ih |i tM}@4i EAc c | A ' ic 2c j Ai? ' E7 7 \ |
tc2 ' tc ' t2c ' *2c @?_ 7 ' f L|ihtic t @ iU|Lh Lu M@*@?U?} i}|t
uLh |i tM}@4ic M| 2 Eic 2j n 2 Eic j n 2 Ei2c j '  2 : EA '  Oi?Uic
|i tM}@4i t ?L| M@*@?Ui_ @?_ tL |i }@4i t ?L| |L|@**) M@*@?Ui_ AihiuLhic
| U@??L| Mi hiThiti?|i_ @t @ 4@h!i| }@4i Lu |i |)Ti UL?t_ihi_ M) 5@T*i) @?_
5M! EbSb
U@hiu* hi@_?} Lu |i UhU4t|@?Uit Lu |i UiU!iht }@4i hii@*t |@| |t _t
^@*€U@|L? @t @ 4@h!i| }@4i 4@) Mi Thi4@|hi Ai iU|Lh Lu M@*@?U?} i}|t
ti_ |L L*@|i |i M@*@?Ui_?itt UL?_|L? uLh |i tM}@4i EAc _Lit ?L| ULhhitTL?_
|L @ ui@tM*i T*@? uLh uLh4?} UL@*|L?tc t?Ui |i ThLTLti_ T@h?}t UL*_ ?L| |@!i
T*@Ui ? L?i Lh AL ThLTih*) i@*@|i |i UiU!iht }@4ic @?_ L|iht *!i |c i
?ii_ |L UL?t_ih @ uh@4iLh! |@| ?ULhTLh@|it |4i hit|hU|L?t W? @| uL**Ltc
i i@*@|i 4@h!i| }@4it ? @ uh@4iLh! ihi @}i?|t tTT*) @ ?| Lu |4i |@| t
i^@* |L |i |4i @@*@M*i uLh uLh4?} UL@*|L?tc @?_ @}i?|t U@??L| Mi |L T*@Uit @|
hpskdvl}h wkdw vxsso|lqj wlph fdq phdq d ydulhw| ri wklqjv/ vxfk dv shuiruplqj sk|vlfdo oderu/
surylglqj eudlq srzhu/ ru frqwulexwlqj wkh vhuylfhv iurp d fdslwdo jrrg1 Iru lqvwdqfh/ dq krxu ri
wlph iurp wkh rzqhu ri d frpelqh kduyhvwhu frxog phdq wkh xvh ri wkh frpelqh kduyhvwhu iru dq
krxu1 Pruhryhu/ rqh frxog ghqh fdslwdo jrrgv wkhpvhoyhv wr eh djhqwv1
6 Wklv jdph lv d vlpsolhg yhuvlrq ri Vkxeln*v _Eulgjh Jdph1% Vhh Vkxeln +4<:4,1
e
L?Ui B@4it |@| U@? Mi }i?ih@|i_ uhL4 4@h!i|t | |iti hit|hU|L?t @hi U@**i_
|4iUL?t|h@?i_ 4@h!i| }@4it
A4iL?t|h@?i_ @h!i| B@4it
Ai ThLUi_hi i uL**L |L U@h@U|ih3i }@4it |@| U@? Mi }i?ih@|i_ M) |4i
UL?t|h@?i_ 4@h!i|t E|4iUL?t|h@?i_ 4@h!i| }@4it t |i L?i ti_ M) 5@T*i)
@?_ 5M! EbSb @4i*)c i t|@h| | @? @hM|h@h) }@4i @?_ ti | |L }i?ih@|i
@ |4iUL?t|h@?i_ _hiU| 4@h!i| Ai? i ti |i |4iUL?t|h@?i_ _hiU| 4@h!i|
|L }i?ih@|i @ |4iUL?t|h@?i_ 4@h!i| }@4i Ai LMiU|i t |L €?_ @ ?iUitt@h)
@?_ tUi?| UL?_|L? L? |i ?|@* }@4i tL |@| | @?_ |i }i?ih@|i_ }@4i @hi |i
t@4i
5|iT L?i t |L ti @? @hM|h@h) }@4i Ec |L }i?ih@|i @ |4iUL?t|h@?i_ _hiU|
4@h!i| Ai ti| Lu @}i?|t ? |i 4@h!i| t c @?_ |i UL44L_|) tT@Ui t U
n
,?_L4i?|t @hi |i iU|Lht et 5 U
c
'
c
c
?
Atc
i@U
@}i?|
t
i?_Li_
|
n
L?i ?| Lu ih L? |4i
6Lh A c *i| SA _i?L|i |i ti| Lu T@h||L?t Lu Ac @?_ S ' ^A \ SA Ai?c iih)
5 S hiThiti?|t @ ti| Lu UL@*|L?t |@| 4@) Mi tUi_*i_ E@U|i t4*|@?iLt*)
}i?|t @hi @tt4i_ |L @i _i?|U@* |*|) u?U|L?t |@| @hi _i€?i_ @t uL**LtG
Bi? % 5 U
nc
#
$
E% ' 4@
S
kG<Un M
k
S
-M
tMiU| |L #
$
S S
E
k
e
' %(
E
M
S
M
E-
E
-M
k 
Ai @) |L ?|ihThi| E t |L |?! Lu @ iU|Lh % @t Mi?} ?tUi_*i_ |4ic @?_
|i tL*|L? @t Mi?} @? LT|44 tUi_*i Ai i}| k tTiU€it |i @4L?| Lu
|4i _h?} U UL@*|L?t ? @hi t4*|@?iLt*) @U|i Ai hit|hU|L? Lu k |L
T@h||L?t hiiU|t |i hi^hi4i?| |@| @}i?|t U@??L| Mi |L T*@Uit @| L?Ui L|i
S
|@| -M e- ' e ihi ' ^-M - Atc UL?_|L? E t |i hi^hi4i?| |@|
i@U @}i?| t tUi_*i_ uLh i @U|*) % ?|t Lu |4i L?_|L? E i?thit |@| |i
tUi_*i U@? Mi UL4T*i|i_ |? L?i ?| Lu |4i
+i4@h! @ `|L| *Ltt Lu }i?ih@*|) @tt4i |@| % %2 %? 5i|
 ' i jc 2 ' i qijjc c ? ' ii?jj L?t_ih k G S $ Un ihi k  ' % c
k ' % S
3
'
% uLh ' 2c c ?c @?_ k ' f L|ihti Ai?c k t@|t€it |i UL?
D
t|h@?|t AihiuLhic |i UL?t|h@?|t Lu E @hi UL?tt|i?|
+i4@h! M Ai ti| Lu TL?|t t@|tu)?} |i UL?t|h@?|t t U*i@h*) U*Lti_ AihiuLhic
|i 4@ 44 i t|t
wi| E% _i?L|i |i ti| Lu tL*|L?t uLh E Ai?c k 5 E% t @? LT|44
@) |L tUi_*i UL@*|L?t }i? |i UL?t|h@?|t |@| |i |4i @@*@M*i uLh tUi_*?}
UL@*|L?t t L?i ?| @?_ @}i?|t U@??L| Mi |L T*@Uit @| L?Ui W? |i U@ti ihi % '
e7 c |i tTTLh| Lu |i tL*|L?t |L E t UL?€?i_ |L T@h||L?t Lu 7 At UL?i?i?|
ThLTih|) t Thiti?|i_ ? |i uL**L?} *i44@
wi44@  Bi? % ' e7 c u k t@|t€it E @?_ E Lu E |i? k : f 4T*it 5 S7
S
@?_ M7 k ' 
hLLu `i? % ' e7 uLh tL4i 7 c E MiUL4it Et?} ' ^-M -c
[
M
At
k e ' e7 Ee
S
S
M k  ) Ec M k ' c U 4T*it |@| Ee t i^@*i?| |L
[
k Ee e7 ' fc
M
Lh
[
M
k Ee .7 e7 . ' f
At *@t| i^@|L? t ? |h? i^@*i?| |L
[
M
k e .7 ' f @?_
[
M
k e7 . ' f
ED
5?Ui k fc uLh @** 5 Sc ED 4T*it k ' f i?iih 9' 7 ",#
A@| UL4T*i|it |i tTiU€U@|L? Lu |i |4iUL?t|h@?i_ _hiU| 4@h!i|
5|iT |L t |L ti |i |4iUL?t|h@?i_ _hiU| 4@h!i| |L }i?ih@|i @ }@4i Ec 6Lh |t i hi^hi |i uL**L?} _i€?|L?c |@| t|@|it |i UL?_|L? uLh UL4T@|M*|)
Lu @ UL**iU|L? Lu ?__@* tL*|L?t |L E
#i€?|L?  6Lh 7 c Ek M7 | k G S $ Un c 5 7c t UL4T@|M*i uLh 7 u
S k t@|t€it E @?_ E | % ' e7 M7
S
Ai }@4i Ec t ?L }i?ih@|i_ @t uL**LtG 6Lh i@U 7 c
E7 '
[
4@
E% M7 Mf 7 M7
E% c
ES
ihi
;
A
A
?
7
f ' E% M7 A
A
=
<
A
A
@
% 5 U
c ; 5 7(
S n 7
% 'e (
M7
; 5 7c <
k
5
E% G
Ek M7
t UL4T@|M*i uLh 7
A
A
>
+i4@h! 2 L?t_ih E% M7 | % ' e7 uLh tL4i 5 7c @?_ % ' fc uLh 5 7 |
S
S
9' Ai?c M) wi44@ c k 5 Ee7 t@|t€it M7 k '  @?_ M7 k e7 ' e7 S
5?Ui Ef ' ifjc |t 4T*it |@| M7 k t UL4T@|M*i uLh 7c uLh @** Ek M7 tU
|@| k 5 E% c 5 7 Oi?Ui |i ti| f 7 t ?L| i4T|)
AL ?_iht|@?_ |i UL?t|hU|L? Lu |i U@h@U|iht|U u?U|L? c | i*Tt |L |?!
Lu @}i?|t uLh U % 9' f ? ES @t Mi?} 4@?@}iht L @**LU@|i @}i?|t< |4i ?|L
LT|44 tUi_*it @UULh_?} |L Ee Ai?c E7 t ?_iht|LL_ @t hiThiti?|?} |i
4@ 44 |L|@* |*|) uLh |i UL@*|L? 7 Lih @** _t|hM|L?t Lu |i |L|@* |4i
i?_L4i?| uLh U |i 4@?@}iht< tL*|L?t |L E @hi UL4T@|M*i
AiLhi4  E5?}*i @?@}ih AiLhi4 E7 ' Ee7 hLLu 6Lh @** E% M7 5 f 7 |ihi i t|t k G S $ Un c 5 7 tU |@| Ek M7
S
t UL4T@|M*i 5i| k ' M7 k Ai?c |i UL4T@|M*|) Lu Ek M7 4T*it |@| k
t@|t€it E @?_ E | % ' e7 Atc
Ee7 ? |i L|ih @?_c
E% '
[
M
[
M
#
k
k
[
-M
#
[
-M
$
E- $
E-
uLh 5 7 5Lc
[
M7
7 Uhfdoo
E% #
$#
$
#
$
[ [
[
[
'
k
E- '
k
E- M M7
-M
M
-M
[
wkdw {l lv d yhfwru zlwk frpsrqhqwv {lm > m 5 V=
.
Atc E7 Ee7 LLti 5 7 @?_ UL?t_ih E% M7 ihi % ' e7 uLh tL4i 5 7c @?_ % ' f
S
uLh 5 7 | 9' Ai?c M) +i4@h! 2c E% M7 5 f 7 5?Ui
E% ' Ee7 c
M7
E7 Ee7 ",#
AiLhi4  t@)t |@| ? @ |4iUL?t|h@?i_ 4@h!i| |i @*i Lu @ UL@*|L? U@? Mi
_i€?i_ M) }?} UL?|hL* Lu |i i?|hi i?_L4i?| Lu |i UL@*|L? |L @ t?}*i @}i?|
A@| UL4T*i|it |i ThLUitt Lu }L?} uhL4 @ }@4i |L @ 4@h!i| @?_ M@U! |L @ }@4i
#i€?|L? 2 }@4i Ec t @ |4iUL?t|h@?i_ 4@h!i| }@4i u E7 ' E7c uLh
@** 7 #i€?|L? }@4i Ec t tTih@__|i u E7 n E7 E7 ^ 7 uLh @**
7c 7 tU |@| 7 _ 7 ' >
AiLhi4 2 }@4i Ec t @ |4iUL?t|h@?i_ 4@h!i| }@4i u @?_ L?*) u | t
tTih@__|i
hLLu 5TTLti Ec t @ |4iUL?t|h@?i_ 4@h!i| }@4i Ai?c M) AiLhi4 c uLh
S
S
@?) 7 c E7 ' Ee7 ) wi44@ c Ee7 ' 4@
k
E- tMiU| |L
M7
-M
S
7 S E-c uLh @** 5 S AihiuLhic
k
'

Oi?Uic
Ee
7
M7 -M
S
E7 E-c uLh @** 5 S7 At tLt |i }@4i Ec t tTih@__|i @?_
-M
k G S7 $ Un |
i?Ui |i UL?_|L? t ?iUitt@h)
5TTLti ?L |@| |i }@4i Ec t tTih@__|i 6Lh @?) E% M7 5 f 7 |ihi
i t| k G S $ Un uLh 5 7 tU |@|
[
M7
ihi k '
 Atc
E% '
#
[
M
k
[
-M
$
E-
S
S
k '
M7 k 5?Ui Ek M7 t UL4T@|M*i uLh UL@*|L? 7c M) wi44@ c
M7
[
M7
5?Ui Ec t tTih@__|ic
E% S
-M
'
#
[
M7
k
[
-M
$
E- E- E7 uLh @** 5 S7 At
S
M7
E% E7
U 4T*it |@| E7 E7 ? |i L|ih @?_c E7 ' Ee7 c M) AiLhi4  )
UL?t|hU|L?c Ee7 E7c U 4T*it |@| E7 E7 AihiuLhic E7 ' E7
tL?} |@| |i UL?_|L? t tUi?| ",#
H
e
Ai iU!iht B@4i +it|i_
+iU@** |i iU!iht }@4i uhL4 5iU|L? 2 `i @i @*hi@_) tL? |@| |i }@4i t
?L| |L|@**) M@*@?Ui_ uLh ? OLiihc |i }@4i t tTih@__|i A@| tc
%
&
%
&
%
&
m7m
m7 m
m7 ^ 7 m
n
' E7 ^ 7 c
E7 n E7 '
2
2
2
uLh @** 7c 7 tU |@| 7 _ 7 ' > Oi?Uic M) AiLhi4 2c |ihi i t|t @ |4i
UL?t|h@?i_ _hiU| 4@h!i| |@| U@? Mi ti_ |L }i?ih@|i |i }@4ic @?_ tL | t @
|4iUL?t|h@?i_ 4@h!i| }@4i
At t i@t*) _i4L?t|h@|i_ uLh |i U@ti Lu ' ic 2c c ej 6Lh 7 tU |@|
m7m 2c | t LMLt |@| E7 @?_ E7 @hi |i t@4i L?t_ih 7 ' ic 2c j Ai?c
@ tL*|L? Lu E | % ' e7 t k 5 Ee7 ihi
+
k '
 uLh ' iic 2jc ijj
f L|ihti
Oi?Uic Ee7 ' Eic 2j n Eij '  L?t_ih 7 ' Ai?c @ tL*|L? Lu E |
% ' e t k 5 Ee ihi
k '
+
 uLh ' iic 2jc ic ejj
f L|ihti
Oi?Uic Ee ' Eic 2jnEic ej ' 2 ) AiLhi4 c E7 ' Ee7 c uLh @** 7 Oi?Uic E7 ' E7c uLh @** 7 D
L4T@htL? | |i wL||ih) L_i*
W? B@hh@|| @?_ "? Ebb.c i UL?t_ih @ tUi?@hL ? U i@U @}i?| U@? T@h|UT@|i
? L?*) L?i UL@*|L? Eic @}i?|t @hi ?_tM*ic M| T@h|UT@|L? @?_ L?ihtT Lu
UL@*|L?t @hi _i|ih4?i_ h@?_L4*) W? |t UL?|i |c i tL |@| |i ti| Lu L?|
*L||ihit Lih T@h||L?t< Lu |i @}i?|t Lu @?) tM}@4i ?_Uit @ t|hU| tMti| Lu |i
ti| Lu iU|Lht Lu M@*@?U?} i}|t uLh |i tM}@4i
AL tii L |t Lh!tc € A c @?_ *i| 5 Mi |i ti| Lu A |T*it E7 MA Lu
UL@*|L?t ETLttM*) i4T|) |@| uLh4 @ Tti_LT@h||L? Lu A Eic 7 _ 7 ' > uLh
9' c @?_ ^MA 7 ' A c @?_ *i| t _i?L|i @ |)TU@* i*i4i?| Lu 5 6Lh i @4T*ic u
A ' ic 2jc |i? 5 ' iEAc c Ec A c Eijc i2jc Ei2jc ijj ,*i4i?|t t 5 5 @hi
U@**i_ @**LU@|L?tc t?Ui |i) tTiUu) @ UL@*|L? uLh i@U @}i?| wi| 5 E7 _i?L|i |i
ti| Lu @**LU@|L?t |@| }i 7 |L T*@)ih c @?_ *i| 5E7 ' ^MA 5 E7 _i?L|i |i ti| Lu
@**LU@|L?t |@| }i 7 |L tL4i T*@)ih 5 A
b
wi| O _i?L|i |i ti| Lu ThLM@M*|) _t|hM|L?t Lih 5c @?_ *i| KEeA _i?L|i |i
ti| Lu iU|Lht Lu M@*@?U?} i}|t uLh |i }@4i | @}i?|ti| A E5ii |i @TTi?_
uLh |i _i€?|L? Lu KEeA ,@U 5 O ?_Uit @ 5 KEeA @t uL**Lt EB@hh@|| @?_
"? Ebb.c hLTLt|L? G 6Lh 7 - Ac 7 ' fc @?_ uLh 7 A
7 ' E5E7 '
[
[
MA tM5 E7 Et
E.
6Lh i @4T*ic u A ' ic 2j |i? t ' Eijc i2j n Ei2jc ij @?_ A ' EAc > n
S
E>c A Atc t n A '  54*@h*)c t2 n A '  Oi?Uic 7 \A 7 e7 ' eA Ai
ti| Lu iU|Lht Lu M@*@?U?} i}|t ?_Ui_ ? |t u@tL? @hi _i?L|i_ M) Ku EeA W? |i Uhhi?| tUi?@hLc | |4i hit|hU|L?tc @ iU|Lh k t@|tu)?} E @?_ E Lu
E | % ' eA c ?_Uit @ iU|Lh 5 KEeA @t uL**LtG 6Lh 7 - Ac 7 ' fc @?_ uLh
7A
7 '
[
M G 7
k EH
Ai ?U*tL?c 5 KEeA c uL**Lt uhL4 wi44@  #i?L|i |i ti| Lu tU <t M)
K|3S EeA ,@U iU|Lh Lu M@*@?U?} i}|t ? K|3S EeA ULhhitTL?_t |L @ ui@tM*i T*@? uLh
uLh4?} UL@*|L?t ? |i |4iUL?t|h@?i_ 4L_i*c *i i@U iU|Lh Lu M@*@?U?}
i}|t ? Ku EeA ULhhitTL?_t |L @ ui@tM*i Et|LU@t|U T*@? uLh uLh4?} UL@*|L?t ?
|i *L||ih) 4L_i* Ai ?i | hit*| tLt |@| |i ti|t Ku EeA @?_ K|3S EeA @hi |i
t@4i
AiLhi4 Ku EeA ' K|3S EeA hLLu ) _i€?|L?c 5 Ku EeA t ?_Ui_ M) @ ThLM@M*|) _t|hM|L? Lih
T@h||L?t L? A Atc Ku EeA K|3S EeA t |h@*
wi| 5 K|3S EeA Ai? |ihi i t|t k G S $ Un t@|tu)?} E @?_ E Lu E |
% ' eA tU |@| t ?_Ui_ M) k @UULh_?} |L EH ) wi44@ c |ihi i t|t @
UL**iU|L? Lu T@h||L?t Lu A c i  c c 6 jc uLh U k & : f @?_
6
S
&'
k & '  6Lh
& ' c c 6c *i| & Mi @ A |T*i Lu UL@*|L?t tU |@| 7 5 & | 7 9' > u @?_ L?*)
u 7 5 & L?t_ih @ ThLM@M*|) _t|hM|L? tU |@| E & ' k & c & ' c c 6c
@?_ Et ' f uLh @** L|ih t 5 5 Ai? ?_Uit |i t@4i _t|hM|L? Lu UL@*|L? _
h@|L?t |@| i t|@h|i_ |c @?_ i?Ui 5 Ku EeA Atc K|3S EeA Ku EeA ",#
`i UL?U*_i |t tiU|L? M) TL?|?} L| |@| uLh mA m ec |ihi t @ t4T*i
@?_ ?||i U@h@U|ih3@|L? Lu Ku EeA @?_ K|3S EeA 5L4i @__|L?@* ?L|@|L? @?_
_i€?|L?t @hi hi^hi_
f
#i€?|L? e u@4*) E Lu UL@*|L?t UL?|@?i_ ? A t _hiU|*) UL??iU|i_ u 7 _ 7 9'
> uLh @?) |L i*i4i?|t 7c 7 ? E
wi| _i?L|i |i UL**iU|L? Lu @** tU u@4*itc @?_ _i€?i | G U2n $ Un M)
A
|EEc '
[
7 M
7 c ; EEc 5 U2n A
tt4?} |@| @}i?|t U@??L| Mi |L T*@Uit @| L?Uic |i UL@*|L?t ? @ _hiU|*) UL?
?iU|i_ u@4*) 4t| uLh4 ti^i?|@**) Atc |EEc t |i @4L?| Lu |4i hi^hi_ |L
uLh4 |i UL@*|L?t ? E }i? |i _h@|L?t Lu UL@*|L?t 7 5 E ThitUhMi_ M) wi|
E ' 4@ |EEc M
hLTLt|L?  5TTLti mA m e iU|Lh t ? K|3S EeA u @?_ L?*) u 5 KEeA @?_ E ' 
hLLu `i L?*) ThLi |i U@ti Lu mA m ' ec MiU@ti u | L*_t uLh |t U@ti |i? | 4t|
L*_ uLh @** mA m e 6ht| i ThLi ?iUitt|) wi| 5 K|3S EeA 6 @?_ UL?t_ih
|i u@4*) E ' i7 5 A G 5 7j At t @ _hiU|*) UL??iU|i_ u@4*) 6h|ih4Lhic
S
|EE c ' 7 M 7 ' c @?_ i?Ui E 
? |i L|ih @?_c uLh @?) _hiU|*) UL??iU|i_ u@4*) Ec wi44@  Lu B@hh@|| @?_
"? Ebb. 4T*it |@| 5E7_5E7 ' > uLh @** 7c 7 5 E Oi?Uic M) E. @?_ AiLhi4
|EEc '
[
7 M
7 '
[
7 M
E5E7 c
Et?Ui ^7 M 5E7 5 @?_ E5 ' c @?_ tL E  L4M?i_ i @i E ' c
tL?} |@| |i UL?_|L? t ?iUitt@h)
AL it|@M*t tUi?U)c *i| 5 KEeA @?_ E '  5i| EE ' i7 A m 7 : fj
@?_ ULLti 7 uhL4 EE tU |@| m7m ' 4@ im7m m 7 5 EEj Wu m7 m ' c |i?
EE t @ T@h||L? Lu Ac @?_ tL |i ThLLu t UL4T*i|i_ |ihtic i ** tL
|@| |ihi i t|t @ T@h||L? Lu A UL?|@??} 7 5TTLti m7 m :  Wu 7 9' Ac
|i? |ihi i t|t 7 5 EE tU |@| 7 _ 7 ' > At t |hi MiU@ti L|ihti
i7j ^ i7 5 EE m 7 6 j L*_ Mi _hiU|*) UL??iU|i_ uLh @?) 5 A q7c @?_ tL
E  n 7 : 
LLti 72 uhL4 EE tU |@| 72 _ 7 ' > @?_ m72 m ' 4@ im7m m 7 5 EE @?_
7 _ 7 ' >j 5?Ui mA m ' ec @?_ m72m m7m c 7 ^ 72 9' A 4T*it m72m '  Atc ?
|t U@tic |i @MLi @h}4i?| U@? Mi hiTi@|i_ |L tL |@| |ihi i t|t 7 ? EE

tU |@| 7 _ 7 ' > @?_ 7 _ 72 ' > 5?Ui m7 m :  @?_ mA m ' ec  ' i7 c 72c 7j
t @ T@h||L? Lu A L _i€?i ' E
7 M)
7 '
;
?
7
u 7 5
* (

= 7 4? 7 u 7 5 Eb
7 M
Mi @?) _hiU|*) UL??iU|i_
Ai?c 5 KEE keA c ihi k ' 4?7 M  7 wi| (
S
u@4*) uhL4 EE
' i7 A m 7 : fj `i ** tL |@| 7 M( 7 E k
5TTLti €ht| |@| m7m ' W? |t U@tic 7 ^ 72 ' A 5?Ui mA m ' e @?_ m7m ' c
u @?_ L?*) u 72 5 (
Atc M) Ebc S 7 ' S 7 4? 7  k 7 5
*(
7 M(
7 M(

7 M
5 ( 4T*it m7m 2 W? |t U@tic MiU@ti (
i7 5 EE
( 2c |i? (
m 7 6 j uLh
S
S
5 _7 M( 7 Oi?Uic 7 M( 7 7 G7 7 '  k tt4i |@| ( : 2 @?_ m7m ' 2
5?Ui @ u@4*) UL?|@??}
uLh @** 7 5 (
4Lhi |@? |hii 2@}i?| UL@*|L?t U@??L| Mi
' iic jc ic &jc ic 6jj Lh
' Atc i|ih (
_hiU|*) UL??iU|i_c i 4t| @i (
' iic &jc ic 6jc i&c 6jj W? |i €ht| U@tic (
E U 4T*it |@| S 7 (
7 M(
 k ' iic &jc ic 6jc i&c 6jj Wu m72 m ' 2c |i? 7 5 (
Lh 72 5 (
MiU@ti
wi| (
S
MiU@ti
i7c 72j t @ T@h||L? Lu A Atc 7 M( 7  k Wu m72 m ' c |i? 7 5 (
L|ihti |ihi L*_ i t| 7 5 EE
tU |@| 7 _ 7 ' > @?_ m7m ' 2 UL?|h@_U|?}
S
S
m72m '  }@?c 7 M( 7 ' 7 M( 7 4? 7  k `i @i |t tL? |@|
5TTLti ?L |@| m7 m ' 2 Ai?c 7
Lh
t _hiU|*) UL??iU|i_c u ij 5 (
7 M
E
 k 5?Ui 5 KEE k eA i @*tL @i E
 kc @?_ i?Ui
E
'  k L?t_ih  ' E7 _i€?i_ M) 7 ' 7 *E kc uLh @** 7 A 5?Ui 5 KEE keA @?_ E
'  k c i @i  5 KEeA @?_ E  '  LhiLihc mEE  m mEEm  5?Ui mEEm t €?|ic M) hiTi@|?} |i @MLi ThLUi_hi @ €?|i ?4Mih Lu
|4itc i LM|@? @ €?|i ?4Mih 6 Lu T@h||L?tc c 2 c c 6c @?_ TLt|i ?4Miht
k  c c k 6 tU |@|
[
7 '
k & c
& G 7 M &
uLh 7 A | 7 : f ",#
+i4@h! Bi? t 5 5c 7 c @?_ 5 c _i€?i K7 Et M) K7 Et '  u 5 7
@?_ 7 5 t( K7 Et ' f L|ihti wi| Et Mi |i 4@|h Lti hLt @hi ?_i i_
M) 5 c UL*4?t @hi ?_i i_ M) 7 c @?_ Lti Ec 7 i?|h) t K7 Et Ai?c
S
uLh @?) 5 Oc |i i?|hit Lu ' tM5 EtEt uLh4 @ M@*@?Ui_ iU|Lh ? Ku Ee wi| 5 KEe Mi }i? L?t_ih E ' EK7 E ihi K7 E ' 7 u 5 7 @?_
K7 E ' f L|ihti 6?_?} UL?_|L?t ?_ih U 5 Ku Ee t i^@*i?| |L
2
S
€?_?} UL?_|L?t L? E ?_ih U E ' tM5 EtEt uLh tL4i 5 O At
Mh?}t |L 4?_ @ i** !?L? hit*| M) h!Lg @?_ L? i4@?? EbSc wi44@ 2c T
eS U t@)t |@| @?) _LM*)t|LU@t|U 4@|h U@? Mi h||i? @t @ h@?_L43@|L? Lu
Tih4|@|L? 4@|hUitD OLiihc i U@??L| @TT*) |i h!Lg%L? i4@?? hit*|
t?Ui E t ?L| @ t^@hi 4@|h 6h|ih4Lhic Lh UL?_|L?t _L ?L| }@h@?|ii |i
S
i t|i?Ui Lu @? 5 O uLh U E ' tM5 EtEt u mA m : e wi| mA m ' Dc @?_
UL?t_ih |i iU|Lh | tc2 ' tc ' t2ce ' tcD ' tecD ' *2c @?_ 7 ' f
L|ihti *i@h*) 5 KEeA @?_ E ' c M| 5
* K|3S EeA S
L?U*_?} +i4@h!t
At T@Tih Mi}@? | |i LMtih@|L? |@| |i ?|ihThi|@|L? Lu iU|Lht Lu M@*@?U?}
i}|t @t ui@tM*i T*@?t uLh uLh4?} UL@*|L?t _iTi?_t TL? |i ?L|L? |@| UL4
4L_|it tTT*i_ M) @}i?|t @hi _tM*i ? @ ih) t|hL?} ti?ti @4i*)c |i) U@? Mi
__i_ @?_ tiT@h@|i_ A4i t _tM*i ? @ i@!ih ti?ti 6h@U|L?t Lu @? @}i?|<t
|4i U@? Mi tTT*i_ |L _gihi?| UL@*|L?tc M| _i*ihit 4t| |@!i T*@Ui ti^i?
|@**)c ?L| t4*|@?iLt*) `i @i @h}i_ |@| u |i |4i @@*@M*i uLh T@h|UT@|?}
? UL@*|L?t t *4|i_ |i? tL4i TLttM*|it uLh uLh4?} UL@*|L?t 4t| Mi h*i_
L| At t }LL_ ?it uLh |Lti ?|ihit|i_ ? €?_?} 4@h!i| ?|ihThi|@|L?t Lu }@4it
ihi @}i?|t tTT*) |ih |4i W| 4i@?t |@| ? t|@|L?t ihi |i |L|@* @4L?|
Lu |4i @@*@M*i uLh uLh4?} UL@*|L?t t *4|i_c |i @TThLTh@|i |it| uLh i|ih
Lh ?L| @ }@4i t @ 4@h!i| }@4i t 4U i@!ih |@? |L|@* M@*@?Ui_?itt ** |@| t
hi^hi_c t |@| |i U@h@U|iht|U u?U|L? Lu |i }@4i Mi tTih@__|i
4L_i* ? U @}i?|t tTT*) |ih |4i t UL4T@hi_ |L L?i | ?_tM*i
UL44L_|it @?_ *L||ihit `*i UL?UiT|@**) |i |L 4L_i*t @hi ^|i _gihi?|c
i _i?|u) @ ti?ti ? U |i) @hi _i?|U@*G Ai ui@tM*i @**LU@|L?t uLh i@U
Lu |i 4L_i*t }i?ih@|i |i t@4i ti| Lu iU|Lht Lu M@*@?U?} i}|t 6h|ih4Lhic
i ThL_i @ t4T*i U@h@U|ih3@|L? Lu |iti iU|Lht i? |ihi @hi uLh Lh uiih
@}i?|t At t @? ?|@* t|iT |L@h_t €?_?} @ tiu* U@h@U|ih3@|L? Lu |i ui@tM*i
@**LU@|L?t Lu |i |4iUL?t|h@?i_ ELh *L||ih) 4L_i* uLh @?) ?4Mih Lu @}i?|t
+iuihi?Uit
do + 4@??c RwiU|hit L? B@4i AiLh)c `it|i hittc L*_ihc bHb
d2o + B@hh@|| @?_ ~ "?c Lhit @?_ UL4Ti||i i^*Mh@ | ?_tM*|it
@?_ *L||ihitc aLh?@* Lu ,UL?L4U AiLh) SH EbbSc DDe
8 Wklv
uhvxow lv xvhg wr vlpsoli| wkh fkdudfwhul}dwlrq ri ihdvleoh orwwhu| doorfdwlrqv lq K|oodqg dqg
]hfnkdxvhu +4<:<, dqg Jduudww dqg Tlq +4<<9,1

do + B@hh@|| @?_ ~ "?c ? @ 4@h!i| uLh UL@*|L?t | ?_tM*i @}i?|t @?_
*L||ihitc aLh?@* Lu ,UL?L4U AiLh) .. Ebb.c Hf
deo O)**@?_ @?_ + ~iU!@tihc Ai iUi?| @**LU@|L? Lu ?__@*t |L TLt|L?tc
aLh?@* Lu L*|U@* ,UL?L4) H. Eb.bc 2be
dDo w5 5@T*i)c ? M@*@?Ui_ ti|t @?_ ULhitc @@* +iti@hU wL}t|Ut "@h|ih*) e
EbS.c eDeSf
dSo w5 5@T*i) @?_  5M!c ? 4@h!i| }@4itc aLh?@* Lu ,UL?L4U AiLh) 
EbSbc b2D
d.o  5M!c Ai Rh_}i B@4i iUL?L4)c aLh?@* Lu L*|U@* ,UL?L4) .b Eb.c
bfbb2
dHo a L? i4@??c Uih|@? 3ihLt4 |L TihtL? }@4i i^@*i?| |L |i LT|4@*
@tt}?4i?| ThLM*i4c ? RaL? L? i4@?? UL**iU|i_ `Lh!tG VL*4i VWc AiLh)
Lu B@4itc t|hLT)tUtc O)_hL_)?@4Ut @?_ i|iLhL*L}) E O A@Mc ,_c TT
eeebc @U**@?c i vLh!c bS
e