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Consider the following two-person non-zero sum game in extensive form to minimize costs ZcZ&" & "&"-"&"&"K"&"&    dNormal form analysis DM1: 3 strategies, L, M, and R DM2: 23 = 8 strategies Game in normal form: Z8ZZ""" & ""&.&" e  RTo overcome the difficulties, we shall analyze the extensive form directly. How? "SZQ" S  "Example. With a slight variation:$#Z   #  Game in normal form: Z    2Q. To analyze the extensive form directly. How? 03"/" 3  !An exercise on backward induction " Z  !Subgames and Subgame Perfection  4     ^Subgames for any non-terminal history h is the part of the game that remains after h occurred.H ZVZ&"V& W ""Some examples that is not subgames&     #_Location Game Example: Dynamic Game of Perfect Information Grocery Shopping on Market Street 0` >N% ` GMarket Street is a one-way street. HG H $#Consumers live along streets 1-100.4$ +;+; $  %H Payoffs An example: Firm 1 locates at 15 and 2 locates at 47. *I.E'. H jP1(15, 47) = 47-15 = 32. P2 (15, 47) = 101-47 =54 5  6 &'(Backward Induction.  Fix a player 2 node i0 (player 1 has located at i0). What maximizes player 2 s payoff? First note that player 2 will always want to be at 1, i0, or i0 + 1. For example suppose player 1 has located at 4 (i.e. player 2 is at node 4). Where will 2 want to locate? Suppose player 1 has located at 75. Where will player 2 want to locate? QZ  ]   Q )'Solving the game via backward induction((+ ( xAt node i , firm 2 plays j= i+1 if 1 i 50 j= 1 if 51 i 100 Back at firm i s node: P1(i, j ) = i+1-i if 1 i 50 =101-i if 51 i 100 Therefore unique subgame perfect equilibrium is: firm 1 plays 51 = i* firm 2 plays j=i+1 if 1 i 50 and j=1 if 51 i 100 = j* Note the way in which the strategies are stated. 7ZOZZNZ1ZnZ3Z%J{=&   *The end of market street  (Equilibrium path: firm 1 plays 51, firm 2 plays 1. Payoffs P1(i*, j* ) = 50 and P2 (i*, j*) = 50 Also note that there is no first mover advantage. pbZ3<2$  /T,-.  ` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> ,$(    6v  `}  X Click to edit Master title style!!   0y  `  RClick to edit Master text styles Second level Third level Fourth level Fifth level!    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N` ,$D0 @ 0 H ,$D0 eQ. How to solve it? Two methods: M1 ~ Convert to normal form M2 ~ Deal directly in extensive form d D    B   f z , [  @ ,  [ ,$D02 @ B jJ?", U 2  @ B jJ?"O, `U 2  @ B jJ?"2 [ H @ 0޽h ? ̙33|1  1 1DDD0(  Dx D c $   z 5 " D 2 y,$D0 D c &A ??5 "8 $D02 D B jJ?"H Z ,$D0" , [  D , [ ,$D02 D B jJ?", U 2 D B jJ?"O, `U 2  D B jJ?"2 [ Z& 8b   D #""8S ,$D0  D <*? 8b  i(-1, 0)"  @`  D </? b  h(2, 1)"  @`  D <7? b  i(-1, 0)"  @` D <x?? b  h(2, 1)"  @` D <A? b  i(-1, 0)"  @` D <O? b  h(2, 1)"  @` D <O?| b  i(-1, 0)"  @` D <0_?b |b  h(2, 1)"  @` D <_? bb  aR   @` D <@n? 8  h(0, 3)"  @` D <h?   h(0, 3)"  @` D <*?   h(3, 2)"  @` D <?    h(3, 2)"  @` D <?   h(0, 3)"  @` D <?  h(0, 3)"  @` D <?|   h(3, 2)"  @` D <?b |  h(3, 2)"  @` D <ȫ? b  aM   @` D <?s8  i(-2, 1)"  @` D <?s  i(-2, 1)"  @` D <?s  i(-2, 1)"  @`  D <h? s  i(-2, 1)"  @` !D <P? s   i(0, -1)"  @` "D <8?s   i(0, -1)"  @` #D < ?|s  i(0, -1)"  @` $D <?bs|  i(0, -1)"  @` %D <?sb  aL   @` &D <?8s cRRR3f   @` 'D <?s cRRL3f   @` (D <?s cRLR3f   @` )D <? s cRLL3f   @` *D <?  s cLRR3f   @` +D <%? s cLRL3f   @` ,D <-?|s cLLR3f   @` -D <5?b|s cLLL3f   @` .D <=?bs aDM1\2   @``B /D 0o ?8ZB 0D s *1 ?s8sZB 1D s *1 ? 8 ZB 2D s *1 ? 8 `B 3D 0o ?b 8b `B 4D 0o ?b ZB 5D s *1 ?bbb ZB 6D s *1 ?||b ZB 7D s *1 ?b ZB 8D s *1 ?  b ZB 9D s *1 ?  b ZB :D s *1 ?b ZB ;D s *1 ?b ZB D 6jJ$h ,$D0" ?D 6jJT {< ,$D0" @D 6jJ( ,$D0" AD 6jJS ; ,$D0 BD 0$J  $,$D0 LQ. Major difficulties? Dimensionality can be very large (Recall the DP example) Dynamic aspects are not appropriately considered Which of the four Nash solutions will actually happen? `l8  l 6   " CD 6jJ ,$D0" DD 6jJ ,$D0H D 0޽h ? ̙33 ^ H#(  Hx H c $|h   H c &A ?? 8 $D02 H B jJ?",$D0z , [  H 8 @,$D02 H B jJ?", U  H <1111H?"j +  b2A$0 e3f   H <1111H?"= b #  b2B$0 e3f  2  H B jJ?"Q, bU 2  H B jJ?"2  [ B  H@ 0D8c&0,$D0B  H@ 0D8co,$D0B  H 0D8c B,$D0z M   H 2~ ,$D 0f" H 61U yf" H 61M \ f" H 61 W  B H 0D8cth,$D 0" H 6jJW ),$D 0# H 08  ,$D 0 The solution process is backward induction Starting from leaf nodes and work backward until the root node is reached, each time solve a simple problem Then moving forward from the root to obtain the solution+ $$" $B  %   ; H 0  ,$D0 MQ. If DM1 selected L, what should DM2 do? How about if DM1 selected M or R?*N ( $ N K H 0  Z( ~,$D0 [The solution is unique (0, -1) is not a solution since DM1 who acts first will not select L,\ $E  \  H 6jJi6,$D0 H 0 L( o,$D0 8Extensive form is a reasonable approach for this problem98  9  H # B~CMDE FjJ~M@Ql ,$D 0H H 0޽h ? ̙33  ^ ? 7  L (  Lx L c $h4   L c &A ?? 8 $D02 L B jJ?"(:G,$D0jz s, U  L q ,$D02 L B jJ?"s, U " L B jJ?"#F N  L <o1111L?"j o+  b2A$0 e    L <s1111 L?" b #  b2B$0 e    L 04w $ K,$D0 }7If DM1 selected M or R, DM2 does not know how DM1 acted88" 8 @  L 00u ,$D0 Again there are two methods: M1 ~ Convert to a normal form M2 ~ Deal directly in extensive form Normal form analysis: How? DM1: 3 strategies, L, M, and R DM2: 22 = 4 strategies F8 D     $,$    L 0 6 ,,$D0 fQ. How to solve it?"    H L 0޽h ? ̙33-  g-_-NNT,(  Tx T c $"u  "F 7 " T g 9v T c &A ??7 "8 $D02 T B jJ?"J \ ,$D0r s, U  T , U ,$D02 T B jJ?"s, U " T B jJ?"#F N   T <1111 T?"j o+  b2A$0 e    T <1111 T?" b #  b2B$0 e  #  6  T#  #ig ,$D0"N  4  T  4N |  T | T 6 +Q DM1\DM220cc  Z T s *|N | T | T 6 LL40c  Z T s *|N  T  T 6H=} LR40c  Z T s *N >  T >  T 6  nRL"0c  Z T s *> N >  T >  T 6i  RR40c  Z T s *> N | T | T 6+Q }L20cc  Z T s *|N | T |  T 6 (0, -1)20cc Z !T s *|N  "T  #T 6X =} u(0, -1)"0c Z $T s *N >  %T >  &T 6  u(-2, 1)"0c Z 'T s *> N >   (T >   )T 6Ti   u(-2, 1)"0c Z *T s *>  N |g +T |g ,T 6#+Qg }M20cc  Z -T s *|gN |g .T |g /T 6`-g (3, 2)20cc Z 0T s *|gN g 1T g 2T 6$7=}g t(0, 3)"0c Z 3T s *gN > g 4T > g 5T 6? g t(3, 2)"0c Z 6T s *> gN >  g 7T >  g 8T 6  gN g|4 :T g|4 ;T 68R+gQ4 }R20cc  Z T 6[g4 (2, 1)20cc Z ?T s *|g4N g4 @T g4 AT 6e=g}4 u(-1, 0)"0c Z BT s *g4N g> 4 CT g> 4 DT 6Lng 4 t(2, 1)"0c Z ET s *g> 4N > g 4 FT > g 4 GT 6(vi g 4 u(-1, 0)"0c Z HT s *> g 4Z IT s * 6" JT 6jJ9cm-,$D0" KT 6jJ_ E O S ,$D0 LT 0<  $,$D0 }Q. Major difficulties? Same as before Dimensionality can be very large Dynamic aspects are not appropriately considered VT   T  ~ " MT 6jJ N,$D0" NT 6jJ7,$D0H T 0޽h ? ̙33& ^ !&&::\%(  \x \ c $e  Vz 7 " \ 9 ,$D0 \ c &A ??7 "8 $D02 \ B jJ?"J \ ,$D0r s, U  \ , U ,$D02 \ B jJ?"s, U " \ B jJ?"#F N   \ <H1111 \?"j o+  b2A$0 e    \ <41111 \?" b #  b2B$0 e  n  \ 0L / ,$D0 \Q. At information set 2A, what should DM2 do? How about at 2B? What should DM1 select?N] ,    ]   \ 0 <,$D0 z.At 2A, DM2 should select L with costs (0, -1) /-  /   i  \#  ,1 ,$D0N  g \  gN  \  \ 6+^ DM1\DM220cc  Z \ s *N - \ - \ 6 }L20cc  Z \ s *-N -  \ -  \ 60X  }R20cc  Z \ s *- N  \  \ 6+^ }M20cc  Z \ s *N - \ - \ 6( (3, 2)20cc Z \ s *-N -  \ -  \ 6X  (0, 3)20cc Z  \ s *- N g !\ g "\ 6+^g }R20cc  Z #\ s *gN -g $\ -g %\ 6g (2, 1)20cc Z &\ s *-gN - g '\ - g (\ 6t X g (-1, 0)20cc Z )\ s *- gZ *\ s * i" +\ 6jJ W a ,$D0 ,\ c &A ?? =d 8 $D0% -\ 0  @,$D 0 7Q. What problem does DM1 face? How should he select? *8 4  8 " .\ 6jJ ,$D0B /\@ ND8c?"I,$D0B 0\ ND8c?"x,$D 0B 1\ ND8c?"W,$D 0B 2\ ND8c?"a9,$D 0" 3\ 6jJ,$D 0" 4\ 6jJ Kh ,$D0 5\ 6jJ ,$D0$ 6\ 0|  4t ,$D0 ,At 2B, DM2 faces the following normal game: 4-  $  - " 7\ 6jJ,$D0B 8\ ND8c?"  ,$D0 9\ 0&  0,$D0 |*The solution process is backward induction"+ $ +  :\ # BpC@DE FjJp@@*Y,$D0H \ 0޽h ? ̙33 ^ NF0 d(  d~ d s *X `}   ~ d s *e `J   d c &A  ?? 8  $D0B d@ ZD8c?W . ,$D0B d@ ZD8c?F ,$D0B d ZD8c?A9 ,$D0B d ZD8c?< ,$D0B  d@ ZD8c?d%,$D0B  d ZD8c?f ,$D0"  d 6jJ ,$D 0  d # BCJDEFjJiwJ @m ,$D 0H d 0޽h ? ̙33   + # @ h(  hx h c $   x h c $P@c   h 0L  ~) ,$D 0 D$  h c &A  ??<z 8  $D 0" h 6̙>  ,$D0" h 63f>  ,$D0" h 6> j j ,$D 0"  h 63f>4T - ,$D0"  h 6>.z ,$D0  h 0 ,$D0 bSubgames( 0(2 g  "  h 6̙>8 ,$D0s  h 0U  ~ ,$D0 aSubgame perfect equilibrium: No subgame can any player do better by choosing a different strategy&b$F 4   : H h 0޽h ? ̙33 ^ 4,Pl(  lF   l   l c &A  ?? 8  $D02 l B jJ?t' ,$D0r" l B jJ? I r2 l B jJ?s~ l s *J `}   ~ l s *M `    l <O1111 l?7 d b2A$0 e    l <PS1111 l?BE Gn b2B$0 e  r  l <G.2>G ,$D0"  l 63f> Q,$D0"  l 6>= ^ 8,$D 0j2 l B jJ? H l 0޽h ? ̙33  `X` p(  p p s *^M<$0    p s *a<$0  "p`PpLB p c $D` ` X2 p 0`  X2 p 0`   p <k   S1 0c  p <o F  U100 0c   p 0tl{  yOne-Way Market Street40gc  Y  p <vZ F oTwo firms locate grocery stores on Market Street sequentially. That is, first firm 1 locates and then firm 2. Bp01cc1co  X  p@ 0 ) H p 0޽h ? ̙337  ptw(  t t s * `}<$0   LB t c $D@ LB t c $D@ @ LB t c $D0@ LB t c $D0@ LB t c $D0@ LB t c $D0 @ X2  t 0X2  t 0X2  t 0 0 LB  t c $D  LB  t c $D LB t c $D p` LB t c $D0@ RB t s *D@@RB t@ s *DPP`P t <6d QN 0c    t <& QW 0c    t <L@ p4:  S1 0c  t <I F C  S2 0c  t <zI C  S3 0c  t <y F   Qi 0c   t 0ģI zC  T99 0c  t <|I C  U100 0c R2 t s * @ R2 t s * `@  t <īz f (Consumers drive to market street, then drive west on market street (there are no left turns onto market street) until they reach a grocery store. d0'c c+cc4c  H t 0޽h ? ̙33   A 9 x (  x x s *Ⱦ, = <$0   LB x c $D(LB x c $D( (LB x c $D8 (LB x c $D(LB x c $D( x <1FZ+  T15 0c   x <1+  T47 0c X2  x 0(X2  x 0 (  x <tl VFirm 1 0c     x <Fl VFirm 2 0c    x < =Consumers: 1 consumer uniformly distributed on each street. D>0cgc >  x 6l 5  ,$0 FSince firm 1 gets all consumers who live on 15th St, 16th St, & 45th St and 46th St. nU.           U  x Bd  <<$0   x <PP J  U100 0c  x <Fl@  S1 0c H x 0޽h ? ̙33 ##|X(  | | <6 JNow let s use backward induction to find all subgame perfect Nash equilibrium.dO0cc c!cc&,   " | 0p6v XRecall that subgame perfection is an equilibrium refinement concept. If SGPNE then NE.  Y0Yc&   F LB | c $D 02 | 0p@  U1"0c X2 | 0 0 X2 | 0  | <$i V c Qi 0c  X2  | 0 X2  | 0p X2  | 0`   | < ~W + U100 0c   | <v2 Q10a  | < Hf" / Q20a LB |@ c $D` LB |@ c $D @LB | c $D P 0 LB |@ c $D` P LB |@ c $D` 0 P LB | c $D` ` LB | c $D` 0 X2 | 0@ p X2 | 0@ P p X2 | 0@  p  | < f    Oj0a  X2 | 0 @ X2 | 0 0 @  | <08 "  S1000a  | <`!h bO  Q10a  | <# &  Q20a 2 | 0'@p`0  U2"0c 2  | 6l+P`  U2"0c 2 !| 6.0@ U2"0c 2 "| 6$2   U2"0c  #| <d5j fP }-What are the pay-offs to Player 1? Player 2? .0.c . 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[mK^uxV_bMMB/x񽛚{M* 0-^xY5މ=<]K4Ćf [[{u,C삵gq, ʻ:sϻ8cwgON-7,1zX9H|;2MC4f7B|ģ!"WLg5 !/ҋ)}%[%< cr7-W?d'b,C^^, mM@B<݅\|?z>,/ӝ\.v}pF`M.~bkyNyrS懩Tz ECGfJxW)x0RIi N:9 EJQ "     P8P(@@L2h6Ы@Χ/Z((h-:@o=-?k_DFmE#B9̙Nq>c "w*%j)Z 㻾c~v(o!@Ch@cL`Ovtb2& ȳ;zzBp[|h>{> p"d~<]7umiI+ Ӽ^,=a/z|wNH(ƓVTt8ϕawvZ4ܧ NayoYϹC{x;uzH,=[$˰7: `"XC<h ];!öݻ4ԬԶ^'( (P@ (o8KFx\ xTE[=!!D VQuEl *(A%, >E )O\PGAeP\gKPޮY|nթsNU:unٝ ?b3O$p2*S0s*9h}@3@2  H2 ,@=@6 P hhhh 44UM B<w5%&L|WvΑ _^8?pOuϻ=x{7Wi,Ƃ ir S|;&Rp, ؽ bn; k t {,XYa ObWev*x%%@ : :UȻwm/f@i¾ {>s}#f–>%׫q-e;O:籵FnJoX=+Xȷad®f`ʰ~>icgyf`/X:i * ǎ:#|{$p&V4u5f!k -3֟-]ne߲)o H;GO(h( WH0Vx &`EU0~8vRH5*8 ^ހp:2WQ74BR-HI{ѝ +,ZO!s+r4ԍ="- c{klf$Dm΍Fn'W4@ݤh QR1!)2lo&֨+C\;'W\04y3aip]ʖ*ݲq8nU9,7;inJw8A WMvpM~4ew;{}n{=:G {^rp/+\cUmO xfly"e+ +8il ThN]`𝈫%~3ţ2M^P),4X1 jCw UT|b$uOsISNRiɽPNt\+̨~e9Y  Ag4:O3|^XRد)Vc֔>IV9͹;&THZ~C7.L4IvRq řl)/s'tΌ<_Itw(BC}F<|†?XnŮ%V(͢5R27d+tnOKzi5}ߵ]'8M|{jaKwYQu9#VWy(,dF%Q%G8تAJ<%Gx]Zf ~tYWQWWi1-r#m7~>);iV' 8Ui. g |8[P/\i <9O EHß/h6".(m!-E:4Ur̅hүJ(g`L ]=t7ow]|<`J&/*FkC#7Fȳl @v00:Y:[IB~ @dtp W)' KSQh.I*OޫpmDEo5dWF=9]*K+ lxxj5NF"[NlyH;Eт-Hwn/oEDXZR/߉x +D*?HoTxT!V!Bm]HCP{M`^"~S;.T2c%0oxh8i /͆l^YY8߹s'3 S`qbfD۶DiHw&"4y"%8DHWs9AlsN^,l"⭜WEzx_"~Co"lP;z-^]<0d{F A͙v}@lwx&w1?(>sKY& wO KhwoM\`昤N/ D:'FzAFC& JI"Azy,>E8VeӪn#%U *"p,3g![\tTdԂTӶ-4Il8=77WSe\etE\^x8*61G,I}B/T=hdΩE nFAg\Bq>!т+;DlJV pٽ59. Als#'@ƹK眨8¹Ik1h5]Ȉ##`h[q{hl3Í5YJr^k&95\8 9\8tF5F&>Æ4<vƭтcG:O+!]Hԅ8&k@2 \ fh2jpN:sHw᠏7Q#Nsi1tPBCׁ.:'b3%gHQOόd4MgFwqg Y@,MCNEH/Ʊ$hbsV>7 fq8sfL^gCLSemd.3 -e9~S?N۟W1yB\ A,08k?II6p)Dgϑ%U vG`.!bvls2SoC^,ykn%=5F]doLL% |(]v~٦ކԷR~[$7]!i_$KMR*~1M;Feڽbzz SeI N9d.`N yd^po ڐ%,\rt#~ XK&/ʟ/v iR)Bx/0wq\i٣C _>yxtqfZE"qrsƚn\9HQG>6 cx=BCzduaޡ^ؑc6tEY?絓[COmK:{/n؁lƼf ]Wt-ڛ6ȓI(;'FI z%[.|)"j~F[5^mIoo%l6;og|((89KJFoNW8FIOZc^X~+md\M es +d[ea4=Y jlsNY,pׁl޺lL<=;a:E}}-^7eNy#e>Ʋ/a4NXY|A'5|<̈fXoMM]vc5#5񦘚8J[&&$q.1o7.) +) 1ѣ 1i^׷C,[,?D-$6%J辖|j--7Z#Rf9۾( J>L2ci/J|?Ǚ?[KM0e'ZZ`xWp{Z-dm<7nNX֞Efc9Ƹ"aYl/\\m5[L6WՎ<#ٖ·Kcf[;m[~HcV[Q?LVұAjfla-I{㯫gnO51=Ot=FcecZYŽNɬl+)(?/wGOc3^>bx}v ;FJkYf,wXJ[SB--瓌ٯжn^B%jk%|_\mPlmd<$_'sP8G^.c]Vל`n jjG|.ja>sCjWۚ?ɟ]g L3 ZZ[HXO 7QuE-{5Yb{j~wĸk|KxE\/#`&ٱ M/1ۻ':Yhu+'<_¯Ǘkr>ڟ$hʏBs{XuTM3y:7yj:{<*O[󏨿SISZڭbnZ|i~^fYӜ%:x3ڮ~Dܽ=`{o4}6bmz^R/ėUDd\!IVy6 +9W棞f:Rף Ő?y~V:pg}a|g>W?J {WG\vpUIi閖_mU$mZ[ ?-M_446H XL,D4icJ|@b)9s.3Mo{s{o}ZP,nSc)S˿-,?E4QR]0ƓXQ[Rώ~`эrJ}6YܾIWb%۴ZzR͖%=Ht8jzuCKSZˑtDfʤ谨5QPB֤)nArRloRgIaE1]Ǽ|>oa=Oۗ"ߚC$@ŪY#XqXKg[ӆ]npl) {$Usr B4j$ ܛSqX"M ^ mu2 =[j0fW8ٷ~ x* δ1ߎW'=r%8<2)$^442pLtQ32_ u hq i֛fh9يK)(oŢ[h cVf3)&qn ?@ȡ&d2 B K{ȝ]*d5Y'o6}gQd?r9|LYwg*=oG0"GPwn YCn5ZAVwfyKېw#;}2' kOTb Ut/"TŽȦ8O #D@tw"^ v{I+HkZX?z10:vghᆍCo2F؎M(@/ȧ1}Wv{E[]&&}˲;9~4wg]^[i [yk55^\S>4^fJ藧Z[::C#Aԏ`>8k9yo(/=VϪdJ Dهo{{Yθa_ι0 _SPPPPPPPPPPPPPHf뗾t:< !ٲdO#4:C`]۟^l##m/ ȡcЃ-Rˍ;\gi 9A|p9A5{w2x\ xTE[=!!D VQuEl *(A%, >E )O\PGAeP\gKPޮY|nթsNU:unٝ ?b3O$p2*S0s*9h}@3@2  H2 ,@=@6 P hhhh 44UM B<w5%&L|WvΑ _^8?pOuϻ=x{7Wi,Ƃ ir S|;&Rp, ؽ bn; k t {,XYa ObWev*x%%@ : :UȻwm/f@i¾ {>s}#f–>%׫q-e;O:籵FnJoX=+Xȷad®f`ʰ~>icgyf`/X:i * ǎ:#|{$p&V4u5f!k -3֟-]ne߲)o H;GO(h( WH0Vx &`EU0~8vRH5*8 ^ހp:2WQ74BR-HI{ѝ +,ZO!s+r4ԍ="- c{klf$Dm΍Fn'W4@ݤh QR1!)2lo&֨+C\;'W\04y3aip]ʖ*ݲq8nU9,7;inJw8A WMvpM~4ew;{}n{=:G {^rp/+\cUmO xfly"e+ +8il ThN]`𝈫%~3ţ2M^P),4X1 jCw UT|b$uOsISNRiɽPNt\+̨~e9Y  Ag4:O3|^XRد)Vc֔>IV9͹;&THZ~C7.L4IvRq řl)/s'tΌ<_Itw(BC}F<|†?XnŮ%V(͢5R27d+tnOKzi5}ߵ]'8M|{jaKwYQu9#VWy(,dF%Q%G8تAJ<%Gx]Zf ~tYWQWWi1-r#m7~>);iV' 8Ui. g |8[P/\i <9O EHß/h6".(m!-E:4Ur̅hүJ(g`L ]=t7ow]|<`J&/*FkC#7Fȳl @v00:Y:[IB~ @dtp W)' KSQh.I*OޫpmDEo5dWF=9]*K+ lxxj5NF"[NlyH;Eт-Hwn/oEDXZR/߉x +D*?HoTxT!V!Bm]HCP{M`^"~S;.T2c%0oxh8i /͆l^YY8߹s'3 S`qbfD۶DiHw&"4y"%8DHWs9AlsN^,l"⭜WEzx_"~Co"lP;z-^]<0d{F A͙v}@lwx&w1?(>sKY& wO KhwoM\`昤N/ D:'FzAFC& JI"Azy,>E8VeӪn#%U *"p,3g![\tTdԂTӶ-4Il8=77WSe\etE\^x8*61G,I}B/T=hdΩE nFAg\Bq>!т+;DlJV pٽ59. 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