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If you are rational, you would NEVER play a strictly dominated strategy. nPP      $$((,,004488<<    $$((,,004488<<  $$((,, 004488<<  " $$((,,004488<<    $$((,,004488<<    $$ ((,, 00(4488<<p       / GAME THEORY    . GAME THEORY    9 GAME THEORY    : GAME THEORY    7 GAME THEORY    A strategy si is strictly dominated for player i if there exists another strategy si `"si such that ui(si , s i) > ui(si, s i) for all the strategies s i that player i s rivals might play.       "$$((,,004488<<<<    $$((,,00448888<<    $$((,,>   - GAME THEORY    , GAME THEORY    A strategy si is a best response for player i to his rivals strategies s i if ui(si, s i) e" ui(si , s i) for all si . A pure-strategy profile s = (s1, & , sI) constitutes a Nash equilibrium (NE) if for every player i = 1, & , I, ui(si, s i) e" ui(si , s i) for all si . 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S  p 0( "  l* 0    p 0\ "@`   l* 0    p 0 "  l* 0   T j  p  "j " p  B$GR o"j  D  hB  p  s *DԔ"55H p 0޽h ? U3ff80___PPT10. 0[  Studio] 0   t ](  t " t <pTG̙" D  " t BtTG+̙ "4  D  " t BTSp"7`   J 0   t 6xS " T X Click to edit Master title style!!  t 6pS "Pw  S [#Click to edit Master subtitle style$$  t 0 S " S l* 0    t 0pS "@`  S l* 0     t 0S " S l* 0   H t 0޽h ? U3ff80___PPT10. 0[30 P C( P$'    0P.T P   T X*   04T    T Z* d  c $ ?  T/  07T  @ T kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7    l  6<>T `P  T X*   6pCT `  T Z* H  0޽h ? 3380___PPT10.pE]0N0 TL@(  x  c $Rt  R x  c $hRt Pw  R R  C *Aimage3252R  C *Aimage3250H  0޽h ? 33___PPT10e.+D=' R= @B + 0 ', R(  , r , S |lTp P   T  , `Ap BD06500_``  TH , 0޽h ? U3ff___PPT10i.;!t+D=' R= @B +A 0 XP$L (  L x L c $\Tp P   T h L  (0e0eA @ 5%8c8c     ?p @A)BCD|E?0  T L 0  fA ? ?p "` P@  TH L 0޽h ? U3ff___PPT10i.y0w=+D=' R= @B + 0 " l(   r  S }Tp P   T   TA  ?p  T  0X;P  - max(ST - K,0) exp(-rT)-c1Z0 2        0T  max(K - ST,0) exp(-rT)-c0N0 2      H  0޽h ? U3ff___PPT10i.yz+D=' R= @B + 0 #4 h(  4 x 4 c $Tp P   T  4 0  fA ? ?p "`P @   T 4 0  fA ? ?p "` 0   T  4 0Tp@ &Black-Scholes model (Nobelova nagrada)'0 2'Z       H 4 0޽h ? U3ff___PPT10i.y09K+D=' R= @B + 0 p#( @(  ( r ( S TTp P   T  ( c $$TAp p`P  T " H ( 0޽h ? U3ff___PPT10i.y+D=' R= @B + 0 '0 v(  0 r 0 S Tp P   T r 0 S Tp  T J 0 C "A Nash@H 0 0޽h ? U3ff___PPT10i.; +D=' R= @B +C 0 BB%#J B(     ' 6T"` 0 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x  1 +1<0   RB ( s *DjJp@ RB ) s *DjJ@ RB * s *DjJp` RB + s *DjJ` ` RB , s *DjJp ` RB - s *DjJ`   . 6(Tp@RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    / 6Tp @RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    0 6Hd"` 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x +1  1<0     1 6Pd"` 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x +1  1<0     2 6d"` `P0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x  1 +1<0   j 3 6 !d"` P0RJB___PPTMAC11   hnamd` Arial&Monotype Typography  LPlayer 1 s payoff: Player 2 s payoff: '0 ' '  4 <DdP 7RJB___PPTMAC11   hnamd` Arial&Monotype Typography  NPlayer 1   RB 5 @ s *D p 6 <+d` `G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  IH   7 <0d RJB___PPTMAC11   hnamd` Arial&Monotype Typography  IH   8 <6d` $ G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  IH   9 < 6Xd0 0 RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    ? 6H^d0  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0   @ <$bd RJB___PPTMAC11   hnamd` Arial&Monotype Typography  NPlayer 2    A <$hdpRJB___PPTMAC11   hnamd` Arial&Monotype Typography  UInformation set  RB B @ s *Dpp C <(nd $ RJB___PPTMAC11   hnamd` Arial&Monotype Typography  TTerminal nodes  RB D @ s *D `  E 0Xud V___PPTMAC110(   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ $Bacanje nov ia A $  F <0}dp p RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0  X" G 0@p  J Bd p P   d H  0޽h ? U3ff___PPT10i.+01]+D=' d= @B +D 0 CC%#& B(   r  S $dp P   d    6d"` 0 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x  1 +1<0   RB  s *DjJp@ RB  s *DjJ@ RB  s *DjJp` RB  s *DjJ` ` RB  s *DjJp ` RB  s *DjJ`    6dp@RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6dp @RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6ܝd"` 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x +1  1<0      6d"` 0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x +1  1<0      6Dd"` `P0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x  1 +1<0     <dP 7RJB___PPTMAC11   hnamd` Arial&Monotype Typography  NPlayer 1   RB  @ s *D p  <,d` `G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WH   <d RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WH   < d` G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WH   <d RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WT   <d` d 0 G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WT   <d` G RJB___PPTMAC11   hnamd` Arial&Monotype Typography  WT    6d0  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     64d0 P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6d0 0 RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6d0  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    <@d gRJB___PPTMAC11   hnamd` Arial&Monotype Typography  NPlayer 2   RB  s *Dp  <Df`pRJB___PPTMAC11   hnamd` Arial&Monotype Typography  NPlayer 2   RB  @ s *Dpp ! <4f $ RJB___PPTMAC11   hnamd` Arial&Monotype Typography  TTerminal nodes  RB " @ s *D `  $ <fp p RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0   % 0f V___PPTMAC110(   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ "Bacanje nov ia B$ j & 6pf"` P0RJB___PPTMAC11   hnamd` Arial&Monotype Typography  LPlayer 1 s payoff: Player 2 s payoff: '0 ' ' H  0޽h ? U3ff___PPT10i.+Ph+D=' d= @B +} 0 % $(   r  S fp P   f r  S fp  f H  0޽h ? U3ff___PPT10i.+pskg+D=' d= @B +} 0 % $(   r  S .fp P   f r  S /fp  f H  0޽h ? U3ff___PPT10i.+ @Yf+D=' d= @B +v7 0 66% 6(   r  S >fp P   f n  p   # #"p` P    <Nf?"H p  p 1, +1      <%f?" H p  n +1,  1      <Wf?"H   n +1,  1      <RP?"H  n  1, +1   nB   0o ?" hB   s *1 ?" nB   0o ?"p p nB   0o ?"p hB   s *1 ?"H H p nB   0o ?"  p   <af \  ___PPTMAC11  (namd Symbol   `Player 1    < hf6 0 ___PPTMAC11  (namd Symbol   `Player 2    <nf  ___PPTMAC11  (namd Symbol   OH   <,tfv p  ___PPTMAC11  (namd Symbol   OT M  <zf  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ ]H$ M  <f )|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ ]T$   6f ___PPTMAC11   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography ___PPT10     R___PPT94,      ; Within each cell the payoffs are: (u1(s1, s2), u2(s1, s2))< cC c ckcc k $c$(k(,c,0k04c48c84E2aa V  <if |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ fNP& I  0i |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP& U  <i  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP&   0j` V___PPTMAC110(   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ xZatvorenikova dilema A$ H  0޽h ? U3ff___PPT10.+tb+7*DO' j= @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+ 0 +g0 0 ))P% C)(   r  S @ jp P   j X r    # #"0    <j?"H `   l 1,  1      <`j?"` H   l  1, 1      <j?"H    l  3, 2      <l,j?" H  l  2, 5      <85j?"H `  l  1, 1      <6j?"H `  l 1,  1   nB   0o ?"hB   s *1 ?"` ` nB   0o ?"  nB   0o ?" hB   s *1 ?"H H nB   0o ?" ZB   s *1 ?    <Bj @|  ___PPTMAC11  (namd Symbol   `Player 1    <Hj@ \ : ___PPTMAC11  (namd Symbol   `Player 2  O  <Oj`. Z|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _L&   6Sj @@$0h___PPTMAC11  (namd Symbol    (namd Symbol    (namd Symbol  <___PPT10R___PPT94, ! No strictly dominant strategies.@"5 aa a> O  <Pej@: |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _U& O  <dlj` Z|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _R& O  <tj  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _M& O  <(}jp j |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _D&   <j(@|HD$0j___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, - D is dominated by both U and M for player 1..5aea a aeaea . H  0޽h ? U3ff\T___PPT104.+`Mza+tGD' j= @B DS' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+p+0+  ++0+ 0 +2 0 G'?'& &(   r  S Pjp P   j n p   # #" Pp    <j?"H p  n  5,  5      <dj?" H p  p 1,  10      <j?"H   p 10,  1      <Lj?"H  n  2,  2   nB   0o ?"hB   s *1 ?"  nB   0o ?"p p nB   0o ?"p hB   s *1 ?"H H p nB   0o ?"p S  0\j0 s |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ oNP &"   6j` 0$0___PPTMAC11  (namd Symbol    (namd Symbol    (namd Symbol     hnamd` Arial&Monotype Typography T___PPT104,___PPT9tl n(P, P) is the unique outcome of the game if both players are rational (and do not cooperate among each other).ocCc C 8cg)ccr  V  <jf |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ fNP& U  <j0 *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP& U  <Xj  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP& B  6DԔ0 0 ,$D0B  6DԔ ,$D02  6Ԕ P@ ,$D0  <k0 P*  ___PPTMAC11  (namd Symbol   ^Z1"   <`k S  ___PPTMAC11  (namd Symbol   VZ2   0P k` V___PPTMAC110(   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ xZatvorenikova dilema A$ H  0޽h ? U3ffB : ___PPT10 .+PTm+[}D ' k= @B Dq ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+ 0 +3 0 0((( & '(   x  c $Pkp P   k ,n p   # #" Pp    <!k?"H p  n  5,  5      <t+k?" H p  p 1,  10      <$k?"H   p 10,  1       <$=k?"H   0,  2$  nB   0o ?"hB   s *1 ?"  nB   0o ?"p p nB   0o ?"p hB   s *1 ?"H H p nB   0o ?"p S  0@Bk0 s |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ oNP &"   6Dk` 0$0___PPTMAC11  (namd Symbol    (namd Symbol    (namd Symbol     hnamd` Arial&Monotype Typography T___PPT104,___PPT9|t a(P, P) is the unique outcome of the game if both players are rational and know that their opponent is rational (and do not cooperate among each other).cCc C 8cgGC$G* c   V  <@skf |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ fNP& U  <T{k0 *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP& U  <hk  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ eP& B  6DԔ0 0 ,$D0B  6DԔ ,$D02  6Ԕ P@ ,$D0  <Hhk0 P*  ___PPTMAC11  (namd Symbol   ^Z1"   <k S  ___PPTMAC11  (namd Symbol   VZ2   0Vk` V___PPTMAC110(   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ xZatvorenikova dilema B$ H  0޽h ? U3ffB : ___PPT10 .+PTm+D ' k= @B Dq ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+ 0 +} 0 % $(   r  S Ƞkp P   k r  S kp  k H  0޽h ? U3ff___PPT10i.+l+D=' k= @B +? 0 66@% j6(   r  S Hkp P   k 6 r    # #" p    <k?"H `   f4, 3      <k?"` H   f4, 2      <8k?"H    g10, 2      <k?" H  f0, 5      <k?"H `  f0, 4      <(k?"H `  g10, 1   nB   0o ?"hB   s *1 ?"` ` nB   0o ?"  nB   0o ?" hB   s *1 ?"H H nB   0o ?" ZB   s *1 ?    <k p  ___PPTMAC11  (namd Symbol   `Player 1    <0kF @ ___PPTMAC11  (namd Symbol   `Player 2  O  <k0m *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _L&   6p  $0Pz___PPTMAC11TL  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  L___PPT10,$r___PPT9TL > No strictly dominated pure strategies for any of the players.?5ccg gc c $c  C  0p|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _U& O  <p00  *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _R& O  <p  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _M& O  <(p@ : |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _D&   0)p  $0p  ___PPTMAC11     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography |___PPT10\T  ___PPT9   C M is dominated by 1/2U+1/2D for player 1 (payoff 5 rather than 4).4D5cgc cc o gogo g $o$(g(((c( D B  6DԔ  ,$D0H  0޽h ? U3ff___PPT10p.+0^`+D' p= @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+p+0+ 0 ++0+ 0 +} 0 0% $(   r  S Wpp P   p r  S Xpp  p H  0޽h ? U3ff___PPT10i.+a_+D=' p= @B +)U 0 99 %%' |9(   r  S gpp P   p  r 80   # #"    <Tjp?"    f0, 4      <p?" `   f5, 5      <\}p?" `  f0, 4      <Tp?"` 0  f4, 0      <p?"8`   f4, 0      <̜p?" 0  f5, 3      <̣p?"8  f3, 5      <p?"0`  f3, 5      <p?"8 `  f5, 3   nB   0o ?"80hB   s *1 ?"8` 0` nB   0o ?"8 0 nB   0o ?"88 hB   s *1 ?"  nB   0o ?"00 hB   s *1 ?"8 0 hB   s *1 ?"   <p   ___PPTMAC11  (namd Symbol   `Player 1    <4p  ___PPTMAC11  (namd Symbol   `Player 2  R  <p0 *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ bl ( O  <p |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _U& Q  <p0 *|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ am( O  <p  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _M& O  <pf y` |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _D&   0m 0$0___PPTMAC11ld   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography X___PPT1080___PPT9ph ](M, m) is mutually best response for the players, hence (M, m) is a unique pure-strategy NE. ]45ccc g  c cC CCCGC40  ' R  <Lp00*|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ br ( 2  6jJp0 ,$D02 ! 6jJ 0 ,$D02 " 6jJp ` ,$D02 # 6jJ ,$D02 $ 6jJ P  ,$D02 % 6jJp P ` ,$D0- & <DmT$ 0 ___PPTMAC11ld   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ e 45cc  2 ' 6o  ,$D 0H  0޽h ? U3ff___PPT10.+0c`^+q]BD!' m= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*! %(D' =-s6Bcircle(in)*<3<*! D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*" %(D' =-s6Bcircle(in)*<3<*" D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*# %(D' =-s6Bcircle(in)*<3<*# D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-s6Bcircle(in)*<3<*$ D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*% %(D' =-s6Bcircle(in)*<3<*% DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*& %(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*' %(D' =-s6Bcircle(in)*<3<*' +p+0+ 0 ++0+& 0 +} 0 0& $(   r  S \$mp P   m r  S .mp  m H  0޽h ? U3ff___PPT10i.4P+D=' m= @B +5 0 1#)#& "(   r  S +B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bcircle(in)*<3<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+p+0+ 0 ++0+ 0 + X 0 NN& gN(   r  S @mp P   m n    # #"P P    <tm?"H `   n  1, +1      <pm?"` H   n +1,  1      <m?"H `  n +1,  1      <(m?"H `  h-1, +1   nB   0o ?"hB   s *1 ?"` ` nB   0o ?"  nB   0o ?" hB   s *1 ?"H H  nB   0o ?"   <mpj  ___PPTMAC11  (namd Symbol   `Player 1    <m7 z ___PPTMAC11  (namd Symbol   `Player 2  O  <m@p Z :|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _H& O  <m|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _H& O  <m@ :|t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _T& O  <m` Z |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _T& e  <nd\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D< [p]R   l  < n "S d\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D<  [1 p]R   e  <nEo r d\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D< [q]R   l  <nE d\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D<  [1 q]R      6D&n  T $0 ___PPTMAC11  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  l___PPT10LD___PPT9 7] Player 2 is indifferent between pl. 1 playing H and T if 1*p -1*(1-p) = -1*p +1*(1-p) :5$4c?cggg g gggg g  c  %   6Gn :T $0 ___PPTMAC11  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  l___PPT10LD___PPT9 8Z Player 1 is indifferent between pl. 2 playing H and T if -1*q +1*(1-q) = 1*q -1*(1-q) ":5!4c<cggg g gggg g  g  "  6 enP h$04V___PPTMAC110(  (namd Symbol    (namd Symbol    (namd Symbol   0namd( Lucida Grande   (namd Symbol    (namd Symbol  P___PPT100(v___PPT9XP  p = 1/2 q = 1/24cgA]gA]gA] g A]gA]H  0޽h ? U3ff___PPT10.4+f7D' n= @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(++0+ 0 ++0+ 0 ++0+ 0 +[ 0 lMdM& L(   r  S ~np P   n 6 r    # #" P    <0hn?"H `   f4, 3      <Hn?"` H   f4, 2      <đn?"H    g10, 2      <tn?" H  f0, 5      <4n?"H `  f0, 4      <ln?"H `  g10, 1   nB   0o ?"hB   s *1 ?"` ` nB   0o ?"  nB   0o ?" hB   s *1 ?"H H nB   0o ?" ZB   s *1 ?    <$n&   ___PPTMAC11  (namd Symbol   `Player 1    <n@ | ___PPTMAC11  (namd Symbol   `Player 2  O  <Hn I |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _L& O  <,npj |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _U& O  <Tn |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _R& O  <8n  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _M& O  <n  |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ _D& B  6DԔ  ,$D0  <np/pj $0\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D< }[p]B     <n  $0\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D<  [1 p]B     <o/ p $0\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D< }[q]B     <\n v$0\___PPTMAC11xp  (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  D___PPT10$b___PPT9D<  [1 q]B     6o 0@:$0:___PPTMAC11   (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol    (namd Symbol  ___PPT10     n___PPT9PH      w] 10*q +0*(1-q) = 0*q +10*(1-q) => q = 1/2 1*p +5*(1-p) = 4*p +2*(1-p) => p = 1/2 ^4cggg g gggg g $g$(g(,g,0g04g48g8+B#style.visibility<* %(D ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 +eo 0 |ntnp&<=  n(   r  S np P   n    6Ro"` Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, x  5  5<0   RB  s *DjJ@ RB  s *DjJ@  RB  s *DjJ ` RB  s *DjJ`  RB  s *DjJ ` RB  s *DjJ` P   6D.o"` Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, z 1  10<0     6dho"` `PPj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, z 10  1<0      6lqo"` Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, v 0  2<0     <4xo  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  LNature  RB  @ s *D   <ioD RJB___PPTMAC11   hnamd` Arial&Monotype Typography  IC    <0o ___PPTMAC11  (namd Symbol   NType I    <o RJB___PPTMAC11   hnamd` Arial&Monotype Typography  OType II     6o0 p RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6ؔo0 p RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6lo P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0     6o P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    <xo  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  P Prisoner 1     <|o p RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0  X"  0   6opPRJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0  J  <o0 |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ Zm(  N  <o 7 |t___PPTMAC11  (namd Symbol    (namd Symbol  4___PPT10 B___PPT9$ ^1 m(    <oPRJB___PPTMAC11   hnamd` Arial&Monotype Typography  JDC  X"  0 0   <8o  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  P Prisoner 2   RB  s *DjJ`  RB ! s *DjJ` P   " 6o  P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    # 6o P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0   $ 6,o"` Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, z 5  11<0   RB % s *DjJ  ` RB & s *DjJ` 0 RB ' s *DjJ ` RB ( s *DjJ`   ) 6Po"` 0 Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, z 1  10<0    * 6Lo"` Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, z 10  7<0     + 6Dr"` 0 Pj___PPTMAC11D<   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, v 0  2<0    , <r`RJB___PPTMAC11   hnamd` Arial&Monotype Typography  IC    - 6o0  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    . 6r0  RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    / 6r ` P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    0 6r `P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    1 6!rPRJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0   2 <0&rRJB___PPTMAC11   hnamd` Arial&Monotype Typography  JDC  X" 3 0 p  4 <,r\` RJB___PPTMAC11   hnamd` Arial&Monotype Typography  P Prisoner 2   RB 5 s *DjJ` 0 RB 6 s *DjJ`    7 6,3r `P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0    8 69r `P RJB___PPTMAC11   hnamd` Arial&Monotype Typography  J 0   9 0|