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Contract bridge as a micro-world for reasoning about communication agents

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9 . 6    -   2 6 5 1  9  - 2 . 6   + (     - 2 -  -   2 6 5 1  , Ô 6 E - 0     1   5 + 2      - G  - + -  1 ›+ , ,   .  - G  . )   +- 7  )  + -   - +) 1.   +  + -(     E   €9 5 6 . 6    +- 2 6 5  5 6    8   )   - + -( 7     2 6 5 1  , ;  +   + 6  + - +   6 7 7 + +  - 1 . 6 - 6  6  1   + +  6 - 1 + E  1. 5  )  - + -  2 +-   -  -    .   ) 2   1    + -   -   + G  5 1 +-      + -  ) + (  + -  16 2  F 0   E   - 2 9 1 -(  2   6 + F9 F      + (      2 +-  9  1        2   F 9 F  1      + (      2 +-  9 2  7  -  +G  1.  + -  2   - 2 F   G  -F 5 + 2 2  5 1 ƒ     6 + 9 ) 2      + (      2    -(  F ,  E - 0 + -( 0  +  7      1   -  +G   +         -  0 + 11  1    1. 5   )  y    - 2 +   0   - 1  - - + -( -   0 - -  8 5 + 2 9 .   2 2 + -(    +7 +  6 1  2   1 0 +   G   .  6    + 6  + - +   2  6 - + -(   E ,

(11)

  - 2 1. 9  6      7 6 1 1  . ›    +  11 . + - 2  7  -   €   ‚ 6 +       5 + 2 2 + -(  ) -  - +   5 1    -   ›  5  5 +1+  +  € +- 7  )  + -  8     2 7  )   5 + 2 2 + -(   1  . + -(  ) -  - , 4  G .   6 ( (    2     +   6   7       2  1  .   +- G 1 G   5  6   7          7  + )  1 1  -  +-     7  1   (  - 6 ) 5   7   +5 1 2 +   +5 6 + -  7      2  H 5 6 +7    .   ) +  6 -  5 1  ( 6    0  +  7     2 +   +5 6 + -       1 +E  1. -   9     +  -     -  6     + 0 +11 1  .   + 6 1   1. 0  11 , 4  6  -    (  + - 1 E   -  +) 1  8  ) 1 , 6   9   2   1     9   6  +   G  1 6  + -( 0  )  + -( 1  -   -  0  E  +7 D           

< 9  - 2      +7   ‘ +  ) - 2  6 + +  2 +   +5 6  2    N       1   7 6  7    +8    2  6 ,  -    5   -   7    + - 7  )  + - 9   7 +  1  - +   »  Õ 5  9  - 2      - 2    1     -   » Õ    -   7  6     2 + -( ,  7 9  0  G   9 D       -  2 0 +   - -  G 6 1 -    5 1      ) +G  5 + 2 7 

9 -  0 6 1 2 -  )  11 .  + - E + 6 - 1+E  1.       2  - <   + -  -     6 + H  + -   -   8      G  - 7  +     2  5   2   9 +  1  5   )   ) 6   )    5  5 1        1      -   17   ‘ +  ) - 2  ,  -   ‚ 6  - 1. 9 -  0 6 1 2   7        - 2 1  - , ;  +  +     1  +G  1.  + ) 1 +   7 2  2 6  + - +7 -  +   5 1     -  5     1 .  5 6   E + - 2 7   - 2 7  0  +    -  - + -( 5 + 2 7 

+     +   9 5 6  (  +- 5   )   7  ) + 2  5 1 . 2 +7 7 + 6 1 +7 + +  2 -  +-   )  7    +7 +   - 2   2  2  6 1   , Ÿ +-  1 1. 9     +    + 2  5 1  )    .   ) 6  + -( 5  6   7    2 6 5 1   2 6 ) ) .  -  1.  +  +  5 . +  -  6   +-    5 1 7     - + -(  5 6    1  .     5  1+ 7   5 6 +  0 -   - 2 , <  2   1     9  +  )   -    1  .  5    2 - 5 1 6 7 7   - -  G   5    1   2 9  G  -  6 (   +  )  . 5    - 1. 0  . ( +G    -  -      -   ( 0  -( , Ÿ   8  ) 1  9 0 +  y 6   )  11    2  -    5 1  (  +-    + -( 1 -/ + -( +-   - 2 9 + )  .  . 1  .   )  11    2 7  )    5 1  - 2     + +  -  G    2 0 +    <   H + 7  +  +  2 -     1. - 9 + 0 +11 6  6  11 . 5  +)   +5 1  7     + (     - 2 -  - 0  E 6        1  .  +  <   ,  -2  7  -   9   +   6  +   G  - )    1     6 , ; 0 2 + 7 7    - 1  .  ) + (  5   ‚ 6 + G  1 - +7 G + 0  2 5 .  2 6 5 1   2 6 ) ) .  -  1.  +  9  G  -  6 (    . +-    1+ . 0 + 11  - G  . 2 +7 7    - +    7 +- 7  )  + -   -   , < 5  6   7    1  . + -(  ) -  -     )   -   6  1  -  7   -  - +     - 2  -   +  ( + -( 5   + (  1. + -  7 7 + + - , ;              7    ) 1  2 6 5 1  2 6 ) ) .  -  1.  +     E     -     - 2 -  -   G + 0  7 +  0 -  - 2 + -    6 - +  y 6  ( + -( 5  +- 7    + 5 1. 1   (  , ƒ 6 )  - 1  .       )     -  5 6  + -( 1  6 +  7 +  9   -  ) 5 +-    1  -  7  )  1  - 7     - +    - 2  , ;  +  +   ) 6   )    7 7 +  + -      9 5 6  G  - + 7  +  ) + (  - 5     + -( 1  7    +5 1   16 + - 9 -    -   - .    2  2 6     5  6   7    2 6 5 1  2 6 ) ) .  -  1 .  +  0 -  0  E ,

(12)

  q ’ A t š t ?  u t ½  A B Š Š B A C º w @  C @ v A   -  +     + - 9 0  0 +1 1     -  - G   G + 0 7     2     +   6   5    2 -   + 2    6 1 +-  2  5 G  , ;   + 6   +      0 - +- 2 +  (   )     0 )  + - ) -  -        6 5  .   )  7  5 + 2 2 + -(  - 2 1  . , ;   7 +  E  . + 2   +-   2   + ( - +  )  +-  +-   1   2 +  +-  + - 5  0   - 1 ( +   1  - 2  5  5 +1+  + +- 7  )  + - , 4 ( +  1 +- 7  )  + -  )   7  )   5 + 2 2 + -(  - 2 1  . 9  - 2   2  7 +- + + -  7    (    2  - 5 + 2 2 + -(  .   ) , ;  +  +  )  + -  +-  2      7 2   1    +G   6 1   , ;    6 1   2  7 +- + -(   5 + 2 2 + -(  .   )  E    + - 6   5    G  2 5 + 2 2 + -( 9  - 2  2 6      7 Ö ~ À Ç Ê | z }À ÊÇ 9 0  +  1 +) +     +5 1     2 2 +   +5 6 + -  0  +    -  8 1  + -   E - 0 - 7              - + - 6  - 6   2   +- 6    5  5 + 1+  +     - + -(  ) -  - 9 0  +  9 ( +G  -    7  -    +-  × 9 6          +   +) 6 1  + -    2 6    2 6    -   5 +    +1. 1   (    7   - 2 ) 2   1  Ø 7  0  +   ×  1 2  , ›D  0 +11 +-     ‚ 6  1   7    1 )  -  7          F  2   1  F € , ;   1   (      +„  7 Ø 9   )      6      + 6   + ( +G   7    .   )   5  5 +1 +  + E - 0 1 2 (  , < 11  ) ) 6 - +  + - 5  0   -   5 + 2 2 + -(  - 2 1  . + -(  ) -  -  +  +-   )  7  -    + -   - 2    7  2   1  ,  - + +  11 . 9      2  1  .   +      -  2 0 +     7  2   1   6 ) )   +„ + -(   + - 7  )  + -(      2 2 6  + -(   5 + 2 2 + -( H +7      2  1  .   0 +     9 +   -  2 2  8    -    +-  (  +-  2   .    + „  2 2 6  + -(    6    7   1  . 9  - 2   E        +   +) 6 1   7   -  0   7  2   1  0  +     7 1     8   +- 7  )  + - ,  Ù Ú Ú Ù  Û N G  16  + -›-  6   1 -  € 3 + 2 2 + -(  .   ) › 6 1 5    2 €      -  +G  2   1  ›  +) 6 1  + - € Ü Ý  % + -( 1   6 +  -  1.  +  ›5  6   7    € ¶ 1 5  1  -  1.  +  ›<  1  - - + -( )   2 €

Probabilistic

information

about

representative

deals

· w B  A B ™ p  † G   G +  0 7    2     +   6  

(13)

 2   1 1. 9   1+- E 5  0   -   5 + 2 2    - 2      2  1  .   0 6 1 2 5   . ) )   +   1   6    5 + 2 2   0 6 1 2  1  5   5 1   E      2  1  .   0     1+E  1+  2 0 6 1 2 5  7 )  E + -(   -    9 ( +G  -  -   6  1 2   1  - 2    7  2   1  0  +     7 1        7 E - 0 1  2 (  7     1  .   ,  -    +  9 +    )     +  +  + -(  -    1 ( + -( 5  7    8  -  +G  +-   )  7  ) 6  + -  1    6     9  - 2  )  F ‚ 6 + E  - 2 2 + . F  G  1 6  + - )   2 +    ‚ 6 +  2 ,  - 6  + - + +  1  .  9 0    G      - +) 1 )  -  +     -  6   1 -  0  E         +- 7   0  6   -   9 -  7  -   6 )   -     9  - 2 -  7   6 +  -     , N    -  +    +-  2 -  - 6 ) 5   7 2   1  0 +  E - 0 -    6 1  9  - 2 +    -    5 1 7  E + -(  - 6 - E - 0 - 2   1   + - 6 9  - 2  2 6  + -(    7 7 6    - 6 6  9       - + -(    5  5 +1+ +  7 )  E + -( „    +   -  + E       +G  1. ,  ) 1  )  -  + - 7   5 + 2 2 + -(  ) -  - 7    .   .   ) +  - 0     -  5 1. 7    2 G  -   2 9  - 2 0  0 +1 1 2    + 5  + +- )   2   + 1 +-    + -  ,  -   + - : 9 0  0 + 11  E    6      2 2   + ( - 7      2  1  .   ,

(14)

´ q = A C º w @  C @ v A  t ¸ @ º  > w u u w s  C t ™ š t s  s @ ´ qp Þ t ¾ @ º  > w u u w s  ¾ t A ¿ ? ‹ B s  ß B ™ š Š  D  0 + 11    5 . ( +G + -(  - +116    +G   8  ) 1  9 +- 0  +     5 + 2 2 + -(  .   )    )  E    +) 1 9 5 6  + 11 - -   +G +  1 2   +  + - H   2 +   6   + - +-  +   6 5     + -0 +11  G + 2    - +  1 +) 1 )  -  + - 2   +1  ,  -  + 2      + 6  + - +- 2 +  (   )  

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· t v > Š  p

’ B ? ? ã · w B  A B ™      E + -(  2   +  + - + -   5 + 2 2 + -( 6      -  2 0 +  

9 0  +   +  )   -    -  6   1 5 + 2   0 + -(   16 5  6 +  - 2   +-   )   , D      2 6 5 1 2 7   E   6 9 +- 2 +   + -(  -  - + -(   - 2  - 2   E + -(   -   5 + 2  +  5    6 + H -  +  9       5 + 2 

9 0  +    6 1 2   0  )   + -(  + ( - + 7 +  - 1. 5      -  ) +- +) 6 )    -   , › +-     -   0 + 11   G   -       -   5 + 2 9     -  7 7  2    0 +      1 ) +- +) 6 ) € , N          2 9 0  +     6 )  5 1. )   -          G   . 0   E   - 2 0 +  - ( 2  6 + H - 0 6     2   + 2  -  +  -  8 5 + 2 ,  +   1          6 1 2 5   +- E + -(  5 6   -    +- ƒ     H 0 +  6  + ) 1 +7 . + -(   + 6   ) 6   9 0    -   .    +  - 1 .  1   -  +G       +     € 5 + 2 (  )  2 +    1 . 0 +  :

9   1   5 € }À Á }Ê Ê~ ä z Ë Â 0 +  

, D    +  )   -  9 +- 6 + + G  1 . 9 +      -     6 1 2 5 + 2 :

+ 7    -  + 2       +    - 2 + 

(15)

 + ( - + 7 +  - 1 . 5      -      + - 2 +   2 5 .  +      2 + -( 5 + 2  H    0 +       6 1 2    , < -  G  1 6  + - 7   7 +   1   -  + G  +  ‚ 6 +     + (   7  0   2 9  +-   0   8   +  - 2   5 + 2 2 + -( H  1 1   +  -        . +    +)    0 1 +E  1 . + +  › -   5   +  7   +- 7  )  + -( + G  - €   :

0 +11 )  E  ,  -    +   9  +  0 +1 1 5  2 -  5 . 6  + -(        +   +) 6 1   (  -        7  2   1  9  - 2   -(  + -(  -  G  16  + - 7      2   1 7  )   -  6   1 -  7   6 +  -     H    8    2 G  16  7    -    +    -  ) 6  2 5 . ) 6 1 + 1. + -(    5  5 +1+ . 7        6 1 5 .       7  )  E + -( + 9  - 2  G    ( + -(  +  G       7  2   1  , ;      - 2 5 + 2 +  )   + -     + -( 9  +-          0   +5 1   - +- 6  + -  7   5 + 2 2 + -(  0  -   2     -  5 6 0   2   +  + -    0 +1 1 )  E  -  +  -  8 5 + 2 , <  + -   7 +    1   -  + G   5 G  9 0  5  ( + - 5 . (  -    + -(    7  2   1  7  )   +- 7  )  + -  G  +1  5 1 6  + -       -  + 6  + - , Ÿ      7      2   1  9 0  ) 6  2   + 2  0         0 +1 1  -  + 2    +    - 2 5  F  + ( - +7 +   - 1. 5      -       1    2 . +- 2 +   2 F , D  0 + 11   7    . +   1 )  ) 5   7  +    7  2   1     9  - 2 7 6     6      - 2    7         - 2 6    - 2  +-  9  5  + -(   E - 0 - 6    - 2 , D  - 0  0 +   6  + - 7 G + 0     0    G     6 )  2    +    - 2 +    , Ÿ  )  +  9 (     0 +    5 + 2 2 + -( 9 0    -(  -        7  2   1  0  +        -     + 5 1   - 2      6 1 2  +- E   6    2 , † -    (  +- 9 0    11  . +   1 )  ) 5   7      9  - 2 1  5    6    - 2 , ›  )  ) 5           - 2 +     6 )  2 5    € , ;   ‚ 6   + - - 0 +  0        +   ( 2   - 2 7  )   + - 7 G + 0   6  0         + 2 -    2 1  G  1 7  2   1  ›  €9  +  +)     6 ) + -(     6    - 2 +   , <  6  6  19 0    11  . +  1      - 2   , D  - 0 0  - E - 0 9 7        9 0         ) 5 +-  + -   œ  +  5      -    G    (  › G    1 1     - 2   € 7   œ  9 0   - 1  . + -(  -     + -ƒ     ,  7 + +  9 0     6 )       0 6 1 2   G  5 + 2 :

H    0 +   9 0     6 )    0 6 1 2   G      2 , <   6 ) + -(    +  5 + 2  - 2    5 + 2 2 + -( 9 0    - - 0   +)      8    2 G  16  7  1   -  +G  5 €9 + -     )  0  .   0  2 + 2 7   €  5 G  ,  -  +    + 6 1       9 + 6  -  6 ›       )  0    6 -    +- 6 + +G  1. €9   5 + 2 2 + -( :

 -   +   5  5 1.    + (    +   H :

0 + 11 7  -   G   ( 2    -   7 )  E + -( 9  G  - + 7          - 2 0  +    0 6 1 2  -  + 2    9  - 2 - 0  +    0 6 1 2  -   ‚ 6  - 1.    

,  -    0  2  9 0    -   1  6 1          6 1 2 - 5   -  6   (  2 )  E    2   +  + - 9 5    6     +  1 +E  1. 2   + 2  0  -( ,

(16)

 -   7 1 1 0 + -(  6 5    + -  9 0  0 + 11 2     +5  +- )   2   + 1  0   G   + 6  7 6 -  + -  1+ +  -   2  2    1 +„     5 G   -  1 .  +     + ) 1 )  -  2 + - 6   .  G    + - 7   5 + 2 2 + -(  ) -  - , ´ q   ˜ º  > w u u w s  ? ž ? @  ™ <  0    G  2     + 5  2  5 G  9   2  7 +- + + - 7   5 + 2 2 + -(  .   ) +- )     1+   (   )     5   -     - +  1 1.    2 6   1 ›       8   + -(      )  - + -²Í 6 +- 1  - “ ³ €H    6 1   E    + - 6   5 + 2 2 + -( 2    - 2    (   )  0 -   2  9  - 2  2 6     -  8 5 + 2 , ;  +  +  +-  6 7 7 +  + - 7    G    1     -  , Ÿ +  1. 9 0     - + -      2 + -     + -(     +  1 9   - 2     7  2 5 + 2 2 + -(  .   ) 1 +E  4 +- 2  1 Ì 7   † 3 < H 0  0  - 6    F-  6   1 F ›- -   - G  - + -  1 €  .   ) 9 0     5 + 2     2  7 +-  2 +-   )  7  ) ) -    -    -         6 )   -  5 +1 + .     -  - 2 2  2 6   å , N G  - )   +)   - 1 . 9 0  )  7  - 2 - 0  - E - 0 0  +    ‚ 6  -         +5 1 7  ( +G  -    2  H 0       0  - E - 0 0    - 2 + + -  5  +- -   2   1 9 + 7  ( + G  -   ‚ 6  -   +  5    +5 1 ,  -    0  2  9   5 + 2 2 + -(  .   )   6 1 2 5   5 1   E    5 + 2 2 + -(  +   .   + - 6 9  - 2 2   + G   -    +-  -      2      1  .   0 6 1 2   G    2  1 2 5   5 1 )  E    5 + 2       )  2  ,

overcall(d,Bidding,Conditions)

:-single_non_pass_bid_so_far(Bidding,bid(Level,Suit)),

is_a_major(Suit),

in_between(1,2,Level),

other_major(Suit,OtherMajor),

Conditions = [strength(13,maxPoints),

biddability(OtherMajor,1),

no(biddability(OtherMajor,3))].

response_to_1_in_a_suit(rd,[d,bid(1,Suit)|_],Conditions)

:-real_suit(Suit),

Conditions = [strength(8,10),

minLength(Suit,3),

balanced].

response_to_1_in_a_suit(rd,[d,bid(1,Suit)|_],Conditions)

:-real_suit(Suit),

Conditions = [strength(10,maxPoints),

balanced].

· w B  A B ™ ´  N 8  ) 1  7 5 + 2 2 + -(  6 1   æ Ï V S ] X Q n X W R ç\ b Yc c Y[ n \ a \ US R Y\ b W \ S c Q [ M Q c S X [ P UW [ c W X c d Ò YZ\ ZW [ c è é j k M P Y\ f ` X X S [ UZa UV S R Q \ U ] Q ] ` ZW X \ a \ US R Y[ P ^ S c S [ ¥ W [ c f Q R b Y[ S \ S ZS R S [ U\ TX Q R UV S P UW [ c W X c K R S X Yf W [ W [ c m X YUY\ V K l Ñ ê \ a \ US R \ k

(17)

 - 2 +  (   )  0    -         8  ) 1   7  6 1  7  )   5 + 2 2 + -(  .   ) , ;   7 +  +  -  7    6 1     2  7 +-   0   -   E   6 2 6 5 1 +  1  (  1 ›          6  1 1. 7 6  )        € , ;  +    + 6 1    6 1    .      E  6 2 6 5 1 +    +5 1 +7   - 1. - -     5 + 2  7      5   -  5 + 2 7    +-  )  y   6 + 9 6 - 2      - 2 + + -     +    6    - 2      + (      2    -(  7  1     +-  9       )  y  +   5 + 2 2  5 1 9 5 6 - 2 6 5 1.    5 + 2 2  5 1  6 + , ;      - 2  - 2  + 2  6 1    - 2 1   2 6 5 1  7  E   6 2 6 5 1      -   1  G  1    +-      + - +        2 6 5 1   0   5  1  -   2   - 2 9 0 +   +        + (      2 +-   - 2  1          2  +-   2 6 5 1  2  6 + 9  )     -   +-  ,  - 2 +  (   ) : 0    0  -  8  ) 1 7  5 + 2 2 + -(   ‚ 6  -   9 (     0 +   )  7   )   + )   - 7    E - 0 - 5 . D    7     5 + 2 7 

›D       - - 6 -   2  1    » + -  9 1   E 7  7 + +- ƒ     9  - 2  5 + 2 2  5 1  2   6 + H       1     -   +-  H N         5 + 2 2  5 1  ƒ     6 + 9  - 2  +       + -  0 +   5  1  -   2   - 2 9      +-  0 +   - 6 - 5  1  -   2 -  € ,

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’ B ? ? p

’ B ? ? ´

'W',[str(5,maxp),no(confirmed_fit('H')),biddability('S',1)].

'N',[str(0,12)].

'E',[str(18,19),balanced,biddability('H',2)].

'E',[str(16,20),unbalanced,biddability('H',2)].

· w B  A B ™ ¼  N 8  ) 1 7 6 6 7  )   5 + 2 2 + -(  .   )

(18)

´ q ´ ë  s  A B @ w s  A  š A  ?  s @ B @ w ½  u  B Š ? D  - 0 2     +5  5  +  7 1.        +   +) 6 1  + - ) 2 6 1 H  +  +     ) -  -       + G      7  -    + -  9  - 2 6 6     7  2   1  , ;   5   +  )     - +  ) +    +) 1 G    + - 7   |  Á  | Ç Â È Ç }Ë Ã Äz ÊÂ È z À À  z Ä}À ä  1 (  +  ) 9  - 2 +   6 ) )   +„  2 +-   7 1 0      5  1 0 › 2 +  (   ) » € ,  - + +  11. 9   6 - E - 0 -    2     2 +   +5 6  2   - 2 ) 1. 5  0   -       6 -    -   - 2  , ;    +) 6 1     - -     1 H      +    + - 9 + 7 +       E     0       11  -    +-      1   2 .   +  7 + 2 9  - 2 + 7 -  +  7 +- 2   + 7    2  0  +  +   -  0  +)  G    2  (    7 7 + 9  - +- 6 + -( 6 - +1     - 2   +  7 +     -    +-  ,

Constraints, own hand

Deal matching the constraints

Randomly distribute unknown cards

Are all constraints satisfied?

Are the constraints satisfied worse?

Randomly exchange a

pair of unknown cards

No

No

Stop

Yes

Yes

Undo swap

· w B  A B ™ ì  ;    +) 6 1  + -  1 (  +  ) ‘ +  (   )   - +- 6      8  ) 1 7  ) 2 +  (   ) : 9  - 2   0   . +   1   7  2   1   2 6   2 5 .    + ) 6 1  + - ) 2 6 1      + 6  + - +  G + 0  2 7  ) D    G +  0 +- 9  - 2 0    -       7  -   +5 1  N     - 2  ›  5 € (  -     2 7  )   ( +G  -  -    +-  ›   €í , î §U V W \ b S S [ ] Q Y[ US c Q ` U UQ ` \ b a K [ c S X \ Ñ UUQ \ \ Q [ UV W U UV S f Q [ \ UX W Y[ U\ Y[ UV Y\ f W \ S W X S W f U` W ZZa [ Q ^ V S X S [ S W X U Yn V U S [ Q ` n V UQ f W ] U ` X S UV S Y[ TQ X R W UYQ [ W _ W YZW b ZS TX Q R UV S b Yc c Y[ n k M Q \ U YR ] Q X UW [ UZa ¥ UV S a c Q [ Q U Y[ f Z` c S U^ Q _ YUW Z ] YS f S \ Q T Y[ TQ X R W UYQ [ ¨ ï W \ U f W [ [ Q U V W _ S W [ a P ] W c S \ ` ] ] Q X U ðQ UV S X ^ Y\ S V S ^ Q ` Zc V W _ S \ V Q ^ [ YUñ¥ W [ c YU Y\ W Z\ Q ` [ ZYg S Za UV W U V S V W \ W \ U X Q [ n b Yc c W b ZS l Z` b \ ` YU k ¢ YUV UV S \ S f Q [ \ UX W Y[ U\ W c c S c ¥ UV S \ S U Q T J oc S W Z\ ^ Q ` Zc b S \ ` b \ UW [ UYW ZZa c YTTS X S [ U k

(19)

ò s t ¾ s ‰  ? @ º B s u ‹ Ž t s ? @ A B w s @ ? t s @ º  t @ º  A º B s u ? ‹

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» N         5 + 2 2  5 1      6 + 9  - 2

< /   Â }Êó Â |     +-  5  1  -   2

à   ~ |      +-  6 - 5  1  -   2 · w B  A B ™ ô B  ¶ +G  -  -    +-  ’ t ? ? w > Š  á B ? @ º B s u ? ‹

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(20)

´ q¼ á ½ B Š v B @ w s  š t ? ? w > Š  C t s @ A B C @ ? D  - 0 2     + 5    -  6   1 -  0  E  6   2 7   G  16  + -(  -     H        0 7     9 -  7  -   6 )  - 2 -  7   6 +  -     , N    -   E     +- 6      7    2  7  )   7 6    - 2  ›0 +     6   2 2   1     7 +  €9  - 2 6 6     7  :    1 - 6 ) 5    9       - + -(    5  5 + 1+ + +         + E  0 +11 5  )  2  ,  -       7   -  7   6 +  -     9    2   7    6 +  +         -(  2       6 )  6 + +  7 +  ,   6   1 -   +-   +  6    7  )  E      0 +- 6 2   9  - 2 1   -  -   6     +   6 6  0 +  6 2 + -(  - .  + -( )     -     1  6 1  + -(   0  + (   -    - -   + -  5  0   -   + - 2   , ƒ 0  G   9 + +  +-    +    -  + 2    5 1 . )    7 7 +  + -   7  )      +-  ) 6 - 7         + -( -   + - 6 9     -   6  G  1 6         - + -( 7   6    0  +   6 )  -   -  + 2   +)   - +-   2 )  +- H    .   ) 0    G  6   2    ) 2  1     +    3   E (  ) ) -  1  .   2     + 5  2 + - ²;    6  Ó  y - 0  E +  ³ , )  7   +- 6 - 2         -         ) 6  2 7   6   +-  9 I Ÿ I  , ;   I Ÿ I     2   - 2  - -  , ( ,    + (      2  9 2 +   + 5 6 + - 9  -  1   - 2     , ;      +- 6 - 2         -    +7 +  + (      2  9   1  6 +  1 -(   , I ›  € I ›  € I › € <

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(21)

I   7     6  6   7 -  -  +    0 - + - 2 +  (   ) “ , ;   -   -  +   7 -  + - 6 1  .   ›    - 2   €9 0  + 2 2  - 1  .    ›   - 2       €9  - 2 -  6 6 1  .   ›  : - 2   € , N    - 2  +-    + 2 2  - 1  .    +   - -    2     - 2  + -   1  .     5 G   - 2 5  1 0 + ›+ , ,   -  +  7 6 11.  - -    2 € , < 11    - -   + -     0  + (   2 H  2 2 + + -  1 1.     - 2   -  +-  - +-   -  1      1 2 G  1 6  , ;   6 6 7  - 2  +   7 6 -  + - 7   0  + (   2  6 ) 7 +  +- 6   - 2 + -   -  1      1 2 , ;   -        + -  2 6  + -(     - 2   2 Æ z Ö ÷ Å { | ~ { z ä z Ê }~ À z Ää ~ | }Êó Ë ² 6 )  1   9 ƒ +- -Ó D + 1 1+  )   “ H 4 + )  -  “ ³ , ;   0  + (   -    - -   + -     + - + +  1 +„  2  )  11   - 2 ) - 6 ) 5    , ;   -      7  2 0 +   1   (  - 6 ) 5   7 ›          2 € 2   1  0 +  E - 0 -    6 1  , <  6  11 . 9 7      2   1 + -     +- + -(   9   -      7  2 0 +  2   1        - + -(  1 1   ) 6 + -  7   ›- -   6 ) €  6 +  , ;   -     1  6 1      + 6 6  9 0  +        -  )    2 0 +       6 1  -   2   1  , ;   0  + (   -    - -   + -  5  0   -   - 2            2     2 + -( 1 . 7  )   6 6 - 2   5   E 0   2    +- 6 - 2   , < 7    - 6 ) 5   7        6 (      + - + -(   9   -      - G   (  2 0   2   ( 1 5  1 +) 6 ) ,  7 - 9    8   +)  - +        2 0 +  -  0 ›  - 2 ) € 0  + (   -    - -   + -  , D   -   -      - G   (  2 9 + +     2 0 +  -  0 2   9   0    - + -    + ( +-  1   +- + -(   ,  - +- 6 + -(    6 - - + -(  8  ) 1  7  ) 2 +  (   ) : 9 2 +  (   )    0    6 6 7  )   -  6   1 -  9 ‚ 6   + 2 7   -     + - ‘ +  ) - 2  0 +  D     2   1     , ;   7 + ( 6       5 ) ( + G     5  5 +1 + +  7 )  E + -(     + E  +-  16  +G  , <    - 5     - 9   -    +)    › ‚ 6 +      -  5 1. 9 +- 6  +- + - €   :

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x 3 4 x 2 xx x 4

100 100 100 100 100 100 100 100 100 100 91 78 5 0

· w B  A B ™ ø ‹ N 8  ) 1 7 -  6   1 -  0  E 6 6 ;      1+ -   + -   2 +  (   )   0   +- 6 2   H 7 +         ) 6  2 7   6   +-   - 2   -     1  .     6 +   1 2 + -(  , < 1 1 G  1 6          -(  2      -    -    - + -(   2   1     ›+ , , D   €  )  7 +  ›7 11 0  2 5 .  9 N  - 2 €9  - 2       6 )  6 + 9 ‘ +  ) - 2  9 +  7 +  ›7 11 0  2 5 .

9

 - 2

€ ,

(22)

´ q ì ˜ º  @ t š ˆ Š  ½  Š ‹ t ½  A B Š Š C t ˆ t A u w s B @ w t s t ¸ u  C w ? w t s ˆ ™ B ¿ w s  <  1 G  1 9     E 7   5 + 2 2 + -(  ) -  -   - 5   6 ) )  2 6 +-  7  0 0  2   +     -  + 2   +   G  + 1  5 1 + - 7  )  + - 9  - 2   G + -(   7  )  2      -  5 1   ) 6 - 7  -  1 .  +  2   + 2  0  +  7     +5 1 5 + 2       5    5   -  , D   F      -  5 1   ) 6 - 7  -  1 .  +  F ) + (  5  +  9 -  6   1 1. 9 2   - 2  - -  -  8 9 5 6 +-     +  1  .   )     0 + 11   - .    5  0 5 G + 6      -    + - E + -(   +      5   5 + 2 +   1    2 . 5 G + 6  9   + )   1 +) +    5   -  8    2  2 , ;   + )   1 +) +   -  +    5  7 +8  2 9    - 5  +) 1 )  -  2 )    6 5 1 . 9       .   )   -   ) 0  + (  6    8    2 (  +- +- 2   +  + - ‚ 6  1 + .  (  + -    1   7 +)  9 0  +1  E   + -(  G    11  G    (  +)   1+) + 7  +  5 + 2  , ;  +  + 2      5   -          2 +- 2   5 . 6    11  - 2  +   1 1  ( 6   9 ² 6    11 Ó D  7  1 2  ³9  - 2 )  . 5  +-      2 + -  7 6 6   G    + - 7 6   .  ,

Bidding history

Bidding plan

Coordinator

Evaluation

Simulation

Probability of

making contract

Bidding system

Constraints on deals

Representative deals

(Bayesian planning system)

(rule-based)

(neural net)

· w B  A B ™ ù  <    +   6   7   5 + 2 2 + -(  ) -  - < 7 1  8 +5 1 0  . 7   ) + -(    + G    2   +  2 7 6 -  + -  1 + . +    6  6      1 G  1    F   7 + -  )  - 1 F    - . ) )  - 9 + +    + 5 1    +- E + -(  - 2    2 6     1  + G          + ( -  2     +5 1  + -  9   1   + -(   -   6    - 1. ( + G  -     + -( , ;         - 6 ) 5   7 F E - 0 1 2 (   6     F ›/  €9 0  +     - 5  6   2  .  - 2 +)  G       6    . 7    .   )   G  16  + - 7     5 + 2  0   H    + ) 1  -   ( +G    6 (    - 2     2 .   +)    1 0   9 0  +1    )     +  +   2 -    E   -    +  5 1 +)    7  )  2   + 1 2  -  1 .  +  , 3  1 0 9 0  0 +1 1 2     +5       +) 1  /  9 0  +  0      6    - 1. + ) 1 )  - + -( , 3  7   0  + (  + -( 6     +5 1  1   -  +G   9   5 + 2 2   ) 6        +- 0     .    , ;   7 +    + -   2   +  + -  )  E + -(      +   6    11    6 1   5    2 2  7 +- + + - 7   5 + 2 2 + -(  .   ) 9 2    ) + -    5 + 2  1 (  1 +-       -

(23)

 + 6  + - ,    - 7  6    5          - 1. -  5 + 2 +   11 0  2  7   8  ) 1 9   -   )  .   G    E  2 7      0 +  3 1   E 0 2 9  )  2     -  7   5 + 2 0  +  7         +7 + 2    -   ,  7  +  +   9 - 7 6      6 (  +  -        . ,  -(  -    19  0  G   9     0 + 11 5  0  )   5 + 2      5  0   - ,  -  -    (  )   1+E       9 -  )  1           + -( +   -  8   )  1.  8  -  + G  / 9  - 2   -     1. 5  6   2 H    5 1  ) +            (    )  - .  1   -  + G   ›  +-        1  .        2     6 - E - 0 - €9  - 2   5  5 +1 +  +   1  6 1  + - G    1 1       +5 + 1 + +   0 +1 1 -  )  11 . 5  + - 7    +5 1.  ) 1 8 , ƒ 0  G   9 G   + 6  E + - 2  7               + -(     +1 1   +5 1 9  - 2 G   . 6   7 6 1 , † 7  - 9 + +  ‚ 6 +   - 6 (   +) 1 .  -  + 2       +5 1 7 +-  1  -         -   +    7      - 2 + 2   5 + 2 9 0 +  6 0   . + -(  5 6   +    1  +G  1  6  +5 +1+ . , D    -   8 +)    +      -  5 1. 0  11 5 . (  -    + -(   )  1 1   7  2   1  9  - 2  6 - - + -(   5 + 2 2 + -(  .   ) - -  2    ) +- +  +   1 1. -     7   ) H 0  0 +11   7       +5 1   7 7 +-  1  -          - 2 + 2   5 + 2   -1   2     Ö ó ~ }Ö Â Ç Â Ê 7    5 + 2 , â â t v @ º ‰  ? @ — t A @ º á B ? @

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· w B  A B ™ p ú  3 + 2 2 + -(     8  ) 1

(24)

;  6  +-    8  ) 1   0 - +- 2 +  (   )    5 G  9     +     7    5 + 2 F I    F +  û   ; üH 7  

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(25)

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(26)

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References

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