slides-chap6A-communication-soft

N 3 3 αn 2 bracehtipupleft bracehtipupright

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/n 3 +3 α/n 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 +3 α 2 /n + α 3 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright 0 )
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Transmission strat´ egique de l’information / Information non certifiable Or x k x k 1 = k/n 2 k b ( n k ) (( k 1) /n 2( k 1) b ( n ( k 1))) = 1 /n + 2 b (2 k n 1) d’o`u EU 2 = 1 12 n k =1 ( 1 /n + 2 b (2 k n 1) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright α ) 3 Dans α les termes en k s’annulent avec les termes en n k + 1 donc EU 2 = 1 12 n summationdisplay k =1 ( 1 /n 3 +3 α/n 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 +3 α 2 /n + α 3 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright 0 ) = 1 12 n 2 1 4 n n summationdisplay k =1 α 2
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Transmission strat´ egique de l’information / Information non certifiable Or x k x k 1 = k/n 2 k b ( n k ) (( k 1) /n 2( k 1) b ( n ( k 1))) = 1 /n + 2 b (2 k n 1) d’o`u EU 2 = 1 12 n k =1 ( 1 /n + 2 b (2 k n 1) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright α ) 3 Dans α les termes en k s’annulent avec les termes en n k + 1 donc EU 2 = 1 12 n summationdisplay k =1 ( 1 /n 3 +3 α/n 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 +3 α 2 /n + α 3 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright 0 ) = 1 12 n 2 1 4 n n summationdisplay k =1 α 2 Apr` es quelques calculs, en utilisant n 1 k 2 = n ( n +1)(2 n +1) 6 , on obtient EU 2 = 1 12 n 2 b 2 ( n 2 1) 3
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Transmission strat´ egique de l’information / Information non certifiable Or x k x k 1 = k/n 2 k b ( n k ) (( k 1) /n 2( k 1) b ( n ( k 1))) = 1 /n + 2 b (2 k n 1) d’o`u EU 2 = 1 12 n k =1 ( 1 /n + 2 b (2 k n 1) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright α ) 3 Dans α les termes en k s’annulent avec les termes en n k + 1 donc EU 2 = 1 12 n summationdisplay k =1 ( 1 /n 3 +3 α/n 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 +3 α 2 /n + α 3 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright 0 ) = 1 12 n 2 1 4 n n summationdisplay k =1 α 2 Apr` es quelques calculs, en utilisant n 1 k 2 = n ( n +1)(2 n +1) 6 , on obtient EU 2 = 1 12 n 2 b 2 ( n 2 1) 3 ` A n fix´ e, le paiement moyen du r´ ecepteur diminue quand b augmente
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Transmission strat´ egique de l’information / Information non certifiable
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Transmission strat´ egique de l’information / Information non certifiable Utilit´ e esp´ er´ ee moyenne de l’´ emetteur (donc ex-ante , avant qu’il connaisse son type) ` a un ´ equilibre n -s´ eparateur :
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Transmission strat´ egique de l’information / Information non certifiable Utilit´ e esp´ er´ ee moyenne de l’´ emetteur (donc ex-ante , avant qu’il connaisse son type) ` a un ´ equilibre n -s´ eparateur : EU 1 =
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Transmission strat´ egique de l’information / Information non certifiable Utilit´ e esp´ er´ ee moyenne de l’´ emetteur (donc
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