slides-chap6A-communication-soft

Ex ante avant quil connaisse son type a un equilibre

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ex-ante , avant qu’il connaisse son type) ` a un ´ equilibre n -s´ eparateur : EU 1 = E bracketleftBig [ σ 2 ( σ 1 ( t )) t b ] 2 bracketrightBig

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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 = E bracketleftBig [ σ 2 ( σ 1 ( t )) t b ] 2 bracketrightBig = n summationdisplay k =1 integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t b bracketrightbigg 2 dt
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 = E bracketleftBig [ σ 2 ( σ 1 ( t )) t b ] 2 bracketrightBig = n summationdisplay k =1 integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t b bracketrightbigg 2 dt = n summationdisplay k =1 parenleftBig integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t bracketrightbigg 2 dt + integraldisplay x k x k - 1 b 2 dt 2 b integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t bracketrightbigg dt bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 parenrightBig

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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 = E bracketleftBig [ σ 2 ( σ 1 ( t )) t b ] 2 bracketrightBig = n summationdisplay k =1 integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t b bracketrightbigg 2 dt = n summationdisplay k =1 parenleftBig integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t bracketrightbigg 2 dt + integraldisplay x k x k - 1 b 2 dt 2 b integraldisplay x k x k - 1 bracketleftbigg x k 1 + x k 2 t bracketrightbigg dt bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright 0 parenrightBig donc le paiement moyen de l’´ emetteur EU 1 = EU 2 b 2 est aussi d´ ecroissant avec b ` a n fix´ e
Transmission strat´ egique de l’information / Information non certifiable Quel est l’´ equilibre le plus efficace ?

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Transmission strat´ egique de l’information / Information non certifiable Quel est l’´ equilibre le plus efficace ? On compare EU 2 (ou EU 1 ) ` a un ´ equilibre n -s´ eparateur ` a EU 2 (ou EU 1 ) ` a un ´ equilibre ( n 1) -s´ eparateur :
Transmission strat´ egique de l’information / Information non certifiable Quel est l’´ equilibre le plus efficace ? On compare EU 2 (ou EU 1 ) ` a un ´ equilibre n -s´ eparateur ` a EU 2 (ou EU 1 ) ` a un ´ equilibre ( n 1) -s´ eparateur : Apr` es quelques calculs on trouve, pour tout n 1 , EU 2 [ n ] EU 2 [ n 1] > 0 si et seulement si b < 1 2 n ( n 1)

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Transmission strat´ egique de l’information / Information non certifiable Quel est l’´ equilibre le plus efficace ?
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