slides-chap6A-communication-soft

Les mˆ emes croyances que lorsquil re coit un

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les mˆ emes croyances que lorsqu’il re¸ coit un message d’´ equilibre ( m 1 ou m 2 ) Exemple : m 1 = 0 , m 2 = 1 et μ ( t | m ) U [0 , x ] si m [0 , x ) U [ x, 1] si m [ x, 1]
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b 0 x/ 2 x/ 2 + 1 / 4 x/ 2 + 1 / 2 1 σ 2 ( m 1 ) σ 2 ( m 2 )
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b 0 x/ 2 x/ 2 + 1 / 4 x/ 2 + 1 / 2 1 σ 2 ( m 1 ) σ 2 ( m 2 ) donc σ 1 ( t ) = m 1 si t + b < x/ 2 + 1 / 4 m 2 si t + b > x/ 2 + 1 / 4
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b 0 x/ 2 x/ 2 + 1 / 4 x/ 2 + 1 / 2 1 σ 2 ( m 1 ) σ 2 ( m 2 ) donc σ 1 ( t ) = m 1 si t + b < x/ 2 + 1 / 4 m 2 si t + b > x/ 2 + 1 / 4 On ´ etait parti de la strat´ egie suppos´ ee d’´ equilibre σ 1 ( t ) = m 1 si t < x m 2 si t x = m 1 si t + b < x + b m 2 si t + b x + b
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b 0 x/ 2 x/ 2 + 1 / 4 x/ 2 + 1 / 2 1 σ 2 ( m 1 ) σ 2 ( m 2 ) donc σ 1 ( t ) = m 1 si t + b < x/ 2 + 1 / 4 m 2 si t + b > x/ 2 + 1 / 4 On ´ etait parti de la strat´ egie suppos´ ee d’´ equilibre σ 1 ( t ) = m 1 si t < x m 2 si t x = m 1 si t + b < x + b m 2 si t + b x + b donc on doit avoir x + b = x/ 2 + 1 / 4 x = 1 / 2 2 b
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Transmission strat´ egique de l’information / Information non certifiable ´ Etant donn´ e la strat´ egie σ 2 du r´ ecepteur l’´ emetteur de type t va envoyer le message m ∈ { m 1 , m 2 } qui le fait jouer le plus pr` es de t + b 0 x/ 2 x/ 2 + 1 / 4 x/ 2 + 1 / 2 1 σ 2 ( m 1 ) σ 2 ( m 2 ) donc σ 1 ( t ) = m 1 si t + b < x/ 2 + 1 / 4 m 2 si t + b > x/ 2 + 1 / 4 On ´ etait parti de la strat´ egie suppos´ ee d’´ equilibre σ 1 ( t ) = m 1 si t < x m 2 si t x = m 1 si t + b < x + b m 2 si t + b x + b donc on doit avoir x + b = x/ 2 + 1 / 4 x = 1 / 2 2 b Il existe un ´ equilibre 2-s´ eparateur si et seulement si b < 1 / 4
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Transmission strat´ egique de l’information / Information non certifiable x < 1 / 2 car l’´ emetteur a tendance ` a vouloir exag´ erer la valeur de t
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Transmission strat´ egique de l’information / Information non certifiable x < 1 / 2 car l’´ emetteur a tendance ` a vouloir exag´ erer la valeur de t L’intervalle [ x, 1] a une longueur 4 b de plus que [0 , x ] 0 x = 1 / 2 2 b 1 / 2 1
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