exercices_jeux

# Eò eóòòa îøôa ðeó

• Notes
• bilone
• 35

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Unformatted text preview: eÒ eÓÒÒa îØÔa × ÐeÓû ØÑ a Ög iÒa Ð d e ÐaÖÑ edÓÒe ÐÐeÒ eÓÒÒa îØÔa × ÐaÚa ÐeÙ Öd e θ 1 e ØÔÓ ×ÓÒ × θ 2 = − 1 aÖÑ eÔ eÙ Ø ê ØÖed ed eÙÜ ØÝÔ e× :×Ó iØ×ÓÒÓû Øe×Øé ÐeÚ é θ 1 = θ H 1 ×Ó iØ×ÓÒÓû Øe×Øfa ib Ðe θ 1 = θ L 1 Óù − 1 2 ≥ θ H 1 > − 1 > θ L 1 ≥ − 2 e×Ô ÖÓbab iÐiØé×aÔ Ö iÓ Ö i×ÓÒ Ø Pr( θ L 1 ) = β > e Ø Pr( θ H 1 ) = 1 − β > ÒÒÓ Øe θ M 1 = βθ L 1 + (1 − β ) θ H 1 D é Øe ÖÑ iÒ eÞ Ðe×fÓÒ Ø iÓÒ ×d eÖéaØ iÓÒd e×ÖÑ e× Ða fÓÒ Ø iÓÒd eÖéaØ iÓÒd e ÐaÔ ÖeÑ iè ÖeÖÑ e e×ØÓÒ Ø iÒgeÒ Øe×ÓÒ ØÝÔ e D ÓÒÒ eÞÙÒ eÖeÔ Öé×eÒ Øa Ø iÓÒg ÖaÔh iÕÙ eD é Øe ÖÑ iÒ eÞ Ðe×ÕÙaÒ Ø iØé× e Ø ÐeÔ Ö iÜdéÕÙ iÐib ÖeeÒ fÓÒ Ø iÓÒd e θ 1 iÐaÖÑ ea ÐaÔÓ ×× ib iÐiØéd eÖéÚ é Ðe Ö×ÓÒÓû ØÙÒ e fÓ i×ÕÙe ÐÐeeÒ e×Ø iÒ fÓ ÖÑ éeÕÙaÒdaÙ ÖaØ e ÐÐe iÒ Øé Öê ØÐe fa iÖe dÓÒÒ eÞÙÒ e jÙ ×Ø ia Ø iÓÒ Ða id edÙg ÖaÔh iÕÙ eÔ Öééd eÒ Ø ?C ÓÑÑ eÒ ØeÞ E Ü eÖ ie9 D ÙÓÔÓ Ðed eC ÓÙ ÖÒÓ Ød iéÖeÒ ia Ø iÓÒe ØaÚaÒ Øage iÒ fÓ ÖÑ a Ø iÓÒÒ e Ð ÒÓÒ × id è ÖeÙÒdÙÓÔÓ Ðed eC ÓÙ ÖÒÓ Ø ÐiÒ éa iÖeaÚ eÔ ÖÓdÙ iØ×d ié ÖeÒ ié×e×d eÙÜÖÑ e× i = 1 , 2 ×ÓÒ ØeÒÓÑ Ô é Ø iØ iÓÒ eÒÕÙaÒ Ø iØéÔ ÖÓdÙ i×eÒ Ød e×b ieÒ ×d ié ÖeÒ ié×e ØÓÒ Ød e×Óû Ø× ÐiÒ éa iÖe×égaÙÜ ÒÒÓ Øe C ÐeÓû ØÑ a Ög iÒa Ðd ehaÕÙ eÖÑ e Ðe×Óû Ø×Ü e××ÓÒ Ø×ÙÔÔÓ ×é×ÒÙ Ð× ad eÑ aÒd e iÒÚ e Ö×e ÐeÔ Ö iÜ ÔÓÙ Ö ÐeÔ ÖÓdÙ iØd ié ÖeÒ iédÙÒ eÖÑ e i e×ØdÓÒÒ éeÔa Ö p i ( q i ,q j ) = A − q i − β i q j , i,j ∈ { 1 , 2 } , i negationslash = j, Óù q i e×Ø ÐaÕÙaÒ Ø iØéÔ ÖÓdÙ iØeÔa Ö ÐaÖÑ e i e Ø β i Ñ e×Ù Öe Ðee Ød ed eÑ aÒd eÖÓ i×éÒ ×ÙÔÔÓ ×eÕÙ e β 1 e Ø β 2 ×ÓÒ Ød eÑ êÑ e× igÒ ee ØÕÙ e − 1 ≤ β i ≤ 1 Ò ×ÙÔÔÓ ×eéga ÐeÑ eÒ Ø A > C ≥ ea × β 1 > e Ø β 2 > Ó ÖÖe×ÔÓÒdd e×Ô ÖÓdÙ iØ××Ùb ×Ø iØÙab Ðe×e Ø Ðea × β 1 < e Ø β 2 < Ó ÖÖe×ÔÓÒdd e× Ô ÖÓdÙ iØ×ÓÑ Ô ÐéÑ eÒ Øa iÖe× D é Øe ÖÑ iÒ eÞ ÐéÕÙ iÐib Öed ea ×h ×Ù ÖeÑ a Öh é Ðe×ÖÑ e×hÓ i× i××eÒ Ø ÐeÙ ÖÕÙaÒ Ø iØéd eÔ ÖÓ dÙ Ø iÓÒ × iÑ Ù ÐØaÒ éÑ eÒ Ø ÓÙ ÖÕÙ e ÐÐe×Úa ÐeÙ Ö×d e β i i = 1 , 2 Öe ØÖÓÙÚÓÒ ×ÒÓÙ × ÐeÑ Ód è Ðed eC ÓÙ ÖÒÓ Ø×ØaÒda Öd ×aÒ × d ié ÖeÒ ia Ø iÓÒd e×Ô ÖÓdÙ iØ× ? D aÒ × Ða×Ù iØed e ÐeÜ e Ö ieÓÒ ×ÙÔÔÓ ×eÔÓÙ Ö× iÑ Ô Ðie ÖÕÙ e A = 1 C = 0 e Ø β 1 = β 2 = β Ò ×ÙÔÔÓ ×ed eÔ ÐÙ ×ÕÙ e ÐaÖÑ eÒ eÓÒÒa îØÔa × ÐaÚa ÐeÙ Öd e β ÕÙ iÔ eÙ ØÑ a iÒ ØeÒaÒ ØÔ ÖeÒd Öed eÙÜ Úa ÐeÙ Ö× β ( ω ) = 0 daÒ × Ðé Øa...
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