D c p d 1 1 3 0 1 1 c 0 3 2 2 2 1 p 1 1 1 2 3 3 th

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D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3)
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es Variante du dilemme des prisonniers. D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Unique EN du jeu de base : ( D, D )
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es Variante du dilemme des prisonniers. D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Unique EN du jeu de base : ( D, D ) Jeu en deux ´ etapes (sans actualisation) :
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es Variante du dilemme des prisonniers. D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Unique EN du jeu de base : ( D, D ) Jeu en deux ´ etapes (sans actualisation) : – Premi` ere ´ etape : s 1 i = C
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es Variante du dilemme des prisonniers. D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Unique EN du jeu de base : ( D, D ) Jeu en deux ´ etapes (sans actualisation) : – Premi` ere ´ etape : s 1 i = C – Deuxi` eme ´ etape : s 2 i ( a 1 1 , a 1 2 ) = D si ( a 1 1 , a 1 2 ) = ( C, C ) P sinon. est un ´ equilibre de Nash
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es Variante du dilemme des prisonniers. D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Unique EN du jeu de base : ( D, D ) Jeu en deux ´ etapes (sans actualisation) : – Premi` ere ´ etape : s 1 i = C – Deuxi` eme ´ etape : s 2 i ( a 1 1 , a 1 2 ) = D si ( a 1 1 , a 1 2 ) = ( C, C ) P sinon. est un ´ equilibre de Nash un ´ equilibre de Nash du jeu r´ ep´ et´ e ne consiste pas n´ ecessairement ` a r´ ep´ eter les ´ equilibres du jeu de base, mˆ eme si le jeu de base a un unique EN
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Mais l’unique ENPSJ est la d´ efection mutuelle aux deux p´ eriodes
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es D C P D (1 , 1) (3 , 0) ( 1 , 1) C (0 , 3) (2 , 2) ( 2 , 1) P ( 1 , 1) ( 1 , 2) ( 3 , 3) Mais l’unique ENPSJ est la d´ efection mutuelle aux deux p´ eriodes Proposition. Si le jeu de base G a un unique ´ equilibre de Nash, alors pour tout T fini et pour tout taux d’actualisation δ (0 , 1] , le jeu r´ ep´ et´ e G ( T, δ ) a un unique ´ equilibre de Nash parfait en sous jeu, o`u l’´ equilibre de Nash du jeu de base est jou´ e ` a chaque ´ etape (quelle que soit l’histoire)
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es ´ Emergence de nouveaux comportements ` a un ENPSJ.
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Th´ eorie des jeux Jeux sous forme extensive / Jeux r´ ep´ et´ es ´ Emergence de nouveaux comportements ` a un ENPSJ.
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