Si elle domine toutes les autres actions th eorie des

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si elle domine strictement/faiblement toutes les autres actions
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Th´ eorie des jeux Jeux sous forme normale L’action s i du joueur i domine faiblement l’action s i du joueur i si s i S i , u i ( s i , s i ) u i ( s i , s i ) s i S i , u i ( s i , s i ) > u i ( s i , s i ) L’action s i domine strictement l’action s i si s i S i , u i ( s i , s i ) > u i ( s i , s i ) Une action est strictement / faiblement dominante si elle domine strictement/faiblement toutes les autres actions Exemple. Dans le jeu suivant H domine faiblement M , M domine faiblement B et H domine strictement B . Aucun ordre de dominance ne peut ˆ etre ´ etabli pour le joueur 2 G D H (2 , 0) (1 , 0) M (2 , 2) (0 , 0) B (1 , 0) (0 , 2)
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Th´ eorie des jeux Jeux sous forme normale Mais insuffisant en g´ en´ eral
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Th´ eorie des jeux Jeux sous forme normale Mais insuffisant en g´ en´ eral Un jeu de coordination. a b a (2 , 2) (0 , 0) b (0 , 0) (1 , 1)
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Th´ eorie des jeux Jeux sous forme normale Mais insuffisant en g´ en´ eral Un jeu de coordination. a b a (2 , 2) (0 , 0) b (0 , 0) (1 , 1) Bataille des sexes. a b a (3 , 2) (1 , 1) b (0 , 0) (2 , 3)
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Th´ eorie des jeux Jeux sous forme normale Jeu de la poule mouill´ ee. (la fureur de vivre) image a b a (2 , 2) (1 , 3) b (3 , 1) (0 , 0)
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Th´ eorie des jeux Jeux sous forme normale Jeu de la poule mouill´ ee. (la fureur de vivre) image a b a (2 , 2) (1 , 3) b (3 , 1) (0 , 0) La chasse au cerf. a b a (3 , 3) (0 , 2) b (2 , 0) (1 , 1)
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Th´ eorie des jeux Jeux sous forme normale Jeux ` a somme nulle (comp´ etition stricte)
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Th´ eorie des jeux Jeux sous forme normale Jeux ` a somme nulle (comp´ etition stricte) Cache bouton. (“ matching pennies ”) G D G ( 1 , 1) (1 , 1) D (1 , 1) ( 1 , 1)
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Th´ eorie des jeux Jeux sous forme normale Jeux ` a somme nulle (comp´ etition stricte) Cache bouton. (“ matching pennies ”) G D G ( 1 , 1) (1 , 1) D (1 , 1) ( 1 , 1) Feuille, Pierre, Ciseaux. F P C F (0 , 0) (1 , 1) ( 1 , 1) P ( 1 , 1) (0 , 0) (1 , 1) C (1 , 1) ( 1 , 1) (0 , 0)
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Th´ eorie des jeux Jeux sous forme normale ´ Equilibre de Nash
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Th´ eorie des jeux Jeux sous forme normale ´ Equilibre de Nash Fig. 1 – John F. Nash Jr (1928– )
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Th´ eorie des jeux Jeux sous forme normale ´ Equilibre de Nash Fig. 1 – John F. Nash Jr (1928– )
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Th´ eorie des jeux Jeux sous forme normale ´ Equilibre de Nash Fig. 1 – John F. Nash Jr (1928– ) Concept de stabilit´ e : situation o`u aucun joueur n’a int´ erˆ et ` a d´ evier unilat´ eralement (individuellement) de sa strat´ egie
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Th´ eorie des jeux Jeux sous forme normale efinition. Un ´ equilibre de Nash en strat´ egies pures d’un jeu sous forme normale ( N, ( S i ) i N , ( u i ) i N ) est un profil d’actions s = ( s 1 , . . . , s n ) S tel que l’action de chaque joueur est une meilleure r´ eponse aux actions choisies par les autres joueurs, c’est-` a-dire u i ( s i , s i ) u i ( s i , s i ) , s i S i , i N
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Th´ eorie des jeux Jeux sous forme normale efinition. Un ´ equilibre de Nash en strat´ egies pures d’un jeu sous forme normale ( N, ( S i ) i N , ( u i ) i N )
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