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prob1csolestcomp - Universitat Pompeu Fabra Introducci a la...

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Universitat Pompeu Fabra Introducci´ o a la Teoria de Jocs Exercisis 1: Teoria de la Decisi´ o Professors: Xavier Calsamiglia, Fabrizio Germano and Helena Perrone En aquesta nota es presenten les solucions dels problemes 1,3,4,6,7 i 8. Els problemes restants — 2,5,9 i 10— s´ on el que cal preparar per a ser presentats al seminari 1. Problema 1 a) Fixa u(0)=0 i u(50)=1. Aleshores u(20) ha de ser 0.5 b) Si, representant gr` aficament la funci´ o veiem que ´ es c` oncava. 10 20 30 40 50 0.2 0.4 0.6 0.8 1.0 u(x) x u c) L 6 L 3 L 5 L 2 L 4 L 2 d) L 2 L 6 L 5 L 3 L 1 L 4 Problema 2 La soluci´ o ´ es id` entica a l’anterior, per` o amb la valoraci´ o personal del par` ametre p de cadascun. Problema 3 v ( x ) = w ( x ) 10 = 1 20 ( x + 900 - 30 ) Problema 4 a) Fixa u (10) = 0 i u (20) = 1. Aleshores u (12) = 2 3 1
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b) Es indiferent entre les dues. Problema 5 a) EV = 0 . 1 × 20 + 0 . 9 × 0 = 2 b) L’individu ´ es avers al risc ( u ´ es c` oncava) per a valors de x petits ( x < 10) i t´ e inclinaci´ o al risc ( u ´ es convexa) per a valors grans de x , ( x > 10).
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