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soln10 - Eco 354K Solutions to PS 10 1 L U-2 0 D 0 5 B L R...

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Eco 354K Solutions to PS 10 1. L R U 0, 0 5, -2 D -2, 7 7, 5 “A” “B” a) No information; prob(A) = 2/3 NE = (U,L) b) Only player 1 observes outcome of die throw. N A B 1.1 1.2 2.1 L D U 0 5 -2 7 -2 5 0 7 0 -2 7 5 0 -2 5 7 L R R R R L L D U NE = (UD, L) 3. a) 0 H L 1.1 1.2 2.1 O W G 1 -1 2 0 0 -2 2 0 1 0 2 0 -2 0 -1 0 O N N N N O O W G 2.1 2.2 2.2 OO ON NO NN GG 0.5, -0.5 0.5, -0.5 -1.5, 0 -1.5, 0 GW 1.5, 0 0.5, 0.5 0.5, -0.5 -0.5, 0 WG 1, 0 0, -1 0, 1 -1, 0 WW 2, 0.5 0, 0 2, 0.5 0, 0 b) (WW, OO) and (WW, NO) are pooling equilibria since Greg works no matter which type he is. (GW, ON) is a separating equilibrium because Greg’s choice differs by his type. Also note that there is a continuum of pooling NE of the form (WW, OO w/ prob q and NO w/ prob 1-q). If Greg mixes when H but not when L, since WG is strictly dominated, he must be mixing between GW and WW. If the employer mixes when he see no advanced degree, the L R U -2, 0 5,-2 D 0, 5 7, 7 L R U -2/3, 0 5, -2 D -4/3, 19/3 7, 17/3 L R UU -2/3, 0 5, -2 UD 0, 5/3 17/3, 1 DU -2, 14/3 19/3, 8/3 DD -4/3, 19/3 7, 17/3

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