# soln9 - Eco 354K Game theory Solutions to Problem Set 9...

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Eco 354K Game theory Solutions to Problem Set 9 1.(a) The set of complete contingency plans for each player. S 1 = {T,B},S 2 = {L,B}. 1.(b) Normal form of this game. L R(q R ) T(p T ) 18 , 12 12, 15 B 16, 13 13 , 12 1.(c) Solve for the unique Nash equilibrium No pure strategy Nash equilibrium. Thus, 12 p T +13 (1- p T ) = 15 p T + 12 (1- p T ) => p T =1/4 18 (1- q R ) + 12 q R = 16 (1- q R ) +13 q R => q R = 2/3 1.(d) The sequentially rational beliefs of player 2. Prob(d|2.1) (3/4)/[3/4 + (1/4)*(3/4)] = 4/5. Thus, EU 2 (L,p T ) = (1/5)*28 + (4/5)*8 = 12 = (1/5)*12 + (4/5)*12 = EU 2 (R,p T ). 2.(a) The set of complete contingency plans for each player. S 1 = {AC,AD,BC,BD},S 2 = {L,R}. 2.(b) Normal form of this game. L R AC 1,2 5, 4 AD 3,0 3,0 BC 0, 5 7 ,4 BD 2, 3 5,0 2.(c) Solve for the Nash equilibrium: by checking off best responses, you find that {AD,L} is a pure-strategy Nash equilibrium. There is also a continuum of mixed-strategy NE.

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## This note was uploaded on 06/09/2011 for the course ECON 354 taught by Professor Econ during the Spring '11 term at University of Texas at Austin.

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soln9 - Eco 354K Game theory Solutions to Problem Set 9...

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