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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online