ECS1050.UNITII.review

ECS1050.UNITII.review - UNIT II The Basic Theory Zero-sum...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Review Midterm 7/16 7/7
Background image of page 1

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

View Full DocumentRight Arrow Icon
Opera Fight O F O F (2,1) (0,0) (0,0) (1,2) Player 1 Player 2 2, 1 0, 0 0, 0 1, 2 O F O F Compare best response and prudent strategies. Battle of the Sexes Review
Background image of page 2
Opera Fight O F O F (2,1) (0,0) (0,0) (1,2) Player 1 Player 2 2, 1 0, 0 0, 0 1, 2 O F O F Battle of the Sexes Review Find all the NE of the game.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Opera Fight O F O F (2,1) (0,0) (0,0) (1,2) Player 1 Player 2 2 , 1 0, 0 0, 0 1 , 2 O F O F Battle of the Sexes Review NE = {(1, 1); (0, 0); }
Background image of page 4
Opera Fight O F O F (2,1) (0,0) (0,0) (1,2) Player 1 Player 2 2 , 1 0, 0 0, 0 1 , 2 O F O F Battle of the Sexes Review NE = {(O, O ); (F, F ); }
Background image of page 5

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

View Full DocumentRight Arrow Icon
O F P 1 P 2 2 1 Battle of the Sexes Mixed Nash Equilibrium Review O F 2 , 1 0, 0 0, 0 1 , 2 NE (1,1) NE (0,0) 1 2 NE = {(1, 1); (0, 0); ( MNE )}
Background image of page 6
O F 2, 1 0, 0 0, 0 1, 2 O F NE = {(1, 1); (0, 0); ( 2/3,1/3 )} Prudent: {1/3, 2/3)} Battle of the Sexes Review Let (p,1-p) = prob 1 (O, F ) (q,1-q) = prob 2 ( O , F ) Then EP 1 (Olq) = 2q EP 1 (Flq) = 1-1q q* = 1/3 EP 2 ( O lp) = 1p EP 2 ( F lp) = 2-2p p* = 2/3
Background image of page 7

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

View Full DocumentRight Arrow Icon
q=1 q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes EP 1 2/3 0 2 p=1 p=0 Review NE = {(1, 1); (0, 0); ( 2/3,1/3 )} EP 1 = 2q +0(1-q) Player 1’s Expected Payoff
Background image of page 8
q=1 q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes EP 1 1 2/3 0 2 0 p=1 p=0 Review p=1 NE = {(1, 1); (0, 0); ( 2/3,1/3 )} EP 1 = 0q+1 (1-q) Player 1’s Expected Payoff
Background image of page 9

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

View Full DocumentRight Arrow Icon
q=1 q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes EP 1 1 2/3 0 2 0 p=1 p=0 Review p=1 p=0 0<p<1 0<p<1 NE = {(1, 1); (0, 0); ( 2/3,1/3 )} Player 1’s Expected Payoff
Background image of page 10
q=1 q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes 2 0 p=1 p=0 Review p=1 p=0 p = 2/3 4/3 EP 1 2/3 1/3 If Player 1 uses her (mixed) b-r strategy (p=2/3), her expected payoff varies from 1/3 to 4/3. NE = {(1, 1); (0, 0); ( 2/3,1/3 )}
Background image of page 11

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

View Full DocumentRight Arrow Icon
q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes 2 0 p=1 p=0 Review p=1 p=0 EP 1 2/3 1/3 2/3 If Player 2 uses his (mixed) b-r strategy (q=1/3), the expected payoff to Player 1 is 2/3, for all p . q = 1/3
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/21/2010 for the course ECON 1050 taught by Professor Neugeboren during the Summer '09 term at Harvard.

Page1 / 32

ECS1050.UNITII.review - UNIT II The Basic Theory Zero-sum...

This preview shows document pages 1 - 13. Sign up to view the full document.

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