ECS1050.UNITII.review

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

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UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Review Midterm 7/16 7/7

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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
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.

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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); }
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 ); }

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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 )}
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

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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
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

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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
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 )}

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

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

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