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ECE1040.07.post

# ECE1040.07.post - UNIT II The Basic Theory Zero-sum Games...

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UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Review Midterm 3/18 3/11

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Midterm Exam Preview Prudent v. Best-Response Strategies 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 Compare best response and prudent strategies.

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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); } Find all the NE of the game. NE = {(O, O ); (F, F ); } Both are correct
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 )}

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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
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

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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 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 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 Opera Fight NE = {(1, 1); (0, 0); ( 2/3,1/3 )} Player 1’s Expected Payoff
q=0 2 , 1 0 , 0 0 , 0 1 , 2 q Battle of the Sexes

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ECE1040.07.post - UNIT II The Basic Theory Zero-sum Games...

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