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Econ546MCLec2 - Nash Equilibrium McGill University Econ 546...

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Nash Equilibrium McGill University Econ 546
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S HARP P REDICTIONS e f g h a 9 , 0 2 , 1 5 , 3 6 , 2 b 6 , 0 3 , 8 2 , 9 1 , 4 c 3 , 7 5 , 3 3 , 7 6 , 3 d 4 , 8 1 , 6 1 , 4 8 , 9 Which outcomes survive the iterated elimination of strictly dominated strategies?
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N ASH E QUILIBRIUM : D EFINITION Nash Equilibrium : An action profile(outcome) a = ( a i , a - i ) is a Nash Equilibrium if for every player i, and every action a i available to player i, the outcome a is no worse than the outcome ( a i , a - i ) according to player i’s preferences. u i ( a ) u i ( a i , a - i ) 8 a i , 8 i
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E XAMPLE e f g h a 9 , 0 2 , 1 5 , 3 6 , 2 b 6 , 0 3 , 8 2 , 9 1 , 4 c 3 , 7 5 , 3 3 , 7 6 , 3 d 4 , 8 1 , 6 1 , 4 8 , 9 Nash Equilibria? ( a , g ) and ( d , h )
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C OORDINATION G AMES Battle of the Sexes Opera Soccer Opera 8 , 5 0 , 0 Soccer 0 , 0 5 , 8 Again none of the strategies are dominated. This is an example of a coordination game.
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A NTI C OORDINATION G AMES Chicken Acquiesce Engage Acquiesce 4 , 4 2 , 7 Engage 7 , 2 0 , 0 An example of an anti coordination game.
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