Econ106G_081_Lecture3

Econ106G_081_Lecture3 - Econ106G Lecture Note 3 Hong Feng...

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Hong Feng Jul 1, 2008 1 Nash Equilibrium Example 1 Push or Pull (Coordination Game) 2 Push Pull 1 Push 1 ; 1 1 ; 1 Pull 1 ; 1 1 ; 1 In this game there is no dominant or dominated strategies, so we can not apply IEDS. If she believes s 2 = push; she will choose pull If she believes s 2 = pull; she will choose push s i is the Best Response to S i i/ u i ( s i ;s i ) ± u i ( s 0 i ;s i ) for all s 0 i 2 S i (1) e.g. in the coordination game, BR 1 ( push ) = pull; BR 1 ( pull ) = push: If there is no communication and no past experience, all beliefs are reasonable and all outcomes are possible, even the bad ones (e.g. ( push;push )) : But what if from communication or learning in repeated interactions people get a better idea of what the others will do? ( s ± 1 ;s ± 2 ) is a Nash equilibrium (NE) i/ u 1 ( s ± 1 ;s ± 2 ) ± u 1 ( s 0 1 ;s ± 2 ) for all s 0 1 2 S 1 (2) u 2 ( s ± 1 ;s ± 2 ) ± u 1 ± s ± 1 ;s 1 2 ² for all s 0 2 2 S 2 (3) More generally, s ± = ( s ± 1 ;s ± 2 ;:::;s ± n ) is a NE in a n-player game i/ u i ± s ± i ;s ± i ² ± u 1 ± s 0 i ;s ± i ² for all s 0 i 2 S i (4) i.e., ( s ± 1 ;s ± 2 ;:::;s ± n ) are mutual best responses. In the coordination game, ( pull;push ) and ( push;pull ) are Nash equilibria. 1
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This note was uploaded on 05/26/2009 for the course ECON 106 taught by Professor Cai during the Winter '04 term at UCLA.

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Econ106G_081_Lecture3 - Econ106G Lecture Note 3 Hong Feng...

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