Econ546MCLec2

This is an example of a coordination game soccer 0 0

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Unformatted text preview: ted. This is an example of a coordination game. Soccer 0, 0 5, 8 A NTI C OORDINATION G AMES Chicken Acquiesce Engage Acquiesce 4, 4 7, 2 An example of an anti coordination game. Models of conflict. Engage 2, 7 0, 0 B EST R ESPONSE F UNCTIONS For any choice of actions made by players other than i, say a i , player i’s best response function(correspondence) chooses the action(s) that give player i the highest possible payoff. BRi (a i ) = {ai 2 Ai : ui (ai , a i ) a b c d BR1 (e) = {a} BR1 (f ) = {c} BR1 (g) = {a} BR1 (h) = {d} e 9⇤ , 0 6, 0 3, 7 4, 8 f 2, 1 3, 8 5⇤ , 3 1, 6 ui (a0 , a i ), 8a0 2 Ai } i i g 5⇤ , 3 2, 9 3, 7 1, 4 h 6, 2 1, 4 6, 3 8⇤ , 9 B EST R ESPONSE F UNCTIONS AND N ASH E QUILIBRIA An outcome a⇤ is a Nash Equilibrium if and only if, a⇤ 2 BRi (a⇤ i ), 8i i A&Nash&Equilibrium&is&the&set&of&the&best&responses&for&both&players&over&all&outcomes a b c d e 9⇤ , 0 6, 0 3, 7⇤ 4, 8 f 2, 1 3, 8 5⇤ , 3 1, 6 g 5⇤ , 3⇤ 2, 9⇤ 3, 7⇤ 1, 4 h 6, 2 1, 4 6, 3 8⇤ , 9⇤ C OURNOT D UOPOLY p = a bx = 0 otherwise = [17 (xi + x i )]xi = [16 a b if x (xi + x i )]xi a = 17, b = 1, c = 1 Profits for firm i in the duopoly Pro0it...
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This document was uploaded on 03/23/2014.

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