# Lecture8 - A Note About Equilibria Some games Get feel for...

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2/5/2009 1 A Note About Equilibria Some games – Get feel for what an equilibrium might be Show that if everyone does it, nobody has an incentive to change Show everything else isn’t equilibrium: for each other possible strategy profile, somebody has an incentive to change Others games – when you’re clueless Calculate best responses Equilibria occur where best responses cross Imperfect Competition: Bertrand Two firms set prices in a market with complete information, especially of prices Consumers only buy from the cheaper firm If two firms set the same price, each firm gets 2 , 1 p p If two firms set the same price, each firm gets half the market demand at that price Again market demand is given by Each firm’s cost is given by Firm 1’s profit: P P D Q = = 302 ) ( q q C 2 ) ( = 1 2 1 1 1 q q p × = Π Imperfect Competition: Bertrand Firm 1’s demand looks like… 1 2 1 p p < 1 302 1 p q = if Recall the monopolists price: 0 1 = q 2 1 p p > 2 1 p p = ) 1 302 ( 2 1 p q = if if 152 = M P 2 p 302 M P Imperfect Competition: Bertrand 1 p 2 2 302 M P Imperfect Competition: Bertrand Finding equilibrium through systematic checking: 0 2 Possible locations for p2 p2 < 2 = MC p2 > 2 = MC p2 = 2 = MC Check for equilibrium in each range Imperfect Competition: Bertrand p2 < 2 = MC p1 < p2 p1 = p2 p1 > p2 Firm 1 wants to raise price Firm 1 wants to raise price Firm 2 wants to raise price p2 > 2 = MC p1 2 < p2 2 < p1 p2 p1 p2 Firm 1 wants to raise price Firm 2 wants to lower price Firm 1 wants to lower price

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