Lecture8 - 1 A Note About Equilibria Some games – Get...

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Unformatted text preview: 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: 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: 2 ¡ Possible locations for p2 ¡ p2 < 2 = MC ¡ p2 > 2 = MC ¡ p2 = 2 = MC ¡ Check for equilibrium in each range 2 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 2/5/2009 2 Imperfect Competition: Bertrand ¡ p2 = 2 = MC ¡ p1 < p2 ¡ p1 > p2 ¡ p1 = p2 ¡ Firm 1 wants to raise price ¡ Firm 2 wants to raise price ¡ Firm 1 can’t make more by ¡ The only Nash equilibrium is (p1=p2=2=MC) raising price ¡ Firm 2 can’t either Philosophy of Nash Equilibrium ¡ What is a Nash Equilibrium?...
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Lecture8 - 1 A Note About Equilibria Some games – Get...

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