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2/5/20091A Note About EquilibriaSome games –Get feel for what an equilibrium might beShow that if everyone does it, nobody has an incentive to changeShow everything else isn’t equilibrium: for each other possible strategy profile, somebody has an incentive to changeOthers games – when you’re cluelessCalculate best responsesEquilibria occur where best responses crossImperfect Competition: BertrandTwo firms set pricesin a market with complete information, especially of pricesConsumers onlybuy from the cheaper firmIf two firms set the same price, each firm gets2,1ppIf two firms set the same price, each firm gets half the market demand at that priceAgain market demand is given byEach firm’s cost is given byFirm 1’s profit:PPDQ−==302)(qqC2)(=12111qqp−×=ΠImperfect Competition: BertrandFirm 1’s demand looks like…121pp<13021pq−=ifRecall the monopolists price:01=q21pp>21pp=)1302(21pq−=ifif152=MP2p302MPImperfect Competition: Bertrand1p22302MPImperfect Competition: BertrandFinding equilibrium through systematic checking:02Possible locations for p2p2 < 2 = MCp2 > 2 = MCp2 = 2 = MCCheck for equilibrium in each rangeImperfect Competition: Bertrandp2 < 2 = MCp1 < p2p1 = p2p1 > p2Firm 1 wants to raise priceFirm 1 wants to raise priceFirm 2 wants to raise pricep2 > 2 = MCp1 ≤2 < p22 < p1 ≤p2p1 ≥p2Firm 1 wants to raise priceFirm 2 wants to lower priceFirm 1 wants to lower price
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