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Econ171_MT1_W10 - Econ 171 Introduction to Game Theory...

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Econ 171 °Introduction to Game Theory Midterm #1 9 February 2010 This test contains three problems. Each part of each question is worth 10 points for a maximum of 100 points. Answer all questions (showing your work where necessary). You have 75 minutes to complete the test. Good Luck! 1. Static Games of Complete Information: Find all the Nash Equilibria (including any mixed strategy Nash Equilibria) in the following 3 games. (a) Player 2 L R Player 1 U 1,2 3,5 D -1,-1 4,2 (b) Player 2 L R Player 1 U 6,3 0,0 D 1,1 2,2 (c) Player 2 L R T 8,0 5,12 Player 1 M 3,0 6,8 B 2,10 10,8 2. Cournot with Increasing Marginal Costs: Consider the Cournot model of compe- tition which we discussed in class. There are two °rms who simultaneously determine a quantity to bring to the market. The price is determined by the total quantity brought to the market: P ( Q ) = P ( q 1 + q 2 ) = 100 ° q 1 ° q 2 . However, assume now that each °rm has increasing marginal costs (with no °xed costs). Speci°cally, assume C 1 ( q 1 ) = 10 q 1 + q 2 1 and C 2 ( q 2 ) = 10 q 2 + q 2 2 .
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