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mid1_2010s

mid1_2010s - Answer Key First Midterm Examination Econ 101...

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Answer Key First Midterm Examination: Econ 101 Richard Buddin Spring 2010 Please answer all questions. The questions are in no particular order. If you do not understand a question, you should skip it and return to it later in the exam. You may need to calculate the roots for a quadratic equation. The roots of a quadratic equation ax 2 + bx + c are 2 4 2 b b ac a x - ± - = 1. Consider the following payoff matrix between two players: Player 2 Left (L) Middle (M) Right (R) Top (T) 6,4 3,2 2,7 Player 1 Center (C) 5,5 7,8 5,9 Bottom (B) 9,6 6,7 3,4 a) Find the pure strategy Nash equilibrium value or values for the game if the players act simultaneously. b) Suppose that the game in part a is played sequentially, and player 1 goes first. What strategy should player 1 choose to maximize its payoff? Is player 1 better off playing first or second? c) Now consider the new game in the payoff matrix below. Find the mixed strategies solution to the game. Player 2 Left (L) Right (R) Player 1 Top (T) 6,4 3,2 Bottom (B) 5,5 7,8 d) Find the expected payoff to the mixed strategy solution in part c. Explain whether the mixed strategy is Pareto efficient compared to any of the pure strategies. Answer (June 2009): a) CR is the only Nash equilibrium in pure strategies. b) If player 1 plays first, then player 1’s best strategy is to play B. Player 2 would then pick M, and player 1 would earn 6 at BM. If player 2 plays first, then they will pick R. Player 1 would then pick M, and player 1 would earn 5 at MR. Player 1 is better off playing first than playing second. c) P T =0.6, P L =0.8. d) Payouts: player 1=5.4, player 2=4.4. They are both better off at BR, but this is not a stable solution.

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2. Lincoln Elementary School raises funds with an annual May Fête (a spring festival).
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