Econ171_Final

# Econ171_Final - Econ 171 Introduction to Game Theory Final...

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Econ 171 °Introduction to Game Theory Final Exam Fall 2009 This test contains 4 problems. Each part of each question is worth 10 points for a maximum of 120 points. Answer all questions (showing your work where necessary). You have 2 hours to complete the test. (Time "recommendations" are listed in parenthesis). Good Luck! 1. Static Games (20 minutes) : Find all the Nash Equilibria (including any mixed strategy Nash Equilibria) in the following 3 games. (a) Player 2 L R Player 1 U 1,6 3,7 D -1,-1 4,2 (b) Player 2 L R Player 1 U 6,-3 0,1 D 1,1 2,2 (c) Player 2 L C R T 8,0 20,10 11,12 Player 1 M 0,0 60,9 10,8 B 2,0 10,9 20,8 [HINT: Remember that a Pure Strategy can be eliminated if it is strictly domi- nated by a Mixed Strategy.] 2. Dynamic Games with Imperfect Information (20 minutes) : Consider the following 2-person, extensive form game (next page): (a) How many subgames are there in this game? [Do not consider the entire game as a subgame.] (b) Represent the game in normal-form (i.e., matrix-form). [Hint: The normal form matrix will be an 8x2 dimensional matrix.] (c) Find all the Pure-Strategy Nash Equilibria.

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