Final_2009

Final_2009 - MS&E 246 Ramesh Johari Final Examination...

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Final Examination Ramesh Johari March 18, 2009 Instructions 1. Take alternate seating. 2. Answer all questions in the blue books provided. If needed, additional paper will be avail- able at the front of the room. Answers given on any other paper will not be counted. 3. Notes, books, calculators, and other aids are not allowed. 4. The examination begins at 7:00 pm, and ends at 10:00 pm. 5. Show your work! Partial credit will be given for correct reasoning. Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
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. Answer the following questions. (a) (10 points) Consider a two player simultaneous move game where player 1 has action set { L,M,R } , and player 2 has actions { l,m,r } . Assume both players receive a payoff of 1 if they play the same action, and zero otherwise. Give two different extensive form represen- tations of this game. (b) (10 points) True or false : A weakly dominated strategy is never rationalizable. If true, justify your answer; if false, give a counterexample. (c) (10 points) Give an example of a two player game with at least two mixed Nash equilibria (that are not pure Nash equilibria). Problem 2 (30 points) . Consider the following two player game: Player 2 H M L H (0,0) (3,4) (6,0) Player 1 M (4,3) (0,0) (0,0) L (0,6) (0,0) (5,5) (a) (5 points) Are any strategies strictly dominated? (b) (5 points) Find all pure Nash equilibria of this game. (c) (10 points) Find a symmetric mixed Nash equilibrium of this game, i.e., where both players play the same mixed strategy. (d) (10 points) Now consider an infinitely repeated game, where both players have discount factor δ . Find a sufficiently large value of δ such that there exists a subgame perfect Nash equilibrium where, on the equilibrium path, both players play ( L,L ) in every period. 2
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Final_2009 - MS&E 246 Ramesh Johari Final Examination...

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