week_9

# week_9 - x3 x4 x5 x6 x7 x8 x9 x10 u d a b c d e f d e f d e...

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Page 1 of 2 122 - Game Theory - Professor Giacomo Bonanno PRACTICE PROBLEMS for WEEK 9 Topic: mixed-strategy equilibria VERY IMPORTANT : do not look at the answers until you have made a VERY serious effort to solve the problem. If you turn to the answers to get clues or help, you are wasting a chance to test how well you are prepared for the exams. I will not give you more practice problems later on. yxop 1. Find the mixed-strategy Nash equilibrium of the following game: Player 2 L R T 1 , 4 4 , 3 C 2 , 0 1 , 2 Player 1 B 1 , 5 0 , 6 yxop 2. Consider the following imperfect-information game: 1 2 2 1 1 L R A B C D E F E F G H G H 2 0 0 6 0 2 4 1 1 4 2 0 4 3 1 2 (a) Write down the corresponding normal form game (the matrix). (b) Find all the pure-strategy equilibria. (c) Find the unique mixed strategy subgame-perfect equilibrium (express it in terms of behavior strategies).

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Page 2 of 2 3. Find the subgame-perfect equilibrium of the following game: 1 2 3 x2 x1
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Unformatted text preview: x3 x4 x5 x6 x7 x8 x9 x10 u d a b c d e f d e f d e f All the players satisfy the axioms of expected utility. They rank the outcomes as indicated below (if outcome w is above outcome y then w is strictly preferred to y, and if w and y are written next to each other then the player is indifferent between the two): 7 9 1 2 4 5 10 3 6 8 , , , , 1: , , x x x x x x Player x x x x , 1 3 4 5 2 7 8 6 9 , , 2: , , x x x x Player x x x x x , 2 7 8 1 4 9 3 5 6 , 3: , , , , x x x Player x x x x x x . Furthermore, player 2 is indifferent between x 4 and the lottery 1 2 1 1 2 2 x x and player 3 is indifferent between x 1 and the lottery 2 5 1 1 2 2 x x ....
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week_9 - x3 x4 x5 x6 x7 x8 x9 x10 u d a b c d e f d e f d e...

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