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PS2-solutions

PS2-solutions - Suggested Solutions to Problem Set 2 Ying...

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Suggested Solutions to Problem Set 2 Ying Chen ECN 416 Game Theory 1 . Consider the following 2 -player game. 2 10 0 0 10 3 3 1 2 10 10 2 6 4 3 3 4 6 6 6 Find the following sets of best responses. (a)  1 ( ) for = ¡ 1 3 1 3 1 3 ¢ . (Notation: The fi rst element in is the probability that player 2 chooses , the second element is the probability that he chooses and the third elemment is the probability that he chooses . Same for part (b).) (b)  1 ( ) for = ¡ 0 1 3 2 3 ¢ (c)  2 ( ) for = ¡ 1 3 1 6 1 2 ¢ (Here is player 2 ’s belief over player 1’s strategy.) 2. Player 1 has to take a soccer penalty shot to decide the game. She can shoot eft, iddle, or ight. Player 2 is the goalie. He can dive to the eft, iddle, or ight. Actions are chosen simultaneously. The payo ff s are as follows. 2 4 6 7 3 9 1 1 6 4 3 7 6 4 9 1 7 3 4 6 (a) For each player, is any strategy dominated by another strategy? No dominated strategies for either player. (b) Is ever a best response for player 1? If so, for what beliefs about player 2 ’s strategy is a best response for player 1 ? Is a ever a best response for player 2 ? If so, for what beliefs about player 1 ’s strategy is a best response for player 2 ? ( Hint: You can write player 1’s belief as
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