5. Suppose that in some two-player game, s is a rationalizable strategy for player 1. If...

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5. Suppose that in some two-player game, s is a rationalizable strategy for player 1. If s2 is a best response to s, is s a rationalizable strategy for player 2? Explain. 6. Suppose that in some two-player game, s is a rationalizable strategy for player 1. If, in addition, you know that s is a best response to $2, can you conclude that s is a rationalizable strategy for player 2? Explain. 7. Consider a guessing game with ten players, numbered 1 through 10. Simultaneously and independently, the players select integers between 0 and 10. Thus player i's strategy space is S; = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, for - - i = 1, 2, ..., 10. The payoffs are determined as follows: First, the of the players' selections is calculated and denoted a. That is, average S1 S2 + +$10 a = 10 where s; denotes player i's selection, for i = 1, 2, ..., 10. Then, player i's payoff is given by u; = (a - i - 1)s;. What is the set of rationalizable strategies for each player in this game? 5. Suppose that in some two-player game, s is a rationalizable strategy for player 1. If s2 is a best response to s, is s a rationalizable strategy for player 2? Explain. 6. Suppose that in some two-player game, s is a rationalizable strategy for player 1. If, in addition, you know that s is a best response to $2, can you conclude that s is a rationalizable strategy for player 2? Explain. 7. Consider a guessing game with ten players, numbered 1 through 10. Simultaneously and independently, the players select integers between 0 and 10. Thus player i's strategy space is S; = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, for - - i = 1, 2, ..., 10. The payoffs are determined as follows: First, the of the players' selections is calculated and denoted a. That is, average S1 S2 + +$10 a = 10 where s; denotes player i's selection, for i = 1, 2, ..., 10. Then, player i's payoff is given by u; = (a - i - 1)s;. What is the set of rationalizable strategies for each player in this game?

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Answer 5 If S1 is a rationalizable strategy for player 1 and S2 is a best response to S1 it does not ... View the full answer