Question 1) (from last year's exam) Ann and Bob play the following game. Each of them...

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Question 1) (from last year's exam) Ann and Bob play the following game. Each of them secretly writes down an integer between 0 and 100, that is, a number in the set {1,2,3,...,100), on a piece of paper. A neutral observer collects the papers and calculates the average of the two numbers x, y € {1,2,3,...,100). The person whose number is closest to 1 x + y == 3 average 3 2 I gets payoff 1; the other person gets payoff 0. If both write down the same number, x = y, then each gets payoff 0.5. (a) Write down the weakly dominant-strategy equilibrium of this game. (b) Does the game have other Nash equilibria than the weakly dominant-strategy equilibrium in (a)? If yes, write down one; if no, briefly explain why. (c) Does the game have any strictly dominant strategies? If yes, write down one; if no, briefly explain why. (d) Does the game have an iterated strictly dominant-strategy equilibrium? If yes, write it down and briefly describe which strategies are deleted in each round of the IDSDS procedure; if no, briefly explain why. Question 1) (from last year's exam) Ann and Bob play the following game. Each of them secretly writes down an integer between 0 and 100, that is, a number in the set {1,2,3,...,100), on a piece of paper. A neutral observer collects the papers and calculates the average of the two numbers x, y € {1,2,3,...,100). The person whose number is closest to 1 x + y == 3 average 3 2 I gets payoff 1; the other person gets payoff 0. If both write down the same number, x = y, then each gets payoff 0.5. (a) Write down the weakly dominant-strategy equilibrium of this game. (b) Does the game have other Nash equilibria than the weakly dominant-strategy equilibrium in (a)? If yes, write down one; if no, briefly explain why. (c) Does the game have any strictly dominant strategies? If yes, write down one; if no, briefly explain why. (d) Does the game have an iterated strictly dominant-strategy equilibrium? If yes, write it down and briefly describe which strategies are deleted in each round of the IDSDS procedure; if no, briefly explain why.

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a The weakly dominantstrategy equilibrium of this game is for bo... View the full answer