There are two players, 1 and 2. Player 1 chooses a positive integer from 1 to...

 

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There are two players, 1 and 2. Player 1 chooses a positive integer from 1 to 10. Player 2 chooses a positive integer from 1 to 10. They make their choices simultaneously. The payoff of player 1 is: ₁ u₁(x1, x₂) = if x₁ > x2 and x2 < 10 if x1 < x2 and 2 = 10 11 otherwise I1 ₁ 0 The payoff of player 2 is: u₂(x1, x2) = { {ő 1 if x₂ = x1 0 otherwise (a) What is the set of pure strategies available to player 1? (b) Show there is no pure strategy Nash equilibrium. (c) What is the set of mixed strategies available to player 1? (d) Find the unique mixed strategy Nash equilibrium (Hint: Simplify the problem). (e) Suppose player 1 and player 2 are both rational. In addition player 2 knows that player 1 is rational, and player 1 knows that player 2 is rational. Suppose too that player 2 knows that player 1 knows that she is rational. However, player 1 does not know that player 2 knows that he is rational. Would you expect the mixed strategy Nash equilibrium to be played? There are two players, 1 and 2. Player 1 chooses a positive integer from 1 to 10. Player 2 chooses a positive integer from 1 to 10. They make their choices simultaneously. The payoff of player 1 is: ₁ u₁(x1, x₂) = if x₁ > x2 and x2 < 10 if x1 < x2 and 2 = 10 11 otherwise I1 ₁ 0 The payoff of player 2 is: u₂(x1, x2) = { {ő 1 if x₂ = x1 0 otherwise (a) What is the set of pure strategies available to player 1? (b) Show there is no pure strategy Nash equilibrium. (c) What is the set of mixed strategies available to player 1? (d) Find the unique mixed strategy Nash equilibrium (Hint: Simplify the problem). (e) Suppose player 1 and player 2 are both rational. In addition player 2 knows that player 1 is rational, and player 1 knows that player 2 is rational. Suppose too that player 2 knows that player 1 knows that she is rational. However, player 1 does not know that player 2 knows that he is rational. Would you expect the mixed strategy Nash equilibrium to be played?

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a The set of pure strategies available to player 1 is 1 2 3 4 5 6 7 8 9 10 b Ther... View the full answer