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Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:

Player 1 Player 2
Left Right
Top 1 2 2 4
Bottom 3 4 0 3

where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. A) (2 points) Does Player 1 have a dominant strategy, and if so what is it? [ Select ] ["Yes; Top", "Yes; Bottom", "Yes; Left", "Yes; Right", "No; Player 1 does not have a dominant strategy"] B) (2 points) Does Player 2 have a dominant strategy and if so what is it? [ Select ] ["Yes; Top", "Yes; Bottom", "Yes; Left", "Yes; Right", "No; Player 2 does not have a dominant strategy"] C) (1 point each) For each of the following strategy combinations, select TRUE if it is a Nash Equilibrium, and FALSE if it is not:

  • i) Top/Left [ Select ] ["True", "False"]
  • ii) Top/Right [ Select ] ["True", "False"]
  • iii) Bottom/Left [ Select ] ["True", "False"]
  • iv) Bottom Right [ Select ] ["True", "False"]

D) (2 points) What is Player 1's maximin strategy? [ Select ] ["Top", "Bottom", "Left", "Right", "Player 1 does not have a maximin strategy"] E) (2 points) What is Player 2's maximin strategy? [ Select ] ["Top", "Bottom", "Left", "Right", "Player 2 does not have a maximin strategy"] F) (2 points) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose? [ Select ] ["Player 1 chooses Top; Player 2 chooses Left", "Player 1 chooses Top; Player 2 chooses Right", "Player 1 chooses Bottom; Player 2 chooses Left", "Player 1 chooses Bottom; Player 2 chooses Right"]

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