Information for Questions 56

Mixed strategies involve randomly choosing each of two or more pure strategies with a particular probability. In the above game, one mixed-strategy Nash equilibrium involves both players choosing each strategy with probability 1/3.

Question 5 (2 points)

Suppose Player 2 played rock with probability 1/2, paper with probability 1/4, and scissors with probability 1/4. Is it optimal for Player 1 to play each pure strategy with probability 1/3 against this strategy of Player 2? Why?

Question 6 (2 points)

Compare the expected payoffs of all three pure strategies for Player 1 against the equilibrium mixed strategy of Player 2 that involves choosing each pure strategy with probability 1/3. Why does the fact that each player playing each pure strategy with probability 1/3 is a Nash equilibrium imply that the relationship you found between the payoffs of Player 1s pure strategies against Player 2s equilibrium strategy must hold?

Question 7 (1 point)

What is a strictly dominated strategy?

Information for Questions 5-6 Mixed strategies involve randomly choosing each of two or more pure strategies with a particular probability. In the above game, one mixed-strategy Nash equilibrium involves both players choosing each strategy with probability 31. Question 5 ( 2 points) Suppose Player 2 played rock with probability 21, paper with probability 41, and scissors with probability 41. Is it optimal for Player 1 to play each pure strategy with probability 31 against this strategy of Player 2? Why? Question 6 ( 2 points) Compare the expected payoffs of all three pure strategies for Player 1 against the equilibrium mixed strategy of Player 2 that involves choosing each pure strategy with probability 31. Why does the fact that each player playing each pure strategy with probability 31 is a Nash equilibrium imply that the relationship you found between the payoffs of Player 1's pure strategies against Player 2's equilibrium strategy must hold? Question 7 (1 point) What is a strictly dominated strategy? Information for Questions 5-6 Mixed strategies involve randomly choosing each of two or more pure strategies with a particular probability. In the above game, one mixed-strategy Nash equilibrium involves both players choosing each strategy with probability 31. Question 5 ( 2 points) Suppose Player 2 played rock with probability 21, paper with probability 41, and scissors with probability 41. Is it optimal for Player 1 to play each pure strategy with probability 31 against this strategy of Player 2? Why? Question 6 ( 2 points) Compare the expected payoffs of all three pure strategies for Player 1 against the equilibrium mixed strategy of Player 2 that involves choosing each pure strategy with probability 31. Why does the fact that each player playing each pure strategy with probability 31 is a Nash equilibrium imply that the relationship you found between the payoffs of Player 1's pure strategies against Player 2's equilibrium strategy must hold? Question 7 (1 point) What is a strictly dominated strategy