Mixed Strategy Nash Equilibrium

Question 1

When do mixed strategy NE’s occur?

Answer 1

When there is no pure strategy nash equilibrium.

Question 2

Mixed Strategy and Pure Strategy probabilities.

Answer 2

Pure strategies are a form of mixed strategies, with probability=1 on one action and =0 on the other.

Mixed strategies are a set of two probabilities (a, 1-a), such that 0 < a < 1.

Question 3

How should player 2 react if player 1 moves left with probability q > 0.5?

Answer 3

Player 2 should move left all the time, p = 1.

Question 4

How should player 2 react if player 1 moves left with probability q < 0.5?

Answer 4

Player 2 should move right all the time, p = 0.

Question 5

What happens with a mixed strategy with p = 0.5?

Answer 5

No matter what strategy is undertook, the pay off will be zero.

This is where the Nash Equilibrium takes place, as no player has an incentive to change their behaviour.