We need to find the mixed strategy nash equilibrium. Can you explain why the Nash equilibrium is as shown below?

Player 2 A B A 1 ,5 4, 3 Player 1 B 2, 6 1 3,8 Solution: Neither player has a dominant or dominated strategy. Therefore, the mixed strategy Nash equilibrium will place positive probabilities on both actions for both players. Consider a mixed strategy where: 1. Player 1 plays A with probability p and B with probability 1 - p. 2. Player 2 plays A with probability q and B with probability 1 - q. For Player 1 to be indifferent between playing A and B, we must have 1 xq+4x (1 -q) = 2xq+3 x (1 -q) So 4 - 3q = 3-q Page 4 Therefore q = 1/2. For Player 2 to be indifferent to be indifferent between playing A and B, we must have 5xp+6x (1 -p) = 3xp+8 x (1 -p) So 6-p=8-5p Therefore p = 1/2. Therefore, the mixed strategy Nash equilibrium is ((1/2,1/2),(2/3,1/3))