Game Theory Question Can some explain how to do this problem

Game Theory Question

Can some explain how to do this problem step by step?

Consider the following two-player game where the first number in a cell is player 1\'s payoff and the second number in a cell is player 2\'s payoff. Is there a Nash equilibrium in pure strategies? Find all Nash equilibrium in mixed strategies.

Solution

a) No there is Nash equilibrium in pure strategies., since there is no cell where row and column are highest.

b)

ax - If player 1 chooses a, then player 2 doesnt choose x and hence it is not nash equilibrium.

xa -  If player 2 chooses x, then player 1 choose a and hence it is nash equilibrium

ay -  Player 1 wont choose a, even if player 2 chooses and hence it is not nash equilibrium

ya- If player 2 chooses x, but then player 1 wont choose a and hence it is not nash equilibrium

bx-  If player 1 chooses b, then player 2 will choose x and hence it is nash equilibrium

xb -If player 2 chooses x, then player 1 doesnt choose and hence it is not nash equilibrium

by - If player 1 chooses b, then player 2 doesnt choose y and hence it is not nash equilibrium

yb -If player 2 chooses y, then player 1 choose b and hence it is nash equilibrium

cx - If player 1 chooses c, then player 2 will not choose x , and hence it is not nash equilibrium

xc - If player 2 chooses x, then player 1 choose a and hence it is not nash equilibrium

cy - If player 1 chooses c, then player 2 will choose y , and hence it is nash equilibrium.

yc -If player 2 chooses y, then player 1 choose b and hence it is not nash equilibrium