Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 1. If a matrix game is strictly determined, then both players have optimal...

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.

1. If a matrix game is strictly determined, then both players have optimal strategies that are pure.

2. If both players of a matrix game have optimal strategies that are mixed, then the game is nonstrictly determined.

3. If a payoff matrix has a row consisting of all 0’s, then that row is recessive.

4. Every payoff matrix either has a recessive row or a recessive column.

5. If the first-column entries of a  payoff matrix are equal, then the game is strictly determined.

6. If a matrix game is fair, then both players have optimal strategies that are pure.