Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 1. There exists a payoff matrix that has exactly two saddle values. 2. There exists...

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

1. There exists a payoff matrix that has exactly two saddle values.

2. There exists a payoff matrix having a saddle value that appears exactly twice.

3. The smallest entry in any payoff matrix is a saddle value.

4. The largest entry in any payoff matrix is a saddle value.

5. If a payoff matrix has a row consisting of all 0’s and a column consisting of all 0’s, then the game is fair.

6. If a strictly determined matrix game is fair, then at least one of the payoffs is 0.