Converting games to linear programming problems Quiz

1. A pay-off matrix has smallest entry $-4$. What is the least integer to add so that no entry is negative?

• A. 3
• B. 5
• C. 4
• D. $-4$

2. After adding $3$ to every entry, the solution of the linear programme gives $V=\frac73$. What is the value of the original game?

• A. $\frac{16}{3}$
• B. $-\frac23$
• C. $\frac73$
• D. $\frac23$

3. What is the objective function in the linear programme for Rowan?

• A. Minimise $p_1+p_2+p_3$
• B. Maximise $p_1+p_2+p_3$
• C. Maximise $V$
• D. Minimise $V$

4. Rowan's adjusted pay-offs in column 1 are $3$, $0$ and $2$ for rows 1, 2, 3. Which constraint comes from column 1?

• A. $V-3p_1-2p_3\leq0$
• B. $V-3p_1-p_2-2p_3\leq0$
• C. $V-3p_1-2p_2\leq0$
• D. $V+3p_1+2p_3\leq0$

5. What is the effect on the optimal mixed strategy of adding a constant to every entry of the matrix?

• A. It is multiplied by the constant
• B. It is unchanged
• C. It is increased by the constant
• D. The probabilities are reversed