Considering the following two-person game, what percentage of the time should Y play strategy Y₁? A)1/3 B)2/3 C)4/9 D)5/9

Question

Quizplus · Accepted Answer

To determine the optimal strategy for player Y, we need to examine the payoffs for both players associated with each strategy. Here is the payoff matrix:

|        | X chooses XS1U0B1 | X chooses XS1U1B0 | X chooses XS1U1B1 |
|--------|------------------|------------------|------------------|
| Y chooses YS0U1B0 | -1, -1           | 0, -10           | 10, 0            |
| Y chooses YS1U1B11| -10, 0           | 5, 5             | 0, 0             |

We can now eliminate any dominated strategies. Strategy YS0U1B0 is dominated by YS1U1B11 because Y gets a higher payoff in the latter strategy regardless of what X chooses. Similarly, XS1U0B1 and XS1U1B1 are dominated by XS1U1B0 because X gets a higher payoff in the latter strategy regardless of what Y chooses. We are now left with the following reduced payoff matrix:

|        | X chooses XS1U1B0 | X chooses XS1U1B1 |
|--------|------------------|------------------|
| Y chooses YS1U1B11| 5, 5             | 0, 0             |

From this matrix, it is clear that Y should play YS1U1B11 half of the time and YS1U1B0 half of the time. Therefore, Y should play strategy YS1U1B11S1U1B0 50% of the time, which corresponds to answer choice D (5/9).

Considering the Following Two-Person Game, What Percentage of the Time