Question

Table 17-13. This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). A Up Middle Down Left (1,4) (2, 2) (3, 2) B Center (6,2) (4, 6) (5,5) Right (3, 1) (5,7) (4,3) Refer to Table 17-13. Which of the following statements regarding this game is true? O Both players have a dominant strategy. O Player A has a dominant strategy, but player B does not have a dominant strategy. O Player A does not have a dominant strategy, but player B does have a dominant strategy. ONeither player has a dominant strategy.

Answer 1

In the given table, a dominant strategy is a strategy that yields the highest payoff for a player regardless of the strategy chosen by the other player.

By examining the payoffs, we can determine if either player has a dominant strategy.

Looking at player A's options:

- If player B chooses Up, A's highest payoff is 3 by choosing Down.

- If player B chooses Center, A's highest payoff is 2 by choosing Middle.

- If player B chooses Right, A's highest payoff is 5 by choosing Middle.

Since player A does not have a single strategy that yields the highest payoff regardless of B's strategy, player A does not have a dominant strategy.

Similarly, looking at player B's options:

- If player A chooses Left, B's highest payoff is 5 by choosing Center.

- If player A chooses Middle, B's highest payoff is 7 by choosing Right.

- If player A chooses Up, B's highest payoff is 4 by choosing Left.

Since player B does not have a single strategy that yields the highest payoff regardless of A's strategy, player B does not have a dominant strategy.

Therefore, the correct statement is:

Neither player has a dominant strategy.