Player 1 chooses a row and Player 2 chooses a column. Which is true for the following game?1 \2 L C RT 4, 4 1, 6 2, 4M 6, 0 6, 4 4, 2B 3, 4 5, 9 2, 2(A) T is strongly dominant(B) M is strongly dominated(C) (M,C) survives iterated elimination of strongly dominated strategies(D) (B,C) survives iterated elimination of strongly dominated strategies

To answer this question, we need to understand the concepts of dominant and dominated strategies in game theory.

A strategy is said to be strongly dominant if, regardless of what any other players do, the strategy earns a player a higher payoff than any other. If the player can do better with another strategy, no matter what the opponents do, then the first strategy is said to be strongly dominated.

(A) T is strongly dominant: This is not true. For Player 1, choosing T does not always yield the highest payoff, regardless of Player 2's choice. For example, if Player 2 chooses C, Player 1 gets a payoff of 6 by choosing M, which is higher than the payoff of 1 by choosing T.

(B) M is strongly dominated: This is true. For Player 1, choosing M always yields a lower payoff than choosing either T or B, regardless of Player 2's choice. For example, if Player 2 chooses L, Player 1 gets a payoff of 4 by choosing T and 3 by choosing B, both of which are lower than the payoff of 6 by choosing M.

(C) (M,C) survives iterated elimination of strongly dominated strategies: This is not true. As we established in (B), M is a strongly dominated strategy for Player 1. Therefore, it would be eliminated in the first round of iterated elimination of strongly dominated strategies, and (M,C) would not survive.

(D) (B,C) survives iterated elimination of strongly dominated strategies: This is true. In the first round of iterated elimination of strongly dominated strategies, we eliminate M for Player 1. In the second round, we see that L is a strongly dominated strategy for Player 2 (since choosing C or R always yields a higher payoff). Therefore, we eliminate L for Player 2. After these two rounds, (B,C) is still a possible outcome, so it survives iterated elimination of strongly dominated strategies.

To answer this question, we need to understand the concepts of dominant and dominated strategies in game theory.

(A) T is strongly dominant: A strategy is strongly dominant if, regardless of what any other players do, the strategy earns a player a higher payoff than any other. Here, T is not strongly dominant because for Player 1, choosing T does not always yield the highest payoff. For example, if Player 2 chooses C, Player 1 gets a payoff of 6 by choosing M, which is higher than the payoff of 1 by choosing T.

(B) M is strongly dominated: A strategy is strongly dominated if there is another strategy that always yields a higher payoff, regardless of what the other players do. Here, M is not strongly dominated because there is no other row that always yields a higher payoff for Player 1. For example, if Player 2 chooses C, Player 1 gets the highest payoff by choosing M.

(C) (M,C) survives iterated elimination of strongly dominated strategies: Iterated elimination of strongly dominated strategies is a process where players successively remove strategies that are strongly dominated. In this game, no strategies are strongly dominated, so all strategies survive, including (M,C).

(D) (B,C) survives iterated elimination of strongly dominated strategies: As mentioned above, no strategies are strongly dominated in this game, so all strategies survive, including (B,C).

So, the correct answer is both (C) and (D).

To answer this question, we first need to understand the concepts of dominant and dominated strategies in game theory.

A strategy is said to be strongly dominant if, regardless of what any other players do, the strategy earns a player a higher payoff than any other. If the player can do better with another strategy, no matter what the opponents do, then the first strategy is strongly dominated.

(A) T is strongly dominant: False. For Player 1, choosing T does not always yield the highest payoff. For example, if Player 2 chooses C, Player 1 gets a payoff of 6 by choosing M, which is higher than the payoff of 1 by choosing T.

(B) M is strongly dominated: True. For Player 1, choosing M always yields a lower payoff than choosing either T or B, regardless of what Player 2 chooses. For example, if Player 2 chooses L, Player 1 gets a payoff of 4 by choosing T and 3 by choosing B, both of which are higher than the payoff of 0 by choosing M.

(C) (M,C) survives iterated elimination of strongly dominated strategies: False. As we established in (B), M is a strongly dominated strategy for Player 1. Therefore, it would be eliminated in the first round of iterated elimination of strongly dominated strategies.

(D) (B,C) survives iterated elimination of strongly dominated strategies: True. After eliminating M (as it is strongly dominated), we are left with T and B for Player 1. Neither of these strategies is strongly dominated, so they both survive the iterated elimination of strongly dominated strategies. If Player 2 chooses C, Player 1 gets a higher payoff by choosing B (9) than by choosing T (6), so (B,C) is a possible outcome of the game after iterated elimination of strongly dominated strategies.