To determine which of the given statements is true, let's analyze the game step by step.

First, let's consider option A: "c is strongly dominated by a for player 2." To check if this statement is true, we need to compare the payoffs of action c for player 2 with the payoffs of action a. Looking at the payoffs in the table, we see that for player 2, action c has a payoff of 4 when player 1 chooses action A, 0 when player 1 chooses action B, and 3 when player 1 chooses action C. On the other hand, action a has a payoff of 3 when player 1 chooses action A, 8 when player 1 chooses action B, and 5 when player 1 chooses action C. Since the payoff of action a is always greater than or equal to the payoff of action c, we can conclude that option A is true. Action c is indeed strongly dominated by action a for player 2.

Next, let's consider option B: "Player 1 has a strongly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 1 are strictly dominated by another action. Looking at the payoffs in the table, we can see that there is no action for player 1 that always has a lower payoff than another action. Therefore, option B is false. Player 1 does not have a strongly dominated strategy.

Finally, let's consider option C: "Player 2 has no weakly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 2 are weakly dominated by another action. Looking at the payoffs in the table, we can see that for each action of player 2, there is at least one action of player 1 that gives a higher payoff. Therefore, option C is true. Player 2 does not have any weakly dominated strategy.

In conclusion, the correct answer is:

C. Player 2 has no weakly dominated strategy.

Question

To determine which of the given statements is true, let's analyze the game step by step.

First, let's consider option A: "c is strongly dominated by a for player 2." To check if this statement is true, we need to compare the payoffs of action c for player 2 with the payoffs of action a. Looking at the payoffs in the table, we see that for player 2, action c has a payoff of 4 when player 1 chooses action A, 0 when player 1 chooses action B, and 3 when player 1 chooses action C. On the other hand, action a has a payoff of 3 when player 1 chooses action A, 8 when player 1 chooses action B, and 5 when player 1 chooses action C. Since the payoff of action a is always greater than or equal to the payoff of action c, we can conclude that option A is true. Action c is indeed strongly dominated by action a for player 2.

Next, let's consider option B: "Player 1 has a strongly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 1 are strictly dominated by another action. Looking at the payoffs in the table, we can see that there is no action for player 1 that always has a lower payoff than another action. Therefore, option B is false. Player 1 does not have a strongly dominated strategy.

Finally, let's consider option C: "Player 2 has no weakly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 2 are weakly dominated by another action. Looking at the payoffs in the table, we can see that for each action of player 2, there is at least one action of player 1 that gives a higher payoff. Therefore, option C is true. Player 2 does not have any weakly dominated strategy.

In conclusion, the correct answer is:

C. Player 2 has no weakly dominated strategy.

Knowee AI · Accepted Answer

To determine which of the given statements is true, let's analyze the game step by step.

First, let's consider option A: "c is strongly dominated by a for player 2." To check if this statement is true, we need to compare the payoffs of action c for player 2 with the payoffs of action a. Looking at the payoffs in the table, we see that for player 2, action c has a payoff of 4 when player 1 chooses action A, 0 when player 1 chooses action B, and 3 when player 1 chooses action C. On the other hand, action a has a payoff of 3 when player 1 chooses action A, 8 when player 1 chooses action B, and 5 when player 1 chooses action C. Since the payoff of action a is always greater than or equal to the payoff of action c, we can conclude that option A is true. Action c is indeed strongly dominated by action a for player 2.

Next, let's consider option B: "Player 1 has a strongly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 1 are strictly dominated by another action. Looking at the payoffs in the table, we can see that there is no action for player 1 that always has a lower payoff than another action. Therefore, option B is false. Player 1 does not have a strongly dominated strategy.

Finally, let's consider option C: "Player 2 has no weakly dominated strategy." To determine if this statement is true, we need to check if any of the actions for player 2 are weakly dominated by another action. Looking at the payoffs in the table, we can see that for each action of player 2, there is at least one action of player 1 that gives a higher payoff. Therefore, option C is true. Player 2 does not have any weakly dominated strategy.

In conclusion, the correct answer is:

C. Player 2 has no weakly dominated strategy.

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