Which of the following is TRUE? A. Every agent in every 2-person game has a strongly dominant action B. An agent has a strongly dominant action if the agent has a best action for each of opponent's action C. An agent can have at most one strongly dominant action
Question
Which of the following is TRUE? A. Every agent in every 2-person game has a strongly dominant action B. An agent has a strongly dominant action if the agent has a best action for each of opponent's action C. An agent can have at most one strongly dominant action
Solution
To determine which statement is true, let's analyze each option step by step:
A. Every agent in every 2-person game has a strongly dominant action. To evaluate this statement, we need to understand what a strongly dominant action is. A strongly dominant action for an agent is an action that yields a higher payoff regardless of the opponent's action. In other words, it is the best action for the agent, regardless of what the opponent does.
In a 2-person game, it is not necessarily true that every agent has a strongly dominant action. There may be cases where both players have strategies that are equally good, or where the optimal strategy depends on the opponent's actions. Therefore, option A is not necessarily true.
B. An agent has a strongly dominant action if the agent has a best action for each of the opponent's actions. This statement is closer to the definition of a strongly dominant action. If an agent has a best action for each possible action of the opponent, then that action can be considered strongly dominant. This means that the agent's action will always yield the highest payoff, regardless of what the opponent does. Therefore, option B is true.
C. An agent can have at most one strongly dominant action. This statement is also true. If an agent has more than one strongly dominant action, it means that there are multiple actions that yield the highest payoff regardless of the opponent's actions. However, by definition, there can only be one action that is the best in all circumstances. Therefore, an agent can have at most one strongly dominant action.
In conclusion, the true statement among the options is B. An agent has a strongly dominant action if the agent has a best action for each of the opponent's actions.
Similar Questions
QUESTION 4Which of the following is FALSE? A. Every strongly dominant action is weakly dominant B. Every 2-person game has an agent who has a weakly dominant action C. A weakly dominant action need not be strongly dominant
Which of the following statements is true? I. If a two-player game has a strictly dominant strategy for one player, then it must have a strictly dominant strategy for the other player. II. If a strategy is strictly dominant, then it is also weakly dominant. III. A Subgame Perfect Nash Equilibrium (SPNE) is always a Nash Equilibrium in the normal form of the game Group of answer choices I and II are correct I and III are correct II and III are correct I, II and III are correct None of the other answers are correct
Consider the following game. Player 1 has three actions: A, B, C. Player 2 has three actions: a, b.c. Payoffs are as follows: abcA0,38,54,2B2,66,34,5C4,40,30,3(Quesiton is also availbe in pdf format here: Question.pdf)Which of the following is TRUE? A. c is strongly dominated by a for player 2 B. Player 1 has a strongly dominated strategy C. Player 2 has no weakly dominated strategy
If a 2 × 2 (2 players with 2 actions each) normal form (matrix) game has no pure strategy Nash equilibria then: (A) Neither player has a dominant strategy. (B) Exactly one player has a dominant strategy. (C) At least one player has a dominant strategy. (D) Both players have dominant strategies. (E) None of the above is necessarily true
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
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.