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Game Theory Homework - Set 1 Instructions: Please choose the correct option (A, B, C, or D) for each question. In game theory, what is a "Nash equilibrium"? A. A situation where players cooperate for mutual benefit. B. A strategy profile where no player has an incentive to unilaterally deviate. C. A scenario where players maximize their own payoffs without considering others. D. A situation where players always compete for resources. What is the "prisoner's dilemma" in game theory? A. A situation where two players collaborate for a common goal. B. A scenario where cooperation leads to the best outcome for both players. C. A game where players face a dilemma between individual and collective interests. D. A game with no clear equilibrium strategy. In a sequential game, players make decisions: A. Simultaneously. B. After observing the decisions of other players. C. Without knowledge of the payoffs. D. Without considering their own preferences. What is the "minimax strategy" in game theory? A. A strategy that minimizes the maximum possible loss. B. A strategy that maximizes the minimum possible gain.

C. A strategy that balances risk and reward. D. A strategy that aims for an equal distribution of payoffs. What does the "zero-sum game" concept imply? A. The total payoff to all players is always zero. B. One player's gain is exactly balanced by another player's loss. C. Players can never achieve a positive sum of payoffs. D. The sum of payoffs is irrelevant in game theory. In game theory, what is a "subgame perfect equilibrium"? A. A strategy that guarantees the best possible outcome for all players. B. A strategy that is always dominated by another strategy. C. A Nash equilibrium that remains optimal at every subgame. D. A strategy that leads to an inefficient outcome. What is the "iterated prisoner's dilemma"? A. A one-time game with no repeated interactions. B. A game where players collaborate for an indefinite number of rounds. C. A scenario where players are never aware of the other's decisions. D. A game without any clear equilibrium. What is the "Battle of the Sexes" game in game theory? A. A game where players compete for a fixed prize. B. A coordination game where players prefer different outcomes. C. A game with no clear equilibrium strategy.

D. A game involving physical combat. In game theory, what does "mixed strategy" refer to? A. A strategy that combines elements of both cooperation and competition. B. A strategy that involves randomizing choices according to a probability distribution. C. A strategy that is dominated by another strategy. D. A strategy that leads to an equilibrium outcome. The concept of "backward induction" in game theory is used to: A. Predict players' actions by working backward from the end of a game. B. Analyze simultaneous moves in a game. C. Determine the optimal strategy for the first mover. D. Minimize regret in decision-making.

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