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Game Theory in Computer Science and Artificial Intelligence

Description: This quiz covers the fundamental concepts and applications of Game Theory in Computer Science and Artificial Intelligence. It explores how game-theoretic principles are used to model and analyze strategic interactions among agents in various computational scenarios.
Number of Questions: 14
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Tags: game theory computer science artificial intelligence strategic interactions nash equilibrium
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In Game Theory, what is the primary goal of each player?

  1. To maximize their own payoff.

  2. To minimize their opponent's payoff.

  3. To achieve a fair and equitable outcome.

  4. To cooperate with other players.

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Correct Option: A
Explanation:

In Game Theory, each player aims to select strategies that yield the highest possible payoff for themselves, regardless of the consequences for other players.

What is a Nash Equilibrium in Game Theory?

  1. A set of strategies where no player can improve their payoff by unilaterally changing their strategy.

  2. A set of strategies where all players cooperate to achieve the best possible outcome.

  3. A set of strategies where all players have equal payoffs.

  4. A set of strategies where the outcome is unpredictable.

Show answer
Correct Option: A
Explanation:

A Nash Equilibrium is a critical concept in Game Theory. It represents a set of strategies where no player has an incentive to deviate from their chosen strategy, assuming other players' strategies remain unchanged.

In a zero-sum game, what is the relationship between the payoffs of the players?

  1. The sum of all players' payoffs is always zero.

  2. The sum of all players' payoffs is always positive.

  3. The sum of all players' payoffs is always negative.

  4. The sum of all players' payoffs is unpredictable.

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Correct Option: A
Explanation:

In a zero-sum game, the gains of one player are exactly balanced by the losses of the other players. Therefore, the sum of all players' payoffs is always zero.

What is the minimax theorem in Game Theory?

  1. It guarantees the existence of a Nash Equilibrium in every game.

  2. It provides a method for finding the optimal strategy for a player in a zero-sum game.

  3. It states that the worst-case outcome for a player is always better than the best-case outcome for their opponent.

  4. It relates the value of a game to the payoffs of the players.

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Correct Option: B
Explanation:

The minimax theorem is a fundamental result in Game Theory. It provides a method for finding the optimal strategy for a player in a zero-sum game, ensuring that the player minimizes their maximum possible loss.

What is the difference between cooperative and non-cooperative games in Game Theory?

  1. In cooperative games, players can communicate and form binding agreements, while in non-cooperative games, they cannot.

  2. In cooperative games, players have complete information about the game, while in non-cooperative games, they have incomplete information.

  3. In cooperative games, the payoffs of the players are always positive, while in non-cooperative games, they can be positive, negative, or zero.

  4. In cooperative games, the outcome is always Pareto efficient, while in non-cooperative games, it may not be.

Show answer
Correct Option: A
Explanation:

The primary distinction between cooperative and non-cooperative games lies in the ability of players to communicate and form binding agreements. In cooperative games, players can engage in negotiations and make commitments, while in non-cooperative games, they act independently without the possibility of communication or agreements.

What is the concept of backward induction in Game Theory?

  1. It is a method for solving dynamic games by starting from the end and working backward.

  2. It is a method for finding the Nash Equilibrium in a game.

  3. It is a method for calculating the value of a game.

  4. It is a method for determining the optimal strategy for a player in a game.

Show answer
Correct Option: A
Explanation:

Backward induction is a technique used to solve dynamic games, which are games played over multiple stages. It involves starting from the last stage of the game and working backward, recursively solving each stage to determine the optimal strategies and payoffs for the players.

In a game with incomplete information, what is the role of Bayesian Nash Equilibrium?

  1. It is a set of strategies where no player can improve their payoff by unilaterally changing their strategy, given their beliefs about other players' strategies.

  2. It is a set of strategies where all players have equal payoffs.

  3. It is a set of strategies where the outcome is unpredictable.

  4. It is a set of strategies where the players cooperate to achieve the best possible outcome.

Show answer
Correct Option: A
Explanation:

Bayesian Nash Equilibrium is a critical concept in games with incomplete information. It represents a set of strategies where no player has an incentive to deviate from their chosen strategy, assuming their beliefs about other players' strategies are correct.

What is the concept of subgame perfect equilibrium in Game Theory?

  1. It is a refinement of the Nash Equilibrium concept that eliminates strategies that are not credible.

  2. It is a set of strategies where all players have equal payoffs.

  3. It is a set of strategies where the outcome is unpredictable.

  4. It is a set of strategies where the players cooperate to achieve the best possible outcome.

Show answer
Correct Option: A
Explanation:

Subgame perfect equilibrium is a refinement of the Nash Equilibrium concept that eliminates strategies that are not credible. It ensures that the Nash Equilibrium is sustainable even if players have the opportunity to deviate from their strategies at various points in the game.

In a repeated game, what is the role of trigger strategies?

  1. They are strategies that punish players for deviating from cooperative agreements.

  2. They are strategies that guarantee a Nash Equilibrium in the game.

  3. They are strategies that maximize the payoffs of all players.

  4. They are strategies that minimize the payoffs of all players.

Show answer
Correct Option: A
Explanation:

Trigger strategies are used in repeated games to enforce cooperation among players. They involve punishing players who deviate from cooperative agreements by reverting to non-cooperative strategies, thereby discouraging deviations and promoting cooperation.

What is the concept of correlated equilibrium in Game Theory?

  1. It is a set of strategies where players' actions are correlated, but not necessarily through communication or agreements.

  2. It is a set of strategies where all players have equal payoffs.

  3. It is a set of strategies where the outcome is unpredictable.

  4. It is a set of strategies where the players cooperate to achieve the best possible outcome.

Show answer
Correct Option: A
Explanation:

Correlated equilibrium is a solution concept in Game Theory that allows for correlations among players' actions without assuming explicit communication or agreements. It represents a set of strategies where no player has an incentive to deviate from their chosen strategy, given the correlation structure.

In mechanism design, what is the role of incentive compatibility?

  1. It ensures that players have an incentive to truthfully reveal their private information.

  2. It guarantees a Nash Equilibrium in the game.

  3. It maximizes the payoffs of all players.

  4. It minimizes the payoffs of all players.

Show answer
Correct Option: A
Explanation:

Incentive compatibility is a critical property in mechanism design. It ensures that players have an incentive to truthfully reveal their private information to the mechanism, even if doing so may not be in their immediate best interest. This property is essential for the effective functioning of many economic and social mechanisms.

What is the concept of dominant strategies in Game Theory?

  1. They are strategies that are always the best choice for a player, regardless of the strategies chosen by other players.

  2. They are strategies that guarantee a Nash Equilibrium in the game.

  3. They are strategies that maximize the payoffs of all players.

  4. They are strategies that minimize the payoffs of all players.

Show answer
Correct Option: A
Explanation:

Dominant strategies are strategies that are always the best choice for a player, regardless of the strategies chosen by other players. They represent actions that yield the highest payoff for a player in all possible scenarios, making them particularly influential in shaping the outcome of a game.

In auction theory, what is the role of the Vickrey-Clarke-Groves (VCG) mechanism?

  1. It is a mechanism that implements efficient and incentive-compatible auctions.

  2. It guarantees a Nash Equilibrium in the auction.

  3. It maximizes the revenue of the auctioneer.

  4. It minimizes the cost of the bidders.

Show answer
Correct Option: A
Explanation:

The Vickrey-Clarke-Groves (VCG) mechanism is a widely used auction mechanism that achieves efficiency and incentive compatibility. It ensures that the auction outcome is economically efficient and that bidders have an incentive to truthfully reveal their valuations for the auctioned goods.

In algorithmic game theory, what is the concept of the Price of Anarchy?

  1. It measures the inefficiency of a Nash Equilibrium in a game.

  2. It guarantees a Nash Equilibrium in the game.

  3. It maximizes the payoffs of all players.

  4. It minimizes the payoffs of all players.

Show answer
Correct Option: A
Explanation:

The Price of Anarchy is a measure of the inefficiency of a Nash Equilibrium in a game. It quantifies the difference between the social optimum and the outcome achieved under a Nash Equilibrium, highlighting the potential costs of strategic interactions among self-interested players.

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