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Mixed Strategies and Randomization

Description: Mixed Strategies and Randomization Quiz
Number of Questions: 15
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Tags: game theory mixed strategies randomization
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In a mixed strategy, a player chooses a _ action with a certain probability.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: B
Explanation:

A mixed strategy involves choosing different actions with different probabilities, rather than committing to a single action.

Randomization is used in game theory to _.

  1. Introduce uncertainty

  2. Guarantee a win

  3. Eliminate risk

  4. Maximize profits


Correct Option: A
Explanation:

Randomization is used to introduce uncertainty into a game, making it more difficult for opponents to predict a player's actions.

In a two-player game, if both players use mixed strategies, then the _ outcome is a Nash equilibrium.

  1. Pure strategy

  2. Mixed strategy

  3. Random strategy

  4. Dominant strategy


Correct Option: B
Explanation:

In a two-player game, if both players use mixed strategies, then the outcome is a Nash equilibrium, meaning that neither player can improve their payoff by unilaterally changing their strategy.

The expected payoff of a mixed strategy is the _ of the payoffs from all possible outcomes, weighted by their probabilities.

  1. Sum

  2. Product

  3. Average

  4. Maximum


Correct Option: C
Explanation:

The expected payoff of a mixed strategy is the average of the payoffs from all possible outcomes, weighted by their probabilities.

In a game with _ strategies, a player's mixed strategy is represented by a probability distribution over the set of strategies.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: B
Explanation:

In a game with mixed strategies, a player's mixed strategy is represented by a probability distribution over the set of strategies.

The Nash equilibrium of a game with mixed strategies is a set of strategies, one for each player, such that _.

  1. No player can improve their payoff by unilaterally changing their strategy

  2. All players have the same payoff

  3. The game ends in a draw

  4. The game is solved


Correct Option: A
Explanation:

The Nash equilibrium of a game with mixed strategies is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy.

In a game with mixed strategies, a player's _ strategy is one in which they choose each action with equal probability.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: C
Explanation:

In a game with mixed strategies, a player's random strategy is one in which they choose each action with equal probability.

The _ of a mixed strategy is the probability that a player chooses a particular action.

  1. Payoff

  2. Expected value

  3. Support

  4. Distribution


Correct Option: C
Explanation:

The support of a mixed strategy is the set of actions that a player chooses with positive probability.

In a game with mixed strategies, a player's _ strategy is one in which they choose a single action with probability 1.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: A
Explanation:

In a game with mixed strategies, a player's pure strategy is one in which they choose a single action with probability 1.

The _ of a mixed strategy is the set of all possible outcomes of the game, weighted by their probabilities.

  1. Payoff

  2. Expected value

  3. Support

  4. Distribution


Correct Option: D
Explanation:

The distribution of a mixed strategy is the set of all possible outcomes of the game, weighted by their probabilities.

In a game with mixed strategies, a player's _ strategy is one in which they choose each action with a probability that is proportional to its payoff.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: D
Explanation:

In a game with mixed strategies, a player's dominant strategy is one in which they choose each action with a probability that is proportional to its payoff.

The _ of a mixed strategy is the probability that a player chooses a particular action.

  1. Payoff

  2. Expected value

  3. Support

  4. Distribution


Correct Option: C
Explanation:

The support of a mixed strategy is the set of actions that a player chooses with positive probability.

In a game with mixed strategies, a player's _ strategy is one in which they choose a single action with probability 1.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: A
Explanation:

In a game with mixed strategies, a player's pure strategy is one in which they choose a single action with probability 1.

The _ of a mixed strategy is the set of all possible outcomes of the game, weighted by their probabilities.

  1. Payoff

  2. Expected value

  3. Support

  4. Distribution


Correct Option: D
Explanation:

The distribution of a mixed strategy is the set of all possible outcomes of the game, weighted by their probabilities.

In a game with mixed strategies, a player's _ strategy is one in which they choose each action with a probability that is proportional to its payoff.

  1. Pure

  2. Mixed

  3. Random

  4. Dominant


Correct Option: D
Explanation:

In a game with mixed strategies, a player's dominant strategy is one in which they choose each action with a probability that is proportional to its payoff.

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