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Mathematical Modeling: Game Theory and Decision Making

Description: Mathematical Modeling: Game Theory and Decision Making
Number of Questions: 15
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Tags: game theory decision making mathematical modeling
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In a zero-sum game, the total gains of all players are:

  1. Always positive

  2. Always negative

  3. Always zero

  4. None of the above


Correct Option: C
Explanation:

In a zero-sum game, the gains of one player are exactly balanced by the losses of the other players, resulting in a total gain of zero.

Which of the following is a type of non-cooperative game?

  1. Prisoner's Dilemma

  2. Nash Equilibrium

  3. Cournot Competition

  4. Bertrand Competition


Correct Option: A
Explanation:

The Prisoner's Dilemma is a classic example of a non-cooperative game, where each player's best strategy depends on the strategy of the other player.

In a Nash Equilibrium, each player's strategy is:

  1. A best response to the strategies of the other players

  2. A worst response to the strategies of the other players

  3. A random strategy

  4. None of the above


Correct Option: A
Explanation:

In a Nash Equilibrium, no player can improve their outcome by unilaterally changing their strategy, given the strategies of the other players.

Which of the following is a type of cooperative game?

  1. Prisoner's Dilemma

  2. Nash Equilibrium

  3. Cournot Competition

  4. Coalitional Game


Correct Option: D
Explanation:

A Coalitional Game is a type of cooperative game where players can form coalitions to achieve a common goal.

The Shapley Value is a solution concept used in:

  1. Cooperative Games

  2. Non-Cooperative Games

  3. Zero-Sum Games

  4. All of the above


Correct Option: A
Explanation:

The Shapley Value is a solution concept used in cooperative games to fairly distribute the gains from cooperation among the players.

Which of the following is a type of decision-making under uncertainty?

  1. Expected Value

  2. Minimax Regret

  3. Hurwicz Criterion

  4. All of the above


Correct Option: D
Explanation:

Expected Value, Minimax Regret, and Hurwicz Criterion are all types of decision-making under uncertainty, where the decision-maker is faced with multiple possible outcomes and must choose a strategy based on their beliefs about the likelihood of each outcome.

The Expected Value of a random variable is:

  1. The sum of all possible outcomes multiplied by their probabilities

  2. The difference between the maximum and minimum possible outcomes

  3. The probability of the most likely outcome

  4. None of the above


Correct Option: A
Explanation:

The Expected Value of a random variable is the weighted average of all possible outcomes, where the weights are the probabilities of each outcome.

The Minimax Regret criterion is used to make decisions under:

  1. Certainty

  2. Risk

  3. Uncertainty

  4. None of the above


Correct Option: C
Explanation:

The Minimax Regret criterion is used to make decisions under uncertainty, where the decision-maker chooses the strategy that minimizes their maximum possible regret.

The Hurwicz Criterion is a decision-making criterion that combines:

  1. Optimism and pessimism

  2. Risk and uncertainty

  3. Expected value and minimax regret

  4. None of the above


Correct Option: A
Explanation:

The Hurwicz Criterion is a decision-making criterion that combines optimism and pessimism by weighting the best and worst possible outcomes.

Which of the following is a type of decision-making under risk?

  1. Expected Value

  2. Minimax Regret

  3. Hurwicz Criterion

  4. All of the above


Correct Option: A
Explanation:

Expected Value is a type of decision-making under risk, where the decision-maker knows the probabilities of all possible outcomes.

In a decision tree, each node represents a:

  1. Possible outcome

  2. Decision point

  3. Chance event

  4. All of the above


Correct Option: D
Explanation:

In a decision tree, each node represents a possible outcome, a decision point, or a chance event.

Which of the following is a type of decision-making under certainty?

  1. Expected Value

  2. Minimax Regret

  3. Hurwicz Criterion

  4. All of the above


Correct Option:
Explanation:

Expected Value, Minimax Regret, and Hurwicz Criterion are all types of decision-making under uncertainty, not certainty.

Which of the following is a type of cooperative game?

  1. Prisoner's Dilemma

  2. Nash Equilibrium

  3. Cournot Competition

  4. Bertrand Competition


Correct Option: A
Explanation:

The Prisoner's Dilemma is a classic example of a cooperative game, where players can cooperate to achieve a mutually beneficial outcome.

Which of the following is a type of non-cooperative game?

  1. Prisoner's Dilemma

  2. Nash Equilibrium

  3. Cournot Competition

  4. Bertrand Competition


Correct Option: B
Explanation:

The Nash Equilibrium is a classic example of a non-cooperative game, where each player's best strategy depends on the strategy of the other player.

Which of the following is a type of cooperative game?

  1. Prisoner's Dilemma

  2. Nash Equilibrium

  3. Cournot Competition

  4. Bertrand Competition


Correct Option: C
Explanation:

Cournot Competition is a classic example of a cooperative game, where players can cooperate to achieve a mutually beneficial outcome.

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