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Zero-Sum Games and Minimax Strategies

Test your understanding of Zero-Sum Games and Minimax Strategies, fundamental concepts in Game Theory.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In a zero-sum game, the gains of one player are:

  1. Exactly equal to the losses of the other player
  2. Always greater than the losses of the other player
  3. Always less than the losses of the other player
  4. Unrelated to the losses of the other player
Question 2 Multiple Choice (Single Answer)

The minimax strategy in a zero-sum game aims to:

  1. Maximize the player's own gains
  2. Minimize the player's own losses
  3. Maximize the difference between the player's gains and losses
  4. Minimize the difference between the player's gains and losses
Question 3 Multiple Choice (Single Answer)

In a zero-sum game, a Nash equilibrium is a situation where:

  1. Neither player has an incentive to change their strategy
  2. Both players have an incentive to change their strategy
  3. One player has an incentive to change their strategy, but the other does not
  4. Both players have an incentive to cooperate with each other
Question 4 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). The minimax value of the game is:

  1. \(max_{i \in I} min_{j \in J} a_{ij}\)
  2. \(min_{i \in I} max_{j \in J} a_{ij}\)
  3. \(max_{i \in I} max_{j \in J} a_{ij}\)
  4. \(min_{i \in I} min_{j \in J} a_{ij}\)
Question 5 Multiple Choice (Single Answer)

In a zero-sum game, if the minimax value is equal to the maximin value, then:

  1. The game has a unique Nash equilibrium
  2. The game has multiple Nash equilibria
  3. The game has no Nash equilibrium
  4. The game is not a zero-sum game
Question 6 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). The maximin value of the game is:

  1. \(max_{i \in I} min_{j \in J} a_{ij}\)
  2. \(min_{i \in I} max_{j \in J} a_{ij}\)
  3. \(max_{i \in I} max_{j \in J} a_{ij}\)
  4. \(min_{i \in I} min_{j \in J} a_{ij}\)
Question 7 Multiple Choice (Single Answer)

In a zero-sum game, if the minimax value is greater than the maximin value, then:

  1. The game has a unique Nash equilibrium
  2. The game has multiple Nash equilibria
  3. The game has no Nash equilibrium
  4. The game is not a zero-sum game
Question 8 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). The saddle point of the game is a pair of strategies ((i^, j^)) such that:

  1. \(a_{i^*j^*} \ge a_{ij} \quad \forall i \in I, j \in J\)
  2. \(a_{i^*j^*} \le a_{ij} \quad \forall i \in I, j \in J\)
  3. \(a_{i^*j^*} \ge a_{ij} \quad \forall i \in I\)
  4. \(a_{i^*j^*} \le a_{ij} \quad \forall j \in J\)
Question 9 Multiple Choice (Single Answer)

In a zero-sum game, if the game has a saddle point, then:

  1. The minimax value is equal to the maximin value
  2. The minimax value is greater than the maximin value
  3. The minimax value is less than the maximin value
  4. The minimax value is unrelated to the maximin value
Question 10 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). The value of the game is:

  1. \(max_{i \in I} min_{j \in J} a_{ij}\)
  2. \(min_{i \in I} max_{j \in J} a_{ij}\)
  3. \(max_{i \in I} max_{j \in J} a_{ij}\)
  4. \(min_{i \in I} min_{j \in J} a_{ij}\)
Question 11 Multiple Choice (Single Answer)

In a zero-sum game, if the game has multiple Nash equilibria, then:

  1. The minimax value is equal to the maximin value
  2. The minimax value is greater than the maximin value
  3. The minimax value is less than the maximin value
  4. The minimax value is unrelated to the maximin value
Question 12 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). If the game has a unique Nash equilibrium, then:

  1. The minimax value is equal to the maximin value
  2. The minimax value is greater than the maximin value
  3. The minimax value is less than the maximin value
  4. The minimax value is unrelated to the maximin value
Question 13 Multiple Choice (Single Answer)

In a zero-sum game, if the minimax value is less than the maximin value, then:

  1. The game has a unique Nash equilibrium
  2. The game has multiple Nash equilibria
  3. The game has no Nash equilibrium
  4. The game is not a zero-sum game
Question 14 Multiple Choice (Single Answer)

Consider a zero-sum game with a payoff matrix (A). If the game has no Nash equilibrium, then:

  1. The minimax value is equal to the maximin value
  2. The minimax value is greater than the maximin value
  3. The minimax value is less than the maximin value
  4. The minimax value is unrelated to the maximin value
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