Zero-Sum Games and Minimax Strategies Online Test

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Zero-Sum Games and Minimax Strategies

Description: Test your understanding of Zero-Sum Games and Minimax Strategies, fundamental concepts in Game Theory.
Number of Questions: 14
Created by: Aliensbrain Bot
Tags: game theory zero-sum games minimax strategies nash equilibrium

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

Exactly equal to the losses of the other player
Always greater than the losses of the other player
Always less than the losses of the other player
Unrelated to the losses of the other player

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

Maximize the player's own gains
Minimize the player's own losses
Maximize the difference between the player's gains and losses
Minimize the difference between the player's gains and losses

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

Neither player has an incentive to change their strategy
Both players have an incentive to change their strategy
One player has an incentive to change their strategy, but the other does not
Both players have an incentive to cooperate with each other

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

(max_{i \in I} min_{j \in J} a_{ij})
(min_{i \in I} max_{j \in J} a_{ij})
(max_{i \in I} max_{j \in J} a_{ij})
(min_{i \in I} min_{j \in J} a_{ij})

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

The game has a unique Nash equilibrium
The game has multiple Nash equilibria
The game has no Nash equilibrium
The game is not a zero-sum game

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

(max_{i \in I} min_{j \in J} a_{ij})
(min_{i \in I} max_{j \in J} a_{ij})
(max_{i \in I} max_{j \in J} a_{ij})
(min_{i \in I} min_{j \in J} a_{ij})

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

The game has a unique Nash equilibrium
The game has multiple Nash equilibria
The game has no Nash equilibrium
The game is not a zero-sum game

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:

(a_{i^j^} \ge a_{ij} \quad \forall i \in I, j \in J)
(a_{i^j^} \le a_{ij} \quad \forall i \in I, j \in J)
(a_{i^j^} \ge a_{ij} \quad \forall i \in I)
(a_{i^j^} \le a_{ij} \quad \forall j \in J)

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

The minimax value is equal to the maximin value
The minimax value is greater than the maximin value
The minimax value is less than the maximin value
The minimax value is unrelated to the maximin value

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

(max_{i \in I} min_{j \in J} a_{ij})
(min_{i \in I} max_{j \in J} a_{ij})
(max_{i \in I} max_{j \in J} a_{ij})
(min_{i \in I} min_{j \in J} a_{ij})

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

The minimax value is equal to the maximin value
The minimax value is greater than the maximin value
The minimax value is less than the maximin value
The minimax value is unrelated to the maximin value

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

The minimax value is equal to the maximin value
The minimax value is greater than the maximin value
The minimax value is less than the maximin value
The minimax value is unrelated to the maximin value

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

The game has a unique Nash equilibrium
The game has multiple Nash equilibria
The game has no Nash equilibrium
The game is not a zero-sum game

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

The minimax value is equal to the maximin value
The minimax value is greater than the maximin value
The minimax value is less than the maximin value
The minimax value is unrelated to the maximin value

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