Game Theory - Nash Equilibrium

Question 1

What is a Nash Equilibrium?

Answer 1

A state in a game where no player can improve their outcome by unilaterally changing their strategy.

Question 2

In a Nash Equilibrium, why does no player have an incentive to change their strategy?

Answer 2

Because each player’s strategy is the best response to the strategies chosen by other players.

Question 3

True or False: A Nash Equilibrium always results in the best possible outcome for all players.

Answer 3

False. Nash equilibrium is stable but not necessarily optimal or fair for all players.

Question 4

Define a ‘Pure Strategy Nash Equilibrium.’

Answer 4

An equilibrium where each player chooses a specific strategy, with no randomization, that no one would benefit from deviating from.

Question 5

What is a ‘Mixed Strategy Nash Equilibrium’?

Answer 5

An equilibrium where players randomize over different strategies, usually when no pure strategy equilibrium exists.

Question 6

What does it mean when a strategy is a ‘Best Response’?

Answer 6

It is the strategy that maximizes a player’s payoff, given the strategies chosen by other players.

Question 7

In which type of games is a Mixed Strategy Nash Equilibrium common?

Answer 7

In games where there is no Pure Strategy Nash Equilibrium, such as Rock-Paper-Scissors.

Question 8

Fill in the blank: Nash Equilibrium is a ______ state in a game.

Answer 8

stable

Question 9

Fill in the blank: In Nash Equilibrium, all players’ strategies are ______ best responses to each other.

Answer 9

mutual

Question 10

What is the Prisoner’s Dilemma example of?

Answer 10

A game theory scenario where Nash Equilibrium leads to a suboptimal outcome for both players if they act in self-interest.

Question 11

Explain why the Prisoner’s Dilemma leads to a suboptimal Nash Equilibrium.

Answer 11

Because both players choose to ‘confess’ as their best response, resulting in worse outcomes for both than if they both stayed silent.

Question 12

In economic terms, where is Nash Equilibrium applied?

Answer 12

In market competition, pricing, and auctions.

Question 13

What concept in game theory illustrates strategic interactions and decision-making?

Answer 13

Game theory.

Question 14

Define ‘Pareto Optimality’ in game theory terms.

Answer 14

A state where no player can improve their outcome without worsening the outcome for another.

Question 15

What is an example of a zero-sum game?

Answer 15

Rock-Paper-Scissors, where one player’s gain is another’s loss.

Question 16

What does the term ‘Players’ mean in game theory?

Answer 16

The decision-makers in the game, who make strategic choices.

Question 17

What are ‘Strategies’ in game theory?

Answer 17

The possible actions or plans that players can choose from in a game.

Question 18

Define ‘Payoffs’ in the context of game theory.

Answer 18

The outcomes or rewards players receive based on the strategies chosen.

Question 19

Fill in the blank: The concept of ______ was introduced by John Nash to describe a stable outcome in strategic games.

Answer 19

Nash Equilibrium

Question 20

What is the main difference between Cooperative and Non-cooperative games?

Answer 20

In cooperative games, players can form alliances or agreements; in non-cooperative games, they act independently.

Question 21

What is a Dominant Strategy?

Answer 21

A strategy that provides a better payoff than any other, regardless of the other players’ choices.

Question 22

Which game theory concept helps predict the stable outcome in competitive situations?

Answer 22

Nash Equilibrium.

Question 23

In which scenario would players use a mixed strategy?

Answer 23

In situations where pure strategies don’t yield equilibrium, as in Rock-Paper-Scissors.

Question 24

What is a ‘Best Response Function’?

Answer 24

A mathematical representation of each player’s best response given other players’ strategies.

Question 25

How is a Nash Equilibrium calculated in complex games?

Answer 25

Using best response functions or mixed strategy probabilities to find where all players’ strategies intersect.

Question 26

What is a potential limitation of Nash Equilibrium in real-world applications?

Answer 26

It assumes players are perfectly rational and fully informed, which may not hold true in reality.

Question 27

Fill in the blank: A Nash Equilibrium does not guarantee ______ or optimal outcomes for all players.

Answer 27

fair

Question 28

True or False: In an oligopoly, Nash Equilibrium represents price and quantity choices that maximize each firm’s profit.

Answer 28

True

Question 29

Why might multiple Nash Equilibria exist in some games?

Answer 29

Because there could be different stable states where players have no incentive to deviate.

Question 30

Define ‘Zero-sum Game’.

Answer 30

A game where one player’s gain is exactly another player’s loss.

Question 31

Explain the concept of the Pareto Frontier.

Answer 31

The set of all Pareto optimal allocations, where no one can improve without making someone else worse off.

Question 32

What is a Coordination Game?

Answer 32

A game where players benefit from choosing the same or complementary strategies, like deciding on a meeting location.

Question 33

Give an example of a game with multiple Nash Equilibria.

Answer 33

The Battle of the Sexes game, where players benefit by coordinating but have different preferred outcomes.

Question 34

Fill in the blank: In game theory, ______ refers to situations where players’ choices affect each other’s outcomes.

Answer 34

strategic interactions

Question 35

How does Nash Equilibrium differ from Pareto Optimality?

Answer 35

Nash Equilibrium is about stability with no incentive to deviate, while Pareto Optimality is about efficient allocation where no one can be made better off without harming another.

Question 36

What is a common application of Nash Equilibrium in computer science?

Answer 36

Algorithm design, network security, and AI decision-making.