Game theory

Question 1

What is a dominant strategy?

Answer 1

A strategy that provides a higher payoff regardless of what the opponent does

Question 2

Define Nash Equilibrium

Answer 2

A strategy where no player can improve their payoff unilaterally changing their strategy

Question 3

Can a game have multiple Nash Equilibria?

Answer 3

Yes

Especially in coordination games (no dominant strategy)

(e.g Luigi’s, Luigi’s)

Question 4

What makes the Prisoner’s Dilemma inefficent?

Answer 4

Both players choose a dominant strategy that leads to a worse collective outcome than if they cooperated

Question 5

What is a Subgame Perfect Nash Equilibrium (SPNE)?

Answer 5

A refinement of Nash Equilibrium where strategies form a NE in every subgame, ensuring credibility

Question 6

How do we solve a Sequential game (one player moves first)?

Answer 6

Use backwards induction - start at the end and reason backward to find optimal strategies

Question 7

What is a best response function?

Answer 7

A players optimal choice given the strategy chosen by their opponent

Question 8

How does incomplete information affect a game?

Answer 8

Players must form beliefs about others’ payoffs or types, often requiring Bayesian reasoning