Lecture 5- Game theory

Question 1

What is Game Theory?

Answer 1

A technique used to study interactive decision making where the outcome of each player depends on the actions of all other players in the game

Question 2

What are the three basic elements of a game?

Answer 2

1. The players, 2. The rules of the game/strategies, 3. The available payoffs

Question 3

What is a game of perfect information?

Answer 3

A game where when any player makes a move, they know all the prior choices made by the other players

Question 4

What is a game of imperfect information?

Answer 4

A game where when a player reaches a decision point, they don’t know all the choices of the other players who preceded them

Question 5

What is a zero-sum game?

Answer 5

A game where the gains of one player equal the losses of other players, making the sum of payoffs always equal to zero

Question 6

What is a non-cooperative game?

Answer 6

A game where players must make strategy choices in isolation without consulting other players, with no possibility of formal binding cooperation

Question 7

What is a dominant strategy?

Answer 7

A strategy that is best for a player no matter what strategy the other player uses

Question 8

What is a Nash equilibrium?

Answer 8

A state where no player wishes to change their behavior given the behavior of other players - each player’s choice is optimal given the other players’ choices

Question 9

What are the three problems with Nash equilibrium?

Answer 9

1. A game may have multiple Nash equilibria, 2. Some games have no Nash equilibrium, 3. Nash equilibrium may not lead to Pareto-optimal choices

Question 10

What is a credible threat?

Answer 10

A threat that a player would actually carry out if the game progressed to that point, making it rational and believable

Question 11

What is a non-credible threat?

Answer 11

A threat that a player would not actually carry out if the game reached that point, making it irrational and unbelievable

Question 12

What is a sub-game perfect equilibrium?

Answer 12

A set of strategies where the actions prescribed for players in any sub-game constitute Nash equilibrium for that sub-game

Question 13

What is backward induction?

Answer 13

A process of solving a game by starting at its end and working backward to figure out what each player will do along the way

Question 14

What is the Prisoner’s Dilemma?

Answer 14

A game showing how individual rational choices can lead to collectively sub-optimal outcomes, where two prisoners must decide whether to confess or remain silent

Question 15

Why is cooperation difficult in the Prisoner’s Dilemma?

Answer 15

Because cooperation is individually irrational - each prisoner has a dominant strategy to confess regardless of what the other does

Question 16

What is an extensive form of a game?

Answer 16

A detailed description of the game rules shown through a game tree diagram, showing all possible moves and their sequence

Question 17

What is a normal form of a game?

Answer 17

The presentation of game strategies in matrix form, showing payoffs for each combination of player strategies

Question 18

What’s the difference between extensive and normal form?

Answer 18

Extensive form shows the sequence of moves through a tree diagram, while normal form presents all strategies and payoffs in a matrix

Question 19

What determines if a game is classified as ‘perfect information’?

Answer 19

Whether players know all prior choices made by other players when making their own moves

Question 20

How do you identify a dominant strategy equilibrium?

Answer 20

When each player has a strategy that dominates all others regardless of what other players do

Question 21

What makes the Nash equilibrium different from dominant strategy equilibrium?

Answer 21

Nash equilibrium requires each player’s choice to be optimal given others’ choices, while dominant strategy is optimal regardless of others’ choices

Question 22

What is the purpose of backward induction?

Answer 22

To find sub-game perfect equilibria by working backwards from end payoffs to determine rational choices at each decision point

Question 23

What is a pure strategy?

Answer 23

A complete plan of action that tells a player what choice to make at any node of the game tree or in any situation that might arise

Question 24

What happens in a cooperative game that’s different from non-cooperative?

Answer 24

In cooperative games, players can communicate and make binding agreements, while in non-cooperative games they must act independently

Question 25

What makes a threat ‘credible’ in game theory?

Answer 25

A threat is credible if it would be rational for the player to actually carry it out if the game reached that point, rather than just threatening to do so