Term 2 Week 4 game theory the basics

Question 1

What is s1 and s2 in game theory

How does utility change in game theory?

Answer 1

s1 is action of person 1
s2 is action of person 2

It is no longer just individual utility but U(s1,s2) for

Question 2

What are the rules of game theory

Question 3

What is the difference between a static and dynamic game

Answer 3

static everyone plays at same time
dynamic they take turns

Question 4

What is the number of players in game theory?

How do you denote set of actions?

How do we denote the utility of a player in the game

Answer 4

L = {1…..

S=(s1,s2,s3…sn) the full set of actions

Question 5

What does prisoner’s dilemma illustrate?

Answer 5

How people do not cooperate even if it is in the best interest to.

Question 6

What is the set up of Rock paper scissors? (Normal variant)

Answer 6

L = {1,2}
S1= {R,P,S} S2 = {R,P,S}

Question 7

What is a best response?

Answer 7

Best response gives the most favourable outcome for a player taking as given the response of another player

Question 8

What is a dominant strategy?

What is the implication of this?

Answer 8

When a player always chooses a strategy regardless of what opponent does.

A player can commit to a strategy without knowing the opponent’s

Question 9

What is the difference between strictly and weakly dominant?

Answer 9

Strictly dominant is when S11 always has a higher payoff than S12

Weakly dominant is when it has greater than or equaled to payoff

Question 10

What is a trap with strict and weak dominance

Answer 10

If something is strictly dominance it implies it is also weakly dominant

Question 11

What is Nash-equilibrium?

Is there always one in pure strategies?

What is an example of a no pure strategy NE game?

Answer 11

-A solution concept in which no player has any incentive to unilaterally deviate from their strategy.

-There may be no pure strategy nash equilibria or be multiple

-Rock paper scissors

Question 12

What is pareto efficiency within game theory?

Answer 12

An outcome is pareto efficient if there is no way to make someone win and no one to lose

Question 13

What is the set up when a player plays strategies with probability?

Answer 13

{s1,2,,……} played with {p1,2…..

Question 13

What does s1,2 and s2,2 show eg

Answer 13

first shows player second shows action

Question 14

How do we denote a mixed strategy?

Answer 14

v1(p1,p2)

Question 15

What is the relation between a pure strategy and a mixed strategy?

Answer 15

A pure strategy is also a mixed strategy just with p = 1

Question 16

What is the game of chicken and what is the set up?

Question 17

How do you find the mixed strategy NE?

Answer 17

Find the probability at which the player is indifferent between to pure strategies.

Then work out for both players to find the probability.

Question 18

How do you draw the reaction function for NE?

Answer 18

First find the pure and mixed NE and pin them down.

Then start with player 1 and look at the values of probability in which they would do the NE

Then do the same for P2