Week 7

Question 1

In game theory we assume

Answer 1

All agents maximise utility

Question 2

Dominant strategy

Answer 2

If U(s1) > U(s2)

S1 dominantes S2; in every scenario, expected utility for S1 is greater than S2

Question 3

weakly dominant

Answer 3

If U(s1) >= U(s2)

S1 weakly dominantes S2; in every scenario, expected utility for S1 is greater than or equal to S2

Question 4

Define a Nash equilibrium

Answer 4

Question 5

Determine if a decision state is in Nash equilibrium

Answer 5

If choosing to change the state leads only to worse scenarios for each agent, that agent will not change its decision

Question 6

Pareto optimality

Answer 6

An outcome ω is not Pareto optimal if there is another outcome ω’ that makes everyone as happy or happier

You can’t move away from Pareto efficiency without making at least one agent worse off
^^^** this is important bit

Question 7

Social welfare

Answer 7

Question 8

Normal form game

Answer 8

Question 9

Payoff matrix

Answer 9

Question 10

Common payoff game

Answer 10

U_i(a) = U_j(a) for all a in A_i x A_j

In every scenario, participants get equal utility

Question 11

Misanthropes coordination game

Answer 11

Question 12

Constant sum game

Answer 12

U_i(a) + U_j(a) = c ; for all a in A_i x A_j

Question 13

Zero sum game

Answer 13

U_i(a) + U_j(a) = 0 ; for all a in A_i x A_j

Question 14

Choosing probabilities for a mixed strategy

Answer 14

Question 15

Represent Nash equilibrium in matrices

Answer 15