5- Game Theory

Question 1

What are the 2 types of Game Theory?

Answer 1

-Analytical (normative): how agents should behave
-Behavioural (positive): how agents tend to behave

Question 2

What is the definition of a game?

Answer 2

A decision problem in which the final outcome depends upon the decisions of all agents, as well as the state of the world

Question 3

What is a strategy?

Answer 3

Complete plan of action that describes what a player will do under all possible circumstances

Question 4

What is a strategy profile?

Answer 4

Vector of strategies, one for each player

Question 5

What is a best response?

Answer 5

Strategy that maximises own utility given the specific strategy of the other players

Question 6

What is a Nash Equilibrium?

Answer 6

Strategy profile such that each strategy in the profile is a best response to the other strategies in the profile (any deviation decreases payoff)

Question 7

What is the Nash Equilibrium existence theorem?

Answer 7

Every finite game (in which all players have a finite number of pure strategies) has a Nash equilibrium

Question 8

When does a strategy profile X dominate profile Y?

Answer 8

Whenever all players weakly prefer the outcome under X over the outcome under Y

Question 9

When is a strategy profile Pareto optimal?

Answer 9

If it is not Pareto dominated by any other strategy profile

Question 10

Why is pre-play communication not effective in games?

Answer 10

‘Cheap talk’ property means it is not credible because players still have the same incentives to deviate

Question 11

What is a Nash Equilibrium in Mixed strategies?

Answer 11

Probability distribution over pure strategies such that each player is indifferent among the pure strategies in her equilibrium strategy given the other player randomizes according to her equilibrium distribution function

Question 12

What’s a trick to find the pure strategy Nash equilibria from a payoff matrix?

Answer 12

Fix the other player’s responses, and mark the best response in each case, do the same for the other player, the choices with 2 marks are NE

Question 13

How do you draw a sequential game in extensive form?

Answer 13

From a player’s decision, draw a tree showing the possible responses and respective payoffs

Question 14

What is a Subgame-perfect equilibrium?

Answer 14

Strategy profile that constitutes a Nash equilibrium in each subgame

Question 15

What is the Subgame-perfect equilibrium existence theorem?

Answer 15

Every finite extensive form game has a subgame-perfect Nash equilibrium

Question 16

How can non-credible threats be overcome?

Answer 16

‘Binding hands’ or implementing an automatic non-stoppable reaction (which must be public knowledge)

Question 17

What are the 5 types of social preferences?

Answer 17

-Altruistic
-Envious/Spiteful
-Rawlsian
-Inequality-averse
-Utilitarian

Question 18

What are altruistic preferences?

Answer 18

Derive payoff from both agents utility with a weighting parameter e.g. a√X + b√Y

Question 19

What are envious/spiteful preferences?

Answer 19

Negative utility from other player’s payoff
e.g. √X - √Y

Question 20

What are Rawlsian preferences?

Answer 20

Solidarity with worst off, payoff is the minimum across players e.g. min{√X, √Y}

Question 21

What are Inequality-averse preferences?

Answer 21

Negatively affected by differences in payoffs, in either player’s favour e.g. -|√X - √Y|

Question 22

What are utilitarian preferences?

Answer 22

Utility derived from total payoff of all players; leads to sharing so that agents avoid diminishing utility

Question 23

How do you find subgame-perfect equilibria of the ultimatum game given the preferences of other player?

Answer 23

1. Find the utility for each player given the payoffs at the terminal nodes
2. Setup an inequality to work out which payoffs agent will reject
3. Proposer knows this so differentiate their utility function to optimise under that constraint

Question 24

How do you find a mixed strategy Nash equilibrium?

Answer 24

1.Form an equation with the payoffs from each decision on each side weighted by the probability the other player makes each decision
2. Solve for p