week 6 Game Theory

Question 1

strategic interaction

Answer 1

modelling situations when an agents utility is affected by others’ choices

Question 2

simultaneous game

Answer 2

situation where players aren’t able to see what other players have chosen before. e.g rock paper scissors

Question 3

Model of simultaneous game in normal form, define key elemets of game

Answer 3

• This has players- an agent who is interacting
  
  • A strategy- choice that a player can make
  • A strategy profile a choice for each player
  • Payoff monetary reward (same as utility, payoff is utility) of a particular strategy profile. (the objective is for players to maximise utility)

Question 4

normal form

Answer 4

Normal form describes- which players play the game, their strategy and the possible strategy profiles and their payoffs.

Question 5

dominant strategy

Answer 5

Dominant strategy- strategy that gives you a strictly higher payoff than all your other strategies.

Question 6

strictly dominated strategy

Answer 6

Strategy x is a strictly dominated strategy if there exists another strategy Y such that Y gives the player a strictly higher payoff than x regardless of what strategy other players play.

Question 7

Iterated Elimination of strictly dominated strategies

Answer 7

1. Delete any strictly dominated strategies for player 1
2. In remaining game delete any strictly dominated strategies for player 2
3. In remaining game delete any strictly dominated strategies for player 1
   Keep going till cant delete any more and therefore we have a solution

Question 8

Nash equilibrium

Answer 8

a strategy profile where each player is playing a best response to their opponents strategy

Question 9

pure Nash equilibrium

Answer 9

Pure- a strategy where you choose 100% probability
(doesn’t work in sport)

Question 10

Mixed Nash equilibrium

Answer 10

randomise between more than one pure strategy

Question 11

sequential game

Answer 11

knowing your opponent’s choice before making yours

Question 12

extensive form game

Answer 12

model that describes a sequential game

Question 13

elements of sequential game

Answer 13

Players- agents who interact
Actions- choices each player can make
Strategy- a complete contingent plan of actions (action component of strategy)
Strategy profile- a strategy for each player
Payoffs- each players utilities for each strategy profile

Question 14

strategies in a sequential game

Answer 14

an action choice for every possibility a player could find themselves in in the game

Question 15

what represents a sequential game

Answer 15

Game tree

Question 16

non credible threats

Answer 16

if firm 1 lowered price they choose between 0 and -1 while 0 is strictly better

Question 17

subgame

Answer 17

Take any decision node in a game tree, the rest of the game starting from that particular node is therefore the subgame.

Question 18

subgame perfect equilibrium

Answer 18

A strategy profile where players best respond to each other’s actions in every subgame

Question 19

Backwards induction

Answer 19

To find subgame perfect equilibrium (SPE) we use backwards induction.

1. Start from final subgame
2. Highlight best responses
3. Move to previous sub games
   Highlight best response