S2 - game theory

Question 1

what is normal form

Answer 1

normal form = matrix shows pay offs to each player from choosing a particular action
Most useful when players move simultaneously
Each firm decides without knowledge of other firms
Played once
Can have a dominant strategy

Question 2

what is extensive form

Answer 2

Extensive form = using game trees which depict the sequences of strategies - all pay offs known at all points in game

Question 3

what is pure and mixed strategy

Answer 3

Pure strategy - no randomisation - player chooses and sticks to available strategy
Mixed strategy - player chooses according to a probability distribution and choices are not fixed

Question 4

what is Nash equilibrium

Answer 4

Nash equilibrium - no player can improve their payoff by changing strategy
When each player chooses his best response probability to his opponents best response probability

Question 5

what is the prisoners dilemma

Answer 5

payoffs in each matrix are all negative decision made independently
Cooperate for mutual benefit or betray for individual reward
Repeated games - new strategic choices available to each player
Can choose to trust each other and can punish each other when they deviate
Not credible if there’s a finite amount of games because they hope cooperation will induce more cooperation
Last game is played like there was only one
Infinite games - each player has opportunity to influence opponents behaviour. Threat of non cooperation may convince each player to play Pareto efficient strategy
Grim trigger strategy - if player A cheats in round 1, player B will cheat in the future

Question 6

what’s the present value of money

Answer 6

PVfirm = (1+i)/i x profit
Does PV of cheating in game 1 exceed PV of future payments from not cheating