Econ Week 10- Class 2

backwards induction

consider best response of 2nd mover, choose option best for 1st mover

to see if player have first move advantage

compare to simultaneous move game

oligopoly

more than one firm

duopoly

2 firms

Bertrand Competition

firms compete on price (what they are choosing is price), firms always have an incentive to lower prices to capture market share (NE P=MC)

MR

same intercept, twice the slope as the demand curve

cournot

firms choose quantity simultaneously (q, choice variable, max profit, objective function)

Cournot steps

1. write objective function in terms of choice function

2. set derivative of objection function equal to zero

3. solve for choice variable

prisoners dilemma, game is finite

won’t cooperate

PV of perpituity

x/r

tit-for-tat

choose to cooperate but if i deviate they will deviate

Cournot NE

solve for intersection of firms’ best response functions

Stackleberg

has leader and follow, leader chooses quantity first (means we use backwad induction)

Stackleberg steps

1. find BR for follower first

2. leader firm choose quantity to maximize profit for themselves taking the other firm’s best response into account

   1. sub BR of follower firm into Demand, sub demand into profit for leader

3. do same next steps for Leader firm (taking derivative, solve for leader firm quantity)