# Game theory: cournot, bertrand + stackelberg oligopoly

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• Created by: charlie
• Created on: 09-05-16 12:47
Oligopoly characteristics and aim
profit depends on price compared to rivals + whether product differentiated/ aim is to maximise profit
1 of 18
Oligopoly: cartel
oligopolistic firms combine and become better off
2 of 18
Oligopoly: Actions (nash equilibrium)
set price/ quantity + holding actions of all firms constant, no firm can obtain higher profit by choosing different strategy
3 of 18
Cournot oligopoly: characteristics
simultaneous/ set quantity levels/ independent/ imperfect information/ quantity one chooses affects others profit as market price depends on total output
4 of 18
Cournot oligopoly: assumptions
market lasts 1 period/ simultaneous firms/ identical/
5 of 18
Oligopoly: Actions (best response)
strategy maximises payoff given the belief about future actions of rival
6 of 18
Stackelberg oligopoly: characteristics
firms make decisions at different times (sequential)/ set quantity levels/ leader (greater power, entered first, reputation, cost adv, greater production) + follower
7 of 18
Stackelberg oligopoly: backward induction
solve COURNOT equation for opposition firm first/ put into profit function for firm A
8 of 18
Betrand oligopoly: characteristics
simultaneous/ maximise profit subject to prices
9 of 18
Bertrand oligopoly: Nash-bertrand eqm
set of prices such that no firm can obtain high profit by charging a different price, if others continue to charge this price
10 of 18
Bertrand oligopoly: quantity function equation
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11 of 18
Bertrand oligopoly: profit function equation
.
12 of 18
Bertrand oligopoly: 4 stages
1) profit function 2) maximise profit=0 (differentiate with respect to own price) 3) find best response function (making price subject of equation) 4) Nash bertrand eqm (best response functions meet)
13 of 18
Cournot oligopoly: profit equation
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14 of 18
Stackelberg oligopoly: profit equation
.
15 of 18
Cournot + Stackelberg oligopoly: price/ quantity equation
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16 of 18
Cournot oligopoly: 5 stages
1) profit function 2) maximise profit=0 (differentiate with respect to own quantity) 3) make quantity subject of equation 4) consistent conjectures (conjectured quantity=optimal quantity) in eqm. 5) Nash equilibrium (substituting in each equation)
17 of 18
Stackelberg oligopoly: 5 stages
1) followers reaction function (COURNOT) 2) profit function of leader 3) max profit=0 (differentiate with respect to own quantity) 4) make quantity subject of equation 5) Nash eqm (substituting equations)
18 of 18

## Other cards in this set

### Card 2

#### Front

Oligopoly: cartel

#### Back

oligopolistic firms combine and become better off

### Card 3

#### Front

Oligopoly: Actions (nash equilibrium)

### Card 4

#### Front

Cournot oligopoly: characteristics

### Card 5

#### Front

Cournot oligopoly: assumptions