[3] Oligopoly Markets

Question 1

What is an Oligopoly?

Example?

Answer 1

is a market structure in which a small group of
firms each influence price and enjoy substantial barriers to entry.

eg: video game/console market - nintendo, sony, xbox

Question 2

Oligopoly theories
– Cournot (1838) →
– Bertrand (1883) →
What do they have in common?

What is the third theory? What is different?

Answer 2

– Cournot: Firms decide quantity, and price adjusts to
consumer demand (automobiles?) – simultaneous
decision.

– Bertrand: firms set prices and sell whatever is
demanded at those prices (most services) –
simultaneous decision.

– Stackelberg: first mover advantage – timing
matters, sequential decision (airlines)

Question 3

Four main assumptions of duopoly for Cournot model?

Eg?

Answer 3

1. There are 2 firms and no others can enter the market
2. The firms have identical costs
3. The firms sell homogenous products
4. The firms set their quantities simulataneously

• Example: airline industry

Question 4

DEF; the payoff

Answer 4

The payoffs of a game are the players’ valuation of the
outcome of the game (e.g. profits for firms, utilities for
individuals).

Question 5

DEF: the rules of the game

Answer 5

The rules of the game determine the timing of players’

moves and the actions players can make at each move.

Question 6

DEF: an action

Answer 6

An action is a move that a player makes at a specified stage of a game.

Question 7

DEF: a strategy

Answer 7

A strategy is a battle plan that specifies the action that a player will make based on the information available at each move and for any possible contingency

Question 8

DEF: strategic interdependence

Answer 8

Strategic interdependence occurs when a player’s optimal strategy depends on the actions of others.

Question 9

ASSUMPTIONS of Game Theory:
• All players are interested in maximizing their
_________(i.e. profit, utility, etc.)
• All players have common knowledge about the ___of the game (i.e. I know that you know, that I know)
• Each player’s payoff depends on _________ taken by all players (i.e. duopoly interaction)
• ___ ____ (payoff function is common
knowledge among all players) is different from perfect
information (player knows full history of game up to the
point he is about to move)

Answer 9

payoffs
rules
action
Complete information

Question 10

In a static game each player …. x3

but has imperfect infomation about…

Answer 10

acts simultaneously, only once and has
complete information about the payoff functions
.. their rivals move

Question 11

DEF: dominant strategy

Answer 11

A strategy that produces a higher payoff than any other strategy for every possible combination of its rivals’ strategies

Question 12

DEF: Best Response

Answer 12

The best response is a strategy that maximizes a
player’s payoff given its beliefs about its rivals’
strategies.

Question 13

DEF: Nash Equilirium

Answer 13

A Nash equilibrium, named after John Nash, is a
set of strategies, one for each player, such that no
player has incentive to Unilaterally change his
action.
• Players are in equilibrium if a change in strategies
by any one of them would lead that player to earn
less than if he remained with her current strategy.

Question 14

• Every game has at least one __ __ and every

__ ___ equilibrium is a Nash equilibrium,

Answer 14

Nash equilibrium

dominant strategy

Question 15

The linear Cournot model
• Firm i sets quantity qi
• Market price given by:
• Linear cost functions: 
• Payoff functions:

Answer 15

P(q) = a - bq
Ci (qi) = ci qi

πi (q1, q2) = [a- c – b(q1 + q2)] qi with i= 1,2.

Question 16

ALGEBRA
General demand: p =
Linear demand: p =

Linear costs: TCi =
MC =
AC =

Answer 16

General Demand: p(Q) = p(q1+q2+q3…)
Linear demand: p = a – bQ with Q=q1+q2+q3…
• Linear costs: TCi = ci qi + Fi
– Marginal cost: MCi = ci
– Average cost: ACi = ci + [Fi/qi]
– If identical firms: c1 = c2 = c3 =… = c; Fi = F

Question 17

Algebra of best replies: two firms (duopoly) case
• Demand: p = a – b[q1+q2]
• max [q1>0] π1 = pq1 – c1q1 – F
= aq1 – b[q1+q2]q1 – c1q1 – F
FOC?
SOC?

Answer 17

FOC: ∂π1/∂q1 = a – 2bq1 – bq2 – c1 = 0
2bq1* = a– bq2 – c1
q1* = [a – c1]/2b – ½ q2 = eqn of BR1

SOC: π’’ = – 2b <0

Question 18

We solve then a system of two equations, by
using the two BR functions:
• q1* = [a – c1]/2b – ½ q2 -> A
• q2* = [a – c2]/2b – ½ q1 -> B

By substitution we substitute, B into A:
[8 stages of workings]

So Q = (q1+ q2) =
p = a - bQ =

Answer 18

q1* = [a – c]/2b – ½ [(a – c)/2b – ½ q1]
q1* = (a – c)/2b – ½ [(a – c)/2b – ½ q1]
q1* = (a – c)/2b – [(a – c)/4b – 1/4 q1]
q1* = (a – c)/2b – (a – c)/4b + 1/4 q1
q1 - 1/4 q1 = (a – c)/2b – (a – c)/4b
q1 (4- 1)/4 = [2(a – c) – (a – c)]/4b
3/4 q1=(a – c)/4b
q1* = q2* = (a-c) /4b

SO Q = (q1+ q2) = 2[a – c]/3b
p = a – bQ = a - b (2[a – c]/3b) = a + 2c / b

Question 19

A Bertrand equilibrium (or Nash-Bertrand

equilibrium) is

Answer 19

a set of Prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices.

Question 20

Products are perfect substitutes: Give the Quantity and Profit for firm 1 and firm 2

• if prices are different, all consumers buy only from the
low-price firm p1 < p2 …

• if prices are equal, consumers are indifferent to buy
from any of the two firms: we can assume that they
equally share industry demand p1 = p2 = p….

• If one firm set a price p > c, then undercutting (i.e.
pricing at p - ԑ) is optimal for the rival. If p2 = p > c…x2

Answer 20

q1 = Q(p1) , π1 = (p1 – c)Q(p1) q2 = 0 , π2 = 0

q1 = q2 = ½ Q(p) π1 = π2 = ½ (p – c)Q(p)

p1 = p -> π1 = ½ (p – c)Q(p)

p1 = p-ԑ -> π1 = (p – ԑ – c)Q(p – ԑ)

Question 21

What does intuition from the Bertrand model suggest about undercut and therefore profits?

What does this mean from price?

Answer 21

There always exists a ԑ small enough to make π1 higher by undercutting
• Undercutting stops when prices equal marginal cost (no firm will ever prices below MC = AC - negative profits if positive sales) £

Question 22

What is the Bertrand Paradox?

Answer 22

In a homogeneous product
Bertrand duopoly with identical and
constant marginal costs, the equilibrium
is such that
•firms set price equal to marginal costs;
•firms do not enjoy any market power. 
[perfectly competitive conditions]

Question 23

Sequential choice: Stackelberg

First-mover advantage?

Answer 23

• Firm gets higher payoff in game in which it is a leader than in symmetric game in which it is a follower.

Question 24

What is a subgame perfect Nash equilibrium?
• It may be found by __ ___, an iterative process for solving finite extensive form or sequential games.
– First, one determines the ___ ___ of the player who makes the __ __ of the game.
– Then, the__ action of the __-__-__ moving
player is determined by taking the last player’s action __ __
– The process continues in this way __ in time until all players’ actions have__ ___.
• Subgame perfect equilibria eliminate __-___ ___.

Answer 24

is an equilibrium such that players’ strategies constitute a Nash equilibrium in every subgame of the original game.

backward induction
optimal strategy
last move
optimal, next-to-last, as given
 backwards, been determined
non-credible threats

Question 25

Work Through Walmart Examples and the maths
STACKLEBURG:
General linear inverse demand function given by:

• The Stackelberg leader knows the follower will use its___-__ function and so the leader views the
___ ____ in the market as its ___

Answer 25

SEE SLIDES AND LECTURE CAPTURE

p = a – bQ

best-response
residual demand, demand