Oligopoly, Cournot and Stackelberg...

Lecture 23Oligopoly, Cournot and Stackelberg

Competition

Econ 301Professor S. Severinov

UBC

Oligopoly – Characteristics

Small number of firms Product differentiation may or may not exist Barriers to entry Each Firm affects the price and the total quantity in the market Each firm’s action depends on the actions of the other

firms

Oligopoly – Equilibrium

If one firm decides to change their quantity or cut their price, they must consider what the other firms in the industry will do Could cut price some, the same amount, or more

than firm Could lead to price war and drastic fall in profits

for all Actions and reactions are dynamic, evolving over

time

Oligopoly – Equilibrium

Defining Equilibrium Firms are doing the best they can and have no incentive to

change their output or price All firms assume competitors are taking rival decisions into

account Nash Equilibrium

Each firm is doing the best it can given what its competitors are doing

We will focus on duopoly Markets in which two firms compete

Oligopoly: Cournot Model

Different modes of competition in real world call for different models of behavior

The Cournot Model: Oligopoly model in which firms produce a homogeneous good, all firms decide simultaneously how much to produce each firm treats the output of its competitors as

fixed and chooses its best response to it.

Firm will adjust its output based on what it thinks the other firm will produce

Oligopoly- Duopoly The market for movies in a medium size city Dixon:

Sony’s Loews Theatres and local Main Street Movies (MSM) are the only two players.

The demand for movies: P=12 – Q.

P is the price of a ticket (in $).

Q is number of seats (in ‘000) demanded per week.

The marginal cost of offering movie shows for each firm is not important, what matters is that both firms have identical and sufficiently small marginal costs which we set to 0.

Loews and MSM have to make capacity choices (in thousands of seats) for theatres to build.

Duopoly: Loews & MSM Let us solve for Nash equilibrium when capacity choices

are made simultaneously (i.e. when making its capacity choice, a firm does not

observe its rival’s capacity).

MSM’s capacity qM ; Loews’ capacity qL.

Zero costs: this assumption is for simplicity, so that we can focus on strategic, not technological factors.

Nash equilibrium q*M and q*L must be best responses to each other:q*M maximizes MSM’s profits when Loews chooses q*L.

q*L maximizes Loews’ profits when MSM chooses q*M.

Duopoly: Loews & MSM Profit Functions of MSM and Loews are:

Nash equilibrium: every firm is at its best response to the rival’s action.

First Step: compute best responses:€

P rM = P ×q M = 1 2 −q M −q L( )×q M

P rL = P ×q L = 1 2 −q M −q L( )×q L

€

q M* m a x i m i z e s

P r M = 1 2 − q M − q L*( )q M = 1 2 q M − q M

2 − q L* q M

q L* m a x i m i z e s

P r L = 1 2 − q M* − q L( )q L = 1 2 q L − q L

2 − q M* q L

Loews & MSM To maximize PrM take its derivative with respect to qM

and set it equal to zero. This would give qM*. Using the General Rule 1, we have:

Set this to zero:

So, the best response function of MSM is:

*212PrLM

M

M qqdq

d −−=

0*212 * =−− LM qq

26

** LM

qq −=

Loews & MSM Repeating the same steps to maximize PrL gives us

the best response of Loews

Recall that MSM’s best response function is:

Solving these two equations in two unknowns gives you the equilibrium quantities:

Profits are: P×q=16 (thousand) for each firm.

2q6q

*M*

L −=

2q6q

*L*

M −=

4qq-12 = P

4qq *L

*M

*L

*M

=−

==

Oligopoly: Graphical Representation

The Reaction Curve The relationship between a firm’s profit-

maximizing output and the amount it thinks its competitor will produce

A firm’s profit-maximizing output is a decreasing schedule of the expected output of Firm 2

Firm 2’s ReactionCurve Q*2(Q1)

Reaction Curves and Cournot Equilibrium

qM

qL

6 12

12

Firm 1’s ReactionCurve Q*1(Q2)

6

x

x

x

In Cournot equilibrium, eachfirm correctly assumes how

much its competitors willproduce and thereby

maximizes its own profits.

CournotEquilibrium

Firm 1’s reaction curve shows how much itwill produce as a function of how much it thinks Firm 2 will produce. The x’s

correspond to the previous model.

Firm 2’s reaction curve shows how much itwill produce as a function of how much

it thinks Firm 1 will produce.

Cournot Equilibrium

Cournot equilibrium is an example of a Nash equilibrium (Cournot-Nash Equilibrium)

Each firm’s reaction curve tells it how much to produce given the output of its competitor

Equilibrium in the Cournot model, in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly

Cournot Equilibrium

Q1

Q2

Firm 2’sReaction Curve

12

6


6

12

4

4

Cournot Equilibrium

The demand curve is P = 12 - Q andboth firms have 0 marginal cost.



Duopoly ExampleQ1

Q2

12

12

4

4

Cournot Equilibrium

CollusionCurve

3

3

Collusive Equilibrium

For the firm, collusion is the bestoutcome followed by the Cournot

Equilibrium and then the competitive equilibrium

6

6

Competitive Equilibrium (P = MC; Profit = 0)

For comparison, consider a monopoly: If Loews and MSM are to collude and act as a single

firm splitting profits in half they will choose q to maximize:

The monopoly price would be P=12-6=6Monopoly profits: 6*6=36If firms will split them equally each will earn 18

( )

60212

i.e. 0,MR :iscondition order -First

1212Pr 2

==−

=

−=−=

qq

qqqqMonop

Profit Maximization w/ Collusion

Collusion (contract) Curve q1 + q2 = 6

Shows all pairs of output q1 and q2 that maximize total profits

For example: q1 = q2 = 3 Less output and higher profits than the Cournot

equilibrium

Conclusion: there is an incentive to collude and split the marketBut is collusion going to be sustainable?

Competition Versus Collusion:The Prisoners’ Dilemma Cournot Nash equilibrium is a noncooperative

equilibrium: each firm makes decision that gives greatest profit, given actions of competitors

Although collusion is illegal, why don’t firms cooperate without explicitly colluding? Why not set profit maximizing collusion price and

hope others follow?

Collusion Game: Payoff Matrix

MSM

Loews

Choose q=3 Choose q=4

Choose q=3

Choose q=4

$18, $18 $15, $20

$16, $16$20, $15

Non-sustainability of Collusion

If the firms try to collude, it will not be sustainable, Will not be a Nash equilibrium Each Firm would like to deviate from the collusive

agreement to produce 3 and produce more (say 4) thereby increasing profits unilaterally.

In fact, best response to q=3 is q=6-3/2=4.5

First-Mover advantage

When one firm chooses its action before competitors (due to faster reaction, earlier investment, history factors,

patents), it gets an opportunity for strategic commitment.

How would that affect the outcome of competition? Naturally, this depends on the market, the nature of the

product, etc.

First Mover Advantage – The Stackelberg Model Oligopoly model in which one firm sets its output

before other firms do Assumptions One firm can set output first MC = 0 Market demand is P = 12 - Q where Q is total

output (as in the Cournot Case)

Stackelberg Model: Sequential Moves

Suppose that Loews gets to choose its capacity first.

MSM will observe Loews’ capacity and choose its capacity second.

Very Important: Loews predicts how MSM will react - it uses ‘look forward and reason back approach.’

MSM’s best response (from above) is:

2q6q L*

M −=

Stackelberg Game: Sequential Moves

Given MSM’s best response function, Loews understands that if it chooses a quantity qL, MSM will respond by choosing

So, Loews’ profits from choosing some qL would be

( ) LL

LLL

LLMLL q

2q6q q)

2q6(12q qq12Pr

−=

−−−=−−=

2q6q L

M −=

Sequential Moves To find Loews’ optimal choice as a leader, maximize

Take the derivative of PrLL

Setting it to zero gives us optimal choice of Loews as a leader qL

*= 6. MSM as a follower will then choose

LL

LL q6

qPr −=

dd

2qq6q

2q6Pr

2L

LLLL

L −=

−=

32

q6q*

L*M =−=

Sequential Moves

With qL*=6K and qM *=3K, price is P=12-qL*-qM

*=$3 Profits are:PrL= $18,000PrM= $9,000

Recall that under simultaneous moves, each firm chooses quantity 4K and earns 16K in profits.

So, the first mover benefits. But the second-mover loses. Question: Why does L raise its quantity?

When does the first mover have an advantage?

Strategic behavior produces different outcomes depending on the order of moves.

It is often an advantage to move first, but whether there is such an advantage depend on the nature of the environment.

What are the features of markets and products where the first mover has an advantage and where it does not?

What about R&D: is it better or worse to move first?

First-Mover Advantage

First-mover advantage is not acquired by luck.

It comes from costly commitments made earlier: product positioning decisions taken in the past, R&D, early investments, smart contracting strategy.

Pursuing the first-mover advantage is risky:If demand is low, an early investment may be lost

First-mover advantage and the airline industry

Air Canada and WestJet are the two main carriers on the Vancouver-Toronto route. They both also serve many other routes in Canada and US.

Capacity decisions in the airline industry take the form of buying or leasing airplanes.

Is AC or WJ likely to be able to secure the kind of first-mover advantage on the Vancouver-Toronto route that Loews was seen to achieve in. Why or why not?

Oligopoly, Cournot and Stackelberg...

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