Competition Versus Collusion:The Prisonersâ€™ Dilemma, Implications of the Prisoners

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Microeconomics ECO402

Lesson 41

Competition Versus Collusion:

The Prisoners' Dilemma

Why wouldn't each firm set the collusion price independently and earn the higher profits that

occur with explicit collusion?

Assume:

FC = $ 20 and VC = $ 0

Firm 1' s Demand : Q = 12 - 2 P1 + P2

Firm 2' s Demand : Q = 12 - 2 P2 + P1

š = $ 12

: P = $4

Nash Equilibriu

š = $ 16

P = $6

Collusion

Possible Pricing Outcomes:

š = $16

Firm 1 : P = $6

Firm 2 : P = $6

P = $6

P = $4

š 2 = P2Q2 - 20

= (4)[12 - (2)(4) + 6] - 20 = $20

š 1 = P1Q1 - 20

= (6)[12 - (2)(6) + 4] - 20 = $4

Payoff Matrix for Pricing Game

Firm 2

Charge $4

Charge $6

Charge $4

$20,

$12,

Firm 1

Charge $6

$4,

$16,

These two firms are playing a non co-operative game.

Each firm independently does the best it can taking its competitor into account.

Question

Why will both firms both choose $4 when $6 will yield higher profits?

An example in game theory, called the Prisoners' Dilemma, illustrates the problem

oligopolistic firms face.

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Microeconomics ECO402

Scenario

Two prisoners have been accused of collaborating in a crime.

They are in separate jail cells and cannot communicate.

Each has been asked to confess to the crime.

Payoff Matrix for Prisoners' Dilemma

Payoff Matrix for Pricing Game

Firm 2

Charge $4

Charge $6

Charge $4

$20,

$12,

Firm 1

Charge $6

$4,

$16,

Conclusions: Oligipolistic Markets

1) Collusion will lead to greater profits

2) Explicit and implicit collusion is possible

3) Once collusion exists, the profit motive to break and lower price is

significant

Implications of the Prisoners'

Dilemma for Oligipolistic Pricing

Observations of Oligopoly Behavior

1) In some oligopoly markets, pricing behavior in time can create a

predictable pricing environment and implied collusion may occur.

Observations of Oligopoly Behavior

2) In other oligopoly markets, the firms are very aggressive and collusion is not

possible.

· Firms are reluctant to change price because of the likely response of their

competitors.

· In this case prices tend to be relatively rigid.

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Microeconomics ECO402

· The Kinked Demand Curve

If the producer raises price the

$/Q

competitors will not and the

demand will be elastic.

If the producer lowers price the

competitors will follow and the

demand will be inelastic.

Quantity

So long as marginal cost is in the

$/Q

vertical region of the marginal

revenue curve, price and output

MC'

will remain constant.

Quantity

PRICE SIGNALING & PRICE LEADERSHIP

Price Signaling

· Implicit collusion in which a firm announces a price increase in the hope that other

firms will follow suit

Price Leadership

· Pattern of pricing in which one firm regularly announces price changes that other

firms then match

The Dominant Firm Model

In some oligopolistic markets, one large firm has a major share of total sales, and a

group of smaller firms supplies the remainder of the market.

The large firm might then act as the dominant firm, setting a price that maximized its

own profits.

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Microeconomics ECO402

Price Setting by a Dominant Firm

The dominant firm's demand

Price

curve is the difference between

market demand (D) and the

supply of the fringe firms (SF).

At this price, fringe

firms sell QF, so that

total sales are QT.

Quantity

QF QD

CARTELS

Characteristics

1) Explicit agreements to set output and price

2) May not include all firms

3) Most often international

Examples of successful cartels

· OPEC

· International Bauxite Association

Examples of unsuccessful cartels

· Copper

· Tin

· Coffee

· Tea

· Cocoa

4) Conditions for success

· Competitive alternative sufficiently deters cheating

· Potential of monopoly power--inelastic demand

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Microeconomics ECO402

The OPEC Oil Cartel

Price

TD is the total world demand

curve for oil, and SC is the

Competitive supply. OPEC's

demand is the difference

between the two.

OPEC's profits maximizing

quantity is found at the

intersection of its MR and

MC curves. At this quantity

OPEC charges price P*.

DOPEC

MCOPEC

MROPEC

QOPEC

Quantity

Cartels

About OPEC

Very low MC

TD is inelastic

Non-OPEC supply is inelastic

DOPEC is relatively inelastic

The OPEC Oil Cartel

Price

The price without the cartel:

·Competitive price (P ) where

DOPEC = MCOPEC

DOPEC

MCOPEC

MROPEC

QOPEC

Quantity

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Microeconomics ECO402

The CIPEC Copper Cartel

·TD and S are relatively elastic

Price

·D is elastic

CIPEC

·CIPEC has little monopoly power

MCCIPEC

DCIPEC

MRCIPEC

Quantity

QCIPEC

Cartels

Observations

To be successful:

· Total demand must not be very price elastic

· Either the cartel must control nearly all of the world's supply or the supply of

noncartel producers must not be price elastic.

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