Chapter
17
Oligopoly
Game Theory Models
Oligopoly
• Oligopoly
– Only a few sellers (< MC < PC, > M)
– Offer similar or identical products
• No product differentiation
– Interdependent
• Because of small numbers
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Strategic Behavior
• Perfect Competition
– Only strategy is to reduce costs (and earn short-run econ profits)
• Price-taker => output decisions do not affect market price
– cross-price elasticity = -1 (perfect substitutes)
– Own-price = -∞
• Monopoly
– Price-Searcher: output decision determines price
• Cross-price = 0 (no substitutes)
• Own-price: < |1|
– Sets market/firm price by output decision (and consumers’ WTP)
– May try and prevent entry by new firms (patents, trademarks)
• Oligopoly
– Cross-price elasticity > 0
– Own-price elasticity < |1|
– Will have to take into account actions of other similar firms when making
output/pricing decisions
– Much more strategy
3
Markets with Only a Few Sellers
• A small group of sellers
– Tension between cooperation and self-interest
– Cooperation (Cournot strategy)
• Acting like a monopolist
– Produce a smaller quantity of output -> set quotas
– Maximizes profit for the industry
– Charge P >MC -> creates incentive for “cheating”
– Non-cooperative
– Self Interest - cares only about its own profit
– Powerful incentives ($$$$) not to cooperate/cheat
– More elaborate game theory (single and multiple
equilibria)
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Oligopoly Behavior
• Cooperative Oligopoly
– Cartels
• Agree to collude; act/price like a single firm monopolist - Cournot
– Price leadership (Stackleberg leader)
• Dominant firm establishes the price; other firms react to “leader”
• Non-cooperative Oligopolies
– Sticky prices (kinked demand curve)
• Sticky upward
– Single Nash equilibrium (similar outcome as Stackelberg
leader model)
• Characterized by stable prices
– Multiple Nash equilibria – more like Perfect Competition
• Completely rivalarous
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A Cartel – Collusion Among Suppliers
•
Three steps: (Cournot Strategy –cooperative)
– Determine Profit Max Output –same as monopolist (MR(mkt) = MC(both) @ Q=20)
– Determine price (at Q=20 -> P= $48)
– Allocate quotas and don’t cheat
• What is Q for each firm at MC(mkt) (=$20)?
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An Economic Application of Game
Theory: the Kinked-Demand Curve
• Above the kink, demand is relatively elastic because all other firm’s prices
remain unchanged. Below the kink, demand is relatively inelastic because
all other firms will introduce a similar price cut, eventually leading to a
price war. Therefore, the best option for the oligopolist is to produce at
point E which is the equilibrium point
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Nash Equilibrium
• If firm facing kinked demand curve tries to
raise price:
– Other firms do not
– As demand is highly elastic and other firms
are “close” substitutes
– Loses market share and revenues
• If firm lowers price
– Competitors match price decreases
• Could be a Stackleberg leader/dominant firm
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or “passive” collusion
Markets with Only a Few Sellers
• Game Theory
– What is it?
• "the study of mathematical models of conflict
and cooperation between intelligent rational
decision-makers“
• Examines alternative strategies and payoffs to the
“players” in order to determine their
incentives/motivation, model their
actions/reactions, and determine if there is a
“stable” (unchanging) outcome
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Markets with Only a Few Sellers
• Game Theory
– Is the outcome stable (unchanging)? If so
then there a single equilibria (one set of
choices best for all -> will be stable)?
• Types of Nash equilibrium
– (Single) Dominant Strategy (Stable)
– Multiple Equilibria – outcome fluctuates
–Stability will require collusion/agreement
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Markets with Only a Few Sellers
• Types of Nash equilibrium
– (Single) Dominant Strategy (Stable)
• Strategy that is best for a player in a game,
Regardless of the strategies chosen by the other
players
– Multiple Equilibria
• Best strategy for player A depends on B’s choice
• Unstable – may require collusion
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Game Theory
• Game theory is a methodology that can be
used to analyze both cooperative and noncooperative oligopolies.
– Recognizes the interdependence of the firms’
actions
• Using a payoff matrix to describe options
(strategies) and payoffs
– Firms are profit maximizers!
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Figure 12.7 Xbox and PlayStation 2
Payoff Matrix for Advertising
Only Strategic Choices: Advertise, or Not
Payoff matrix shows payoffs under 4 alternative combinations of strategies
13
Markets with Only a Few Sellers
• Types of Nash equilibrium
– (Single) Dominant Strategy (Stable)
• Strategy that is best for a player in a game, regardless of
the strategies chosen by the other player(s)
• Best strategy – each firm chooses to advertise
their products
• Payoff (profit) is best when one firm advertises,
regardless of what the competitor does (ad or
not)
• Each will choose to advertise
• Does not require an agreement/collusion
• Just Do It! (Regardless of what the other guy does!)
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Multiple Equilibria
• Sometimes there are come cases where there are
multiple Nash equilibria.
– In this case, the outcome is uncertain/unpredictable unless
they collude (agree to target only 1 of the markets and not
compete in the other’s)
• An example:
– Sony/Microsoft can create games for either one of two new
markets
• One set of games appeals only to YOUTH market (PG)
• Other set appeals only to TEEN market (R17)
• Incentive to reach agreement on both firms offering the same new
(one only) feature
– Compete? Or agree to split the markets?
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Payoff Table
Multiple Nash Equilibria
16
Multiple Equilibria
• An example:
– Sony/Microsoft can add one of two new features
• One feature appeals only to YOUTH market
• Other feature appeals only to TEEN market
• Two Strategies
– Produce in the same markets and compete against each
other for customers
– Each firm produces in the one market where their competitor
isn’t producing games
• Requires agreement on a) which market you will produce games for
and b) agree not to compete in the other market
• If both firms produce games for the same market ( Y or T)
then competition drives prices and profits down (it’s a PC
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world)
Multiple Equilibria
• Two Strategies
– Produce in the same market
– Produce in different
• Outcome
– If both firms produce games for the same market ( Y or
T) then competition drives prices and profits down (it’s a
PC world)
– If agree to produce in different markets and not
compete
• Monopoly power -> monopoly profits
• But have to “cede” the other market to your competitor
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Markets with Only a Few Sellers
• Game Theory
• What are we looking for?
– Is the outcome stable (unchanging)?
– Single or multiple equilibria?
– How does it model behavior?
– Economic actors interacting with one another
– Each choose their best strategy
• Given the strategies that all the other actors have
chosen -use a pay-off matrix to look at options
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Nash Equilibrium
Nash equilibrium
• a solution to a non-cooperative game involving two or more players
• each player is assumed to know the equilibrium strategies of the other
players
• no player has anything to gain by changing only his own strategy
unilaterally
Hence, a Nash equilibrium will be stable (once you get there!)
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Prisoner's Dilemma – Unstable Games
• A prisoner’s dilemma occurs when the
dominate strategy leads all players to an
undesired outcome.
• No single dominant strategy, multiple nash
equilibria, but requires “strong” cooperation
– how would you know what the other party is
going to do?
– How do you “enforce” their choice
– Unstable/unpredictable
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Figure 12.9 Prisoners’ Dilemma
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A Cartel – Collusion Among Suppliers
•
Two strategies
–
–
1) cooperate – charge Monopoly price and restrict output to cartel authorized quota
2) cheat – increase output above quota (price will drop to = MC)
•
And then what does the other firm do?
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Figure 2
Jack and Jill’s Oligopoly Game – Cartel as Game Theory
Jack’s decision
High production: 40 Gallons
Jill’s
Decision
High
production:
40 Gallons Jill gets
$1,600 profit
Low
production:
30 Gallons Jill gets
$1,500 profit
Low production: 30 Gallons
Jack gets
$1,600 profit
Jack gets
$1,500 profit
Jill gets
$2,000 profit
Jack gets
$2,000 profit
Jack gets
$1,800 profit
Jill gets
$1,800 profit
In this game between Jack and Jill, the profit that each earns from selling water
depends on both the quantity he or she chooses to sell and the quantity the other
chooses to sell.
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The Economics of Cooperation
• Other examples of prisoners’ dilemma
• Common resources
– Two companies – own a common pool of oil
– Strategies
• Each company drills one well
• Each company drills a second well
– Get more oil
– Dominant strategy
• Each company drills two wells
– Lower profit
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Figure 4
A Common-Resources Game
Exxon’s Decision
Drill Two Wells
Drill
Two
Wells
Texaco’s
Decision
Drill
One
Well
Exxon gets $4
million profit
Texaco gets $4
million profit
Drill One Well
Exxon gets $3
million profit
Texaco gets $6
million profit
Exxon gets $6
million profit
Texaco gets $3
million profit
Exxon gets $5
million profit
Texaco gets $5
million profit
In this game between firms pumping oil from a common pool, the profit that each
earns depends on both the number of wells it drills and the number of wells drilled
by the other firm.
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Markets with Only a Few Sellers
• Game Theory
– Other factors that affect the outcome (or add
details to the game)
– What does everybody know?
• Does each player know the payoff and strategy
for all?
• Who moves first? Or do both move at the same
time?
– Is this a repeated game?
• Do you play only once or do we do it again?
– Can we “learn” from past moves?
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The Economics of Cooperation
• The prisoners’ dilemma and the welfare of
society
• Dominant strategy
– Noncooperative equilibrium
• May be bad for society and the players
– Arms race game
– Common resource game
• May be good for society
– Quantity and price – closer to optimal level
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The Economics of Cooperation
• Why people sometimes cooperate
• Game of repeated prisoners’ dilemma
– Repeat the game
– Agree on penalties if one cheats
– Both have incentive to cooperate
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The prisoners’ dilemma tournament
• Repeated prisoners’ dilemma
– Encourage cooperation
• Penalty for not cooperating
– Better strategy
• Return to cooperative outcome after a period of
noncooperation
– Best strategy: tit-for-tat
• Player - start by cooperating
– Then do whatever the other player did last time
• Starts out friendly
• Penalizes unfriendly players
• Forgives them if warranted
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Public Policy Toward Oligopolies
• Restraint of trade and the antitrust laws
• Common law: antitrust laws
– The Sherman Antitrust Act, 1890
• Elevated agreements among oligopolists from an
unenforceable contract to a criminal conspiracy
– The Clayton Act, 1914
• Further strengthened the antitrust laws
– Used to prevent mergers
– Used to prevent oligopolists from colluding
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An illegal phone call
– Robert Crandall - president of American Airlines
– Howard Putnam - president of Braniff Airways
• CRANDALL: I think it’s dumb as hell . . . to sit here and
pound the @#$% out of each other and neither one of us
making a #$%& dime.
• PUTNAM: Do you have a suggestion for me?
• CRANDALL: Yes, I have a suggestion for you. Raise your
$%*& fares 20 percent. I’ll raise mine the next morning.
• PUTNAM: Robert, we . . .
• CRANDALL: You’ll make more money, and I will, too.
• PUTNAM: We can’t talk about pricing!
• CRANDALL: Oh @#$%, Howard. We can talk about any
&*#@ thing we want to talk about.
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The Economics of Cooperation
• Other examples of prisoners’ dilemma
• Arms races
– After World War II, United States and the
Soviet Union
• Engaged in a prolonged competition over military
power
– Strategies
• Build new weapons
• Disarm
– Dominant strategy: Arm
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3
An arms-race game
Decision of the United States (U.S.)
Arm
Disarm
U.S. at risk
U.S. at risk and weak
Arm
Decision
of the
Soviet
Union
(USSR)
USSR at risk
USSR safe and powerful
U.S. safe and powerful
U.S. safe
Disarm
USSR at risk and weak
USSR safe
In this game between two countries, the safety and power of each country depend
on both its decision whether to arm and the decision made by the other country
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Markets with Only a Few Sellers
• How the size of an oligopoly affects the
market outcome
• More sellers
– Transaction costs are higher with more
• Getting to together to set prices, quotas
• Enforcing agreement
– Form a cartel - Maximize profit
• Produce monopoly quantity
• Charge monopoly price
• Difficult to reach & enforce an agreement
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Markets with Only a Few Sellers
• How the size of an oligopoly affects the
market outcome
• More sellers
– Do not form a cartel – Each firm:
• The output effect
– P > MC
– Sell one more unit: Increase profit
• The price effect
– Increase production: increase total amount sold
– Decrease in price: Lower profit
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Markets with Only a Few Sellers
• How the size of an oligopoly affects the
market outcome
– As the number of sellers in an oligopoly grows
larger
• Oligopolistic market - looks more like a
competitive market
• Price - approaches marginal cost
• Quantity produced – approaches socially efficient
level
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Public Policy Toward Oligopolies
• Controversies over antitrust policies
• Resale price maintenance (fair trade)
– Require retailers to charge customers a given
price
– Might seem anticompetitive
• Prevents the retailers from competing on price
– Defenders:
• Not aimed at reducing competition
• Legitimate goal
– Some retailers offer service
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Public Policy Toward Oligopolies
• Controversies over antitrust policies
• Predatory pricing
– Charge prices that are too low
• Anticompetitive
– Price cuts may be intended to drive other firms out of
the market
– Skeptics
• Predatory pricing – not a profitable strategy
• Price war - to drive out a rival
– Prices - driven below cost
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Public Policy Toward Oligopolies
• Controversies over antitrust policies
• Tying
– Offer two goods together at a single price
• Expand market power
– Skeptics
• Cannot increase market power by binding two
goods together
– Form of price discrimination
• Tying may increase profit
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The Microsoft case
• U.S. government’s suit against the Microsoft
Corporation, 1998
– Central issue: tying
• Should Microsoft be allowed to integrate its Internet
browser into its Windows operating system
• The government’s claim:
– Microsoft was bundling - to expand market power
into the market of Internet browsers
– Would deter other software companies from
entering the market and offering new products
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The Microsoft case
• Microsoft responded
– New features into old products - natural part of
technological progress
• Cars - include CD players, air conditioners
• Cameras - built-in flashes
• Operating systems - added many features to Windows
– Previously stand-alone products
– Computers - more reliable and easier to use
– Integration of Internet technology,
• The next natural next step
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The Microsoft case
• Disagreement
– Extent of Microsoft’s market power
• The government
– More than 80% of new personal computers
• Use a Microsoft operating system
• Substantial monopoly power
• Microsoft
– Software market is always changing
– Competitors: Apple Mac & Linux operating systems
– Low price – limited market power
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The Microsoft case
• November 1999 ruling
• Microsoft - great monopoly power
• Illegally abused that power
• June 2000
• Microsoft – to be broken up into two companies
– Operating system & Applications software
• 2001, appeals court
– Overturned the breakup order
• September 2001
– Justice Department - wanted to settle the case
quickly
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The Microsoft case
• Settlement: November 2002
– Microsoft – some restrictions
– Government – browser would remain part of the
Windows operating system
• Private antitrust suits
• Suits brought by the European Union
– Alleging a variety of anticompetitive behaviors
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