ANTITRUST ECONOMICS 2013
David S. Evans
University of Chicago, Global Economics Group
TOPIC 8:
Date
Elisa Mariscal
CIDE, ITAM, CPI
OLIGOPOLY AND GAME THEORY
Topic 8 | Part 1
30 May 2013
Overview
2
Part 1
Part 2
Role of Oligopolies
in the Economy
Oligopoly Theory:
Cournot and
Bertrand
Game Theory and
Strategic Behavior
Dynamic Games
and Competition
3
Role of Oligopolies in the
Economy
The “rough” spectrum of competition
4
Industries are competitive when there is a large number of firms and
none of them is large enough to influence price (atomistic
competition) or the threat of entry prevents incumbents from
increasing prices beyond the competitive level (contestable markets).
• Industries appear to be “pretty competitive” with many fewer firms than
under atomistic competition; e.g. an industry with 10 firms, each with 10
percent market shares would ordinarily be pretty competitive.
Industries are monopolies when there is a single firm.
• Industry is effectively a monopoly if there is a single firm that is so large
that it can dictate price; its ability to do so requires barriers that prevent
the competitive fringe from expanding and new entrants from coming in.
Industries are oligopolies when there are a few large firms that
compete with each other.
• Industry is often said to be an oligopoly when there are a handful of
significant firms that have to take each other’s actions into account in
deciding on pricing and other business decisions (the lines aren’t firm
though).
Firms act largely independently of each other in
competition and monopoly but not in oligopoly
5
A monopoly firm faces no direct competitor and therefore sets its
price constraint only based on the level of demand.
A competitive firm cannot affect price because it is too small
relative to the market (or because it faces a credible threat of
entry). It takes the market price as given.
An oligopoly has to consider the actions and reactions of each of
its rivals; as a result an oligopoly’s price depends on its rivals’ prices.
A small number of firms dominate many industries
6
Game consoles (Xbox, Sony Playstation, Nintendo)
Large commercial aircraft manufacturing (Airbus and Boeing)
Mobile phone operators (Vodafone, T-Mobile, Orange, O2, ...)
Supermarkets (Tesco, Sainsbury, …)
Stock exchanges (NYSE/Euronext, LSE, Deutsche-Borse, …)
Concentration in selected US industries
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Industry
4 largest
companies
8 largest
companies
20 largest
companies
Motor Vehicle
82.4%
91.8%
98.8%
Aircraft Manufacturing
62.3%
78.1%
88.0%
Soft Drinks
47.5%
55.6%
77.9%
Breweries
89.7%
93.4%
95.2%
Tobacco
83.4%
93.3%
99%
Source: US Economic Census
Oligopoly industries are ripe for competition issues
8
Mergers—more likely lead to harm to consumers when industry will
become more concentrated and farther from competition and
closer to oligopoly
Cartels—may be easier to form cartels when there are fewer
players to coordinate.
Abuse—greater ability to engage in strategic behavior targeted to
rivals when a firm has more pricing ability.
It is important that competition policy have tools that can help
analyze issues in these industries.
Economic models of oligopoly account for
strategic interactions among firms
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Perfect competition—assumes interactions away because firms are
too small to matter
Single-firm profit maximization models—monopoly and
monopolistic competition—take demand as given including the
price of substitutes.
We need a theory which takes interdependencies into account
when there is a small number of firms.
Modeling interactions among firms and people is
tricky
10
Why don’t you bump into people traveling in the opposite direction
when you walk down the sidewalk?
You and a friend agree to meet in Paris but don’t have any way to
communicate because of global meltdown of the internet and
phones and haven’t agreed where. Will you meet and where?
EasyJet can make more profits through a fare decrease but only if
British Air doesn’t follow on competing routes. Should it decrease
fares?
Game theory provides a set of tools for thinking through these sorts
of questions and provides the basis for analyzing strategic
interactions among firms.
11
Game Theory and Strategic
Behavior
“Game theory” provides insights into many
problems involving interactions
12
Game theory recognizes the mutual interdependence between
players and that players take these into account in making decisions.
Field established by John von Neumann, a mathematician who is also
credited with inventing the modern computer. See Theory of Games
and Economic Behavior with Oskar Morgenstern (1944).
Game theory is like statistics: it is a field that is applied in many diverse
areas ranging from biology to sociology to political science to law (in
the Cold War it was the theoretical foundation of the theory of
“mutually assured destruction” (MAD)). It is a mathematical field with
heavy influence from economics and psychology.
Major development was the paper by John Nash “Non-Cooperative
Games” that established what is now called the “Nash equilibrium”
(Nash won the Nobel Prize in Economics shortly after having come out
of a 25 year period of being delusional. See A Beautiful Mind by Sylvia
Nasar or the movie with Russell Crowe.)
Basics of game theory
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A “game” refers to any situation in which decisions are made in
anticipation of decisions made by others.
A game is a stylized model that depicts situations of strategic
behavior, where the payoff (the reward at the end of the game) for
one agent depends on its own actions as well as on the actions of
other agents.
Each “player” forms a “strategy” and hopes to receive a “payoff”.
In a “cooperative” game each player can make side-payments to
the other players. A cartel is the result of a cooperative game.
In a “non-cooperative” game players cannot make side-payments.
Competition laws generally require that market rivalry be “noncooperative”.
Components of games
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Games are defined by:
• A set of players:
• Players 1 and 2
• A set of rules, such as who can do what and when:
• Play available strategies simultaneously
• Player 1 moves first
• A set of strategies:
• Choose LEFT, RIGHT, UP, DOWN
• Move rook
• A set of payoffs:
• If Player 1 plays UP and 2 plays RIGHT player 1 gets 3 and
player 2 gets 6
• If I checkmate your King I earn the prize
Games are analyzed by examining optimal payoffs for players
given the rules of game and the strategies available.
The “payoff matrix” describes the game
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The payoffs of a one-period game are often expressed as a payoff
matrix (Player 1, Player 2).
The game is one period because players make simultaneous
decisions. It is non-cooperative and we are excluding side
payments between players.
Player 2
(player 1 payoff, player 2 payoff)
LEFT
RIGHT
UP
(5,5)
(3,6)
DOWN
(6,3)
(4,4)
Player 1
Player 1 gets 6 and Player 2 gets 3 if Player
1 moves Down and Player 2 moves Left
Optimal strategies with simple one-period noncooperative game
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If P1 played UP  P2 would choose RIGHT, and P2 would receive a payoff of 6.
If P1 played DOWN  P2 would choose RIGHT, and P2 would receive a payoff of
4.
Therefore, P2 will choose to play RIGHT regardless of what P1’s action is in this
case.
Same logic shows, P1 will choose to play DOWN regardless of what P2’s action is.
Player 2
(player 1 payoff, player 2 payoff)
Player 1
LEFT
RIGHT
UP
(5,5)
(3,6)
DOWN
(6,3)
(4,4)
The “dominant strategy” is a key concept
17
A strategy is said to be “dominant” whenever this strategy is strictly
better than any other possible strategy, regardless of what the
other players’ actions are:
• For P1, playing DOWN is a dominant strategy.
• For P2, playing RIGHT is a dominant strategy.
Player 2
Player 1
LEFT
RIGHT
UP
(5,5)
(3,6)
DOWN
(6,3)
(4,4)
The dominant strategies point to game equilibrium
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Dominant strategies yield an easy solution to the game
Therefore [DOWN, RIGHT] is the equilibrium set of strategies and (4,4)
the equilibrium set of payoffs given that the game is noncooperative.
Player 2
(player 1 payoff, player 2 payoff)
Player 1
LEFT
RIGHT
UP
(5,5)
(3,6)
DOWN
(6,3)
(4,4)
The cost of not cooperating
19
The payoff box considered above demonstrates that “noncooperative games” results in an equilibrium that is worse for both
players than another outcome in total: 8<9<10!
Non-cooperative equilibrium (DOWN,RIGHT) is worse for both
players individually than cooperative equilibrium (UP,LEFT) : (5,5) vs.
(4,4)
Player 2
Player 1
UP
DOWN
LEFT
RIGHT
(10=5,5)
(9=3,6)
(9=6,3)
(8=4,4)
The prisoner’s dilemma game
20
You and your partner in crime have been busted; police have evidence on
minor crime but need confession to convict for major crime.
You are each better off if neither confesses: cooperation (with each other) is the
best strategy.
But if your partner confesses and you don’t get 40 years; and if you turn in your
partner and he doesn’t confess you avoid a long sentence.
It doesn’t take much mistrust for the best strategy to be to confess.
Then, you both get 20 years even though you are both worse off as a result.
Player 2
(player 1 payoff, player 2 payoff)
Do not
Confess
Confess
Do not
Confess
(1,1)
(40,0)
Confess
(0,40)
(20,20)
Player 1
Prisoner 2 goes
free and prisoner 1
gets 40 years.
The Nash equilibrium
21
The previous examples have used
the important concept of the
“Nash equilibrium”
• The “Nash equilibrium” of a
game is the set of actions such
that, for each player, the chosen
action is the best response to the
action of all other players.
• OR
• The “Nash equilibrium” of a
game is when no player could
change her action, given the
chosen actions of all other
players, and make herself better
off.
John Forbes Nash (1928)
Games don’t always have just one equilibrium
22
Another example: The battle of the sexes
You have different preferences over entertainment but want to get
together more than anything;
If you don’t coordinate (of course you will!) one of you might be
alone at the ballet and your partner at the football match.
He
(Her Payoff, His Payoff)
She
Ballet
Football
Ballet
(3,2)
(1,1)
Football
(0,0)
(2,3)
What to do when there are many equilibria?
23
Focal points (let’s meet in Paris—with no more information where
would you meet?)
“Pareto dominance”—you eliminate equilibria where one party is
worse off and the other party isn’t better off (you’d rather go to the
football match and I’m ok so long as I’m with you)
“Mixed strategies”—this is due to Nash. The idea is that you aren’t
certain what the other party will do. Therefore, you randomly
choose among your best strategies and so does the other player.
End Part 1, Next Class Part 2
24
Part 1
Part 2
Role of Oligopolies
in the Economy
Oligopoly Theory:
Cournot and
Bertrand
Game Theory and
Strategic Behavior
Dynamic Games
and Competition