Download Nash equilibrium

Oligopoly and Game Theory
ETP Economics
Jack Wu
Key Feature
 Because of the few sellers, the key feature
of oligopoly is the tension between
cooperation and self-interest.
Characteristics
 Characteristics of an Oligopoly Market
Few sellers offering similar or identical products
Interdependent firms
Best off cooperating and acting like a
monopolist by producing a small quantity of
output and charging a price above marginal cost
Simple Type: Duopoly
 A duopoly is an oligopoly with only two
members. It is the simplest type of oligopoly.
 Duopoly
Oligopoly with only two members
Decide quantity to sell
Price – determined on the market
 By demand
 Duopoly
Collude and form a cartel
 Act as a monopoly
Total level of production
Quantity produced by each member
Don’t collude – self-interest
 Difficult to agree; Antitrust laws
 Higher quantity; lower price; lower profit
Not competitive allocation
 Nash equilibrium
5
Collusion and Cartel
 The duopolists may agree on a monopoly
outcome.
Collusion
 An agreement among firms in a market about
quantities to produce or prices to charge.
Cartel
 A group of firms acting in unison.
Is Cartel Possible?
 Although oligopolists would like to form
cartels and earn monopoly profits, often that
is not possible. Antitrust laws prohibit
explicit agreements among oligopolists as a
matter of public policy.
The Equilibrium for an Oligopoly
 A Nash equilibrium is a situation in which
economic actors interacting with one
another each choose their best strategy
given the strategies that all the others have
chosen.
The equilibrium for an Oligopoly
 When firms in an oligopoly individually choose
production to maximize profit, they produce
quantity of output greater than the level produced
by monopoly and less than the level produced by
competition.
 The oligopoly price is less than the monopoly price
but greater than the competitive price (which
equals marginal cost).
Size of an Oligopoly
 How increasing the number of sellers affects
the price and quantity:
The output effect: Because price is above
marginal cost, selling more at the going price
raises profits.
The price effect: Raising production will
increase the amount sold, which will lower the
price and the profit per unit on all units sold.
Size of an Oligopoly
 As the number of sellers in an oligopoly
grows larger, an oligopolistic market looks
more and more like a competitive market.
 The price approaches marginal cost, and
the quantity produced approaches the
socially efficient level.
Strategic Action
 Because the number of firms in an
oligopolistic market is small, each firm must
act strategically.
 Each firm knows that its profit depends not
only on how much it produces but also on
how much the other firms produce.
Game Theory
 Game theory is the study of how people
behave in strategic situations.
 Strategic decisions are those in which each
person, in deciding what actions to take,
must consider how others might respond to
that action.
Prisoners’ Dilemma
 The prisoners’ dilemma provides insight into the
difficulty in maintaining cooperation.
 Often people (firms) fail to cooperate with one
another even when cooperation would make
them better off.
 The prisoners’ dilemma is a particular “game”
between two captured prisoners that illustrates
why cooperation is difficult to maintain even when
it is mutually beneficial.
Bonnie’ s Decision
Confess
Bonnie gets 8 years
Remain Silent
Bonnie gets 20 years
Confess
Clyde gets 8 years
Clyde’s
Decision
Bonnie goes free
Clyde goes free
Bonnie gets 1 year
Remain
Silent
Clyde gets 20 years
Clyde gets 1 year
Copyright©2003 Southwestern/Thomson Learning
Dominant Strategy
 The dominant strategy is the best strategy for a
player to follow regardless of the strategies
chosen by the other players.
 Dominant strategies in Prisoners’ dilemma:
_ Clyde: Confess
_ Bonnie: Confess
Nash Equilibrium & Best
Outcome
 Nash Equilibrium (self-interest):
_ Clyde: Confess & Bonnie: Confess
 Best Outcome (cooperation):
_ Clyde: Silent & Bonnie: Silent
 Cooperation is difficult to maintain, because
cooperation is not in the best interest of the
individual player.
Game Example: OPEC
 Iraq and Iran: Members of OPEC
 Their decisions on oil production.
 Decisions: High Production or Low
Production
Iraq’s Decision
High Production
Iraq gets $40 billion
Low Production
Iraq gets $30 billion
High
Production
Iran’s
Decision
Iran gets $40 billion
Iraq gets $60 billion
Iran gets $60 billion
Iraq gets $50 billion
Low
Production
Iran gets $30 billion
Iran gets $50 billion
Copyright©2003 Southwestern/Thomson Learning
Nash Equilibrium
 Dominant strategies:
_ Iran: High Production
_ Iraq: High Production
 Nash Equilibrium (self-interest):
_ Iran: High Production & Iraq: High Production
 Best Outcome (cooperation):
_ Iran: low production & Iraq: low production
Game Example: Where to
Advertise?
 Players: Competitor.com or We.com
 Decisions: NBA and NHL
Where to advertise?
Competitor.com
NBA
We.com
NHL
NBA
W: 4,
C: 3
W: 3,
C: 4
NHL
W: 3,
C: 4
W: 4,
C: 3
No Nash equilibrium in pure strategies
No Nash Equilibrium
 Dominant strategies:
_ We.com: none
_ Competitor.com: none
Nash Equilibrium (self-interest):
_ We.com: none
_ Competitor.com: none
Game Example: Evening News
 Players: ATV and TVB
 Decisions: 7:30 pm or 8:00 pm
Evening News:
TVB
7:30pm
7:30pm A: 1,
ATV 8:0pm
B: 1
A: 4,
B: 3
8:0pm
A: 3,
B: 4
A: 2.5,
B: 2.5
Nash Equilibrium
 Dominant strategies:
_ ATV: none
_ TVB: none
Two Nash Equilibria (self-interest):
_ ATV: 7:30pm & TVB: 8:00pm
or
_ ATV: 8:00pm & TVB: 7:30pm
Why People Sometimes
Cooperate
 Firms that care about future profits will
cooperate in repeated games rather than
cheating in a single game to achieve a onetime gain.
 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
28