This document provides an overview of key concepts in game theory and oligopoly models. It discusses oligopoly market structures where a few firms account for most production. It also covers the Cournot and Bertrand models of oligopoly competition. The document explores game theory concepts such as the prisoner's dilemma, Nash equilibrium, dominant strategies, and repeated games. It examines how these concepts apply to oligopolistic pricing behaviors and the implications of threats, commitments and credibility in strategic interactions between firms.

1. Microeconomics
Session 13-16
GAME THEORY and OLIGOPOLY

2. OLIGOPOLY
In oligopolistic markets, the products may or may not be
differentiated.
What matters is that only a few firms account for most or all of total
production.
In some oligopolistic markets, some or all firms earn substantial
profits over the long run because barriers to entry make it difficult or
impossible for new firms to enter – patents, access to technology,
reputation (natural barriers); excess production capacity with a threat
to flood the market (strategic barriers)
• Complex environment – price, quantity, investment decisions affects
rivals and elicit reaction from rivals

3. OLIGOPOLY
• Equilibrium in an Oligopolistic Market
When a market is in equilibrium, firms are doing the best they can
and have no reason to change their price or output.
Oligopoly is a prevalent form of market structure. Examples of
oligopolistic industries include automobiles, steel, aluminum,
petrochemicals, electrical equipment, and computers.
Duopoly - Market in which two firms compete with each other.

4. The Jargon of Game Theory
 Player: decision makers
 Strategy: one of the alternatives open to a
decision maker
 Strategy set: the set of all possible strategies for
a particular decision maker
 Strategy profile: a list of strategies, one for each
player
 Payoffs: the value accruing to each player for a
particular strategy profile

5. DOMINANT STRATEGIES
● dominant strategy - a strategy which is the best choice for a player
regardless of what the other players do.
Suppose Firms A and B sell competing products and are deciding
whether to undertake advertising campaigns. Each firm will be
affected by its competitor’s decision.

6. The Jargon (contd.)
 Dominant strategy: a strategy which is the
best choice for a player regardless of
what the other players do.
 Equilibrium in dominant strategies: a
strategy profile in which each player is
playing a dominant strategy.

7. Unfortunately, not every game has a dominant strategy for each
player. To see this, let’s change our advertising example slightly.

8. Best Response and Nash Equilibrium

9. Battle of Sexes
Cricket
Romantic
Movie
Cricket Romantic Movie
1,2
0,0
0,0
2,1
HUSBAND
WIFE

10. Matching Pennies
HEAD
TAIL
HEAD TAIL
1,-1
-1,1
-1,1
1,-1
JOHN
JACK

11. Matching Pennies
HEAD
TAIL
HEAD TAIL
1,-1
-1,1
-1,1
1,-1
JOHN
JACK

12. Nash Equilibrium
 Nash Equilibrium: A strategy profile where
every player’s strategy is his best response to
the strategies of the other players.
 There may be many Nash Equilibria
 There may be none
 Both Nash and dominant strategies are stable
or self-enforcing. Since many games do not
have a dominant strategy equilibrium, Nash
equilibrium is useful as a more general
equilibrium concept.

13. Story
• KGB picks two “enemies of the state” at
midnight.
• KGB tells them
– If you both confess, both will be sent to Gulag
for 20 years
– If you both do not confess, there will be prison
for 2 years.
– If one of you confess and the other not, the
confessing partner will be state witness
(imprisonment of 1 year). But, the non-
confessing partner will be sent to Gulag
(Siberia) for 30 years.

14. Prisoner's Dilemma
Confess
Don't
confess
Confess Don't
confess
-20,-20
-30,-1
-1,-30
-2,-2
PRISONER B
PRISONERA

15. • Both of them confess of the crime!

16. OLIGOPOLY
● Cournot model
 Oligopoly model in which firms
produce a homogeneous good,
 each firm treats the output of its
competitors as fixed,
 and all firms decide simultaneously
how much to produce.

17. The Cournot Model
● reaction curve Relationship between a firm’s profit-maximizing
output and the amount it thinks its competitor will produce.
● Cournot equilibrium Equilibrium in the Cournot model in which each firm correctly
assumes how much its competitor will produce and sets its own production level
accordingly.
Firm 1’s reaction curve
shows how much it will
produce as a function of how
much it thinks Firm 2 will
produce.
Firm 2’s reaction curve
shows its output as a
function of how much it
thinks Firm 1 will produce.

18. Example
• Demand Curve: P = 30 – Q1 – Q2
• Q1 and Q2 are quantities supplied by firms
1 and 2.
• Marginal Cost is Zero; Fixed Cost Zero.
• Clearly, if one of the firms supply more,
the other firms demand is lower.
• The profit of one firm depends on the other
firm.
Page 421, Chapter 12 of the Text Book

19. Profits of Firm 2

20. Reaction
Curve
Relationship
between a firm’s
profit-maximizing
output and the
amount it thinks its
competitor will
produce.

21. OLIGOPOLY
• The Linear Demand Curve—An Example
The demand curve is P =
30 − Q, and both firms
have zero marginal cost.
In Cournot equilibrium,
each firm produces 10.
The collusion curve shows
combinations of Q1 and Q2
that maximize total profits.
If the firms collude and
share profits equally, each
will produce 7.5.
Also shown is the
competitive equilibrium, in
which price equals
marginal cost and profit is
zero.
Duopoly Example
Figure 12.5

22. Homeworks
• Page 401, Chapter 11, Exercise 6
• Page 401, Chapter 11, Exercise 7
• Page 402, Chapter 11, Exercise 10

23. PRICE COMPETITION
● Bertrand model
Firms produce a homogeneous good,
Each firm treats the price of its competitors as
fixed,
All firms decide simultaneously what price to
charge.
The firms set price at marginal cost and make
no profit.

24. IMPLICATIONS OF THE PRISONERS’ DILEMMA
FOR OLIGOPOLISTIC PRICING
● price rigidity Characteristic of oligopolistic
markets by which firms are reluctant to change
prices even if costs or demands change.
● kinked demand curve model Oligopoly model in
which each firm faces a demand curve kinked at the
currently prevailing price: at higher prices demand is
very elastic, whereas at lower prices it is inelastic.

25. IMPLICATIONS OF THE PRISONERS’ DILEMMA
FOR OLIGOPOLISTIC PRICING
• Price Rigidity
Each firm believes that if it raises
its price above the current price
P*, none of its competitors will
follow suit, so it will lose most of its
sales.
Each firm also believes that if it
lowers price, everyone will follow
suit, and its sales will increase
only to the extent that market
demand increases.
As a result, the firm’s demand
curve D is kinked at price P*, and
its marginal revenue curve MR is
discontinuous at that point.
If marginal cost increases from MC
to MC’, the firm will still produce
the same output level Q* and
charge the same price P*.
The Kinked Demand Curve
Figure 12.7

26. IMPLICATIONS OF THE PRISONERS’ DILEMMA
FOR OLIGOPOLISTIC PRICING
• Price Signaling and Price Leadership
● price signaling Form of 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.

27. REPEATED GAMES
How does repetition change the likely outcome of the game?
● repeated game Game in which actions are
taken and payoffs received over and over again.
Confess
Don't
confess
Confess Don't
confess
-20,-20
-30,-1
-1,-30
-2,-2
PRISONER B

28. REPEATED GAMES
Suppose the game is infinitely repeated. In other words, my
competitor and I repeatedly set prices month after month, forever.
With infinite repetition of the game, the expected gains from
cooperation will outweigh those from undercutting.
● tit-for-tat strategy Repeated-game strategy in
which a player responds in kind to an opponent’s
previous play, cooperating with cooperative
opponents and retaliating against uncooperative
ones.
Tit-for-Tat Strategy
Infinitely Repeated Game

29. REPEATED GAMES
Finite Number of Repetitions
Now suppose the game is repeated a finite number of times—say, N
months. If my competitor (Firm 2) is rational and believes that I am
rational, he will reason as follows:
“Because Firm 1 is playing tit-for-tat, I (Firm 2) cannot undercut—that
is, until the last month. I should undercut the last month because then
I can make a large profit that month, and afterward the game is over,
so Firm 1 cannot retaliate. Therefore, I will charge a high price until
the last month, and then I will charge a low price.”
However, since I (Firm 1) have also figured this out, I also plan to
charge a low price in the last month. Firm 2 figures that it should
undercut and charge a low price in the next-to-last month.
And because the same reasoning applies to each preceding month,
the game unravels: The only rational outcome is for both of us to
charge a low price every month.

30. REPEATED GAMES
Tit-for-Tat in Practice
Since most of us do not expect to live forever, the unraveling
argument would seem to make the tit-for-tat strategy of little value,
leaving us stuck in the prisoners’ dilemma. In practice, however, tit-for-
tat can sometimes work and cooperation can prevail.
There are two primary reasons.
Most managers don’t know how long they will be competing with
their rivals, and this also serves to make cooperative behavior a
good strategy.
My competitor might have some doubt about the extent of my
rationality.
In a repeated game, the prisoners’ dilemma can have a cooperative
outcome.

31. SEQUENTIAL GAMES
As a simple example, let’s return to the product choice
problem. This time, let’s change the payoff matrix slightly.
● sequential game Game in which
players move in turn, responding to
each other’s actions and reactions.

32. SEQUENTIAL GAMES
● extensive form of a game Representation of possible moves
in a game in the form of a decision tree.
• The Extensive Form of a Game

33. OLIGOPOLY
• The Linear Demand Curve—An Example
Duopolists face the following market demand curve
P = 30 – Q
Also, MC1 = MC2 = 0
Total revenue for firm 1: R1 = PQ1 = (30 –Q)Q1 = 30Q1 – Q2
1 – Q1Q2
then MR1 = ∆R1/∆Q1 = 30 – 2Q1 –Q2
Setting MR1 = 0 (the firm’s marginal cost) and solving for Q1, we find
Firm 1’s reaction curve:
By the same calculation, Firm 2’s reaction curve:
Cournot equilibrium:
Total quantity produced:
1 2
115-
2
Q Q
2 1
115-
2
Q Q
1 2
10Q Q 
1 2
20Q Q Q  
(12.1)
(12.2)

34. OLIGOPOLY
• The Linear Demand Curve—An Example
If the two firms collude, then the total profit-maximizing quantity can
be obtained as follows:
Total revenue for the two firms: R = PQ = (30 –Q)Q = 30Q – Q2,
then MR = ∆R/∆Q = 30 – 2Q
Setting MR = 0 (the firms’ marginal cost) we find that total profit is
maximized at Q = 15.
Then, Q1 + Q2 = 15 is the collusion curve.
If the firms agree to share profits equally, each will produce half of
the total output:
Q1 = Q2 = 7.5

35. OLIGOPOLY
• First Mover Advantage—The Stackelberg Model
● Stackelberg model Oligopoly model in which one firm sets its
output before other firms do.
Suppose Firm 1 sets its output first and then Firm 2, after observing
Firm 1’s output, makes its output decision. In setting output, Firm 1
must therefore consider how Firm 2 will react.
P = 30 – Q
Also, MC1 = MC2 = 0
Firm 2’s reaction curve:
Firm 1’s revenue:
And MR1 = ∆R1/∆Q1 = 15 – Q1
Setting MR1 = 0 gives Q1 = 15, and Q2 = 7.5
We conclude that Firm 1 produces twice as much as Firm 2 and
makes twice as much profit. Going first gives Firm 1 an advantage.
2
1 1 1 1 2 1
30R PQ Q Q Q Q   
2 1
115
2
Q Q  (12.2)
(12.3)
(12.4)

36. SEQUENTIAL GAMES
• The Advantage of Moving First

37. Game Theory in Practise - I
• Bruce Bueno de Mesquita of New York
University predicted that Egypt’s
president, Hosni Mubarak, would fall
from power within a year in May 2010 .
– Nine months later Mr Mubarak fled Cairo
amid massive street protests.
http://www.economist.com/node/21527025

38. Game Theory in Practise - II
• In online auction of 2006 of radio-spectrum
licenses by America’s Federal
Communications Commission, Paul
Milgrom, a consultant and Stanford
University professor, customised his
game-theory software.
– Two of his clients, Time Warner and Comcast,
paid about a third less than their competitors
for equivalent spectrum, saving almost $1.2
billion.

39. THREATS, COMMITMENTS, AND CREDIBILITY
Suppose Firm 1 produces personal computers that can be used both
as word processors and to do other tasks. Firm 2 produces only
dedicated word processors.
• Empty Threats

40. THREATS, COMMITMENTS, AND CREDIBILITY
Race Car Motors, Inc., produces cars, and Far Out Engines, Ltd.,
produces specialty car engines.
Far Out Engines sells most of its engines to Race Car Motors, and a
few to a limited outside market.
Nonetheless, it depends heavily on Race Car Motors and makes its
production decisions in response to Race Car’s production plans.
• Commitment and Credibility

41. THREATS, COMMITMENTS, AND CREDIBILITY
Suppose Far Out threatens to produce big engines no matter what Race
Car does. If Race Car believed Far Out’s threat, it would produce big
cars: Otherwise, it would have trouble finding engines for its small cars.
Far Out can make its threat credible by visibly and irreversibly reducing
some of its own payoffs in the matrix, thereby constraining its own
choices.
Far Out must reduce its profits from small engines. It might do this by
shutting down or destroying some of its small engine production
capacity.
• Commitment and Credibility

42. THREATS, COMMITMENTS, AND CREDIBILITY
Developing the right kind of reputation can also give one a strategic
advantage.
Suppose that the managers of Far Out Engines develop a reputation
for being irrational—perhaps downright crazy.
They threaten to produce big engines no matter what Race Car
Motors does.
Now the threat might be credible without any further action; after all,
you can’t be sure that an irrational manager will always make a profit-
maximizing decision.
In gaming situations, the party that is known (or thought) to be a little
crazy can have a significant advantage.
• Commitment and Credibility
The Role of Reputation

43. THREATS, COMMITMENTS, AND CREDIBILITY
Our discussion of commitment and credibility also applies to
bargaining problems. The outcome of a bargaining situation can
depend on the ability of either side to take an action that alters its
relative bargaining position.
Consider two firms that are each planning to introduce one of two
products which are complementary goods.
• Bargaining Strategy

44. THREATS, COMMITMENTS, AND CREDIBILITY
Suppose that Firms 1 and 2 are also bargaining over a second issue—
whether to join a research consortium that a third firm is trying to form.
• Bargaining Strategy

45. ENTRY DETERRENCE
To deter entry, the incumbent firm must convince any
potential competitor that entry will be unprofitable.
But what if you can make an irrevocable commitment that will
alter your incentives once entry occurs—a commitment that
will give you little choice but to charge a low price if entry
occurs?

46. ENTRY DETERRENCE
• Strategic Trade Policy and International Competition
The development and production of a new line of aircraft are subject
to substantial economies of scale; it would not pay to develop a new
aircraft unless a firm expected to sell many of them.
Suppose it is only economical for one firm to produce the new aircraft.
The Commercial Aircraft Market

47. ENTRY DETERRENCE
• Strategic Trade Policy and International Competition
The Commercial Aircraft Market
European governments, of course, would prefer that Airbus produce the
new aircraft. Can they change the outcome of this game?
Suppose they commit to subsidizing Airbus and make this commitment
before Boeing has committed itself to produce. If the European
governments commit to a subsidy of 20 to Airbus if it produces the plane
regardless of what Boeing does, the payoff matrix would change.

48. ENTRY DETERRENCE
The disposable diaper industry in the United States has
been dominated by two firms: Procter & Gamble, with an
approximately 50-percent market share, and Kimberly-
Clark, with another 30–40 percent.
How do these firms compete? And
why haven’t other firms been able to
enter and take a significant share of
this $5-billion-per-year market?
The competition occurs mostly in the
form of cost-reducing innovation. As a
result, both firms are forced to spend
heavily on research and development
in a race to reduce cost.

49. Homeworks
• Page 434, Chapter 12, Exercise 3, parts b-
c
• Page 434, Chapter 12, Exercise 4
• Page 434, Chapter 12, Exercise 5