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 2
6 June 2013
Overview:
2
Part 1
Part 2
Role of Oligopolies
in Economy
Oligopoly Theory:
Cournot and
Bertrand
Game Theory and
Strategic Behavior
Dynamic Games
and Competition
3
Oligopoly and Interdependent
Behavior
Oligopoly and interdependent behavior
4
Oligopoly refers to industries with a handful of firms:
• Practically, we use this term for cases where there are a
handful firms that account for most of the output.
• Oligopoly (like monopoly) requires the existence of barriers
that prevent entry or expansion of fringe firms such as
economies of scale or network effects.
Oligopoly firms can’t act independently of each other.
Any change in price or output by one firm will materially affect the
price, sales, and profits of other firms.
Each firm recognizes that the ultimate effect of its decision to
change its price or output depends on how other firms react (in
particular, do they follow or not?)
The Role of strategic behavior: key features
5
A key feature of oligopolies is strategic interdependence between
competitors:
• Best action of each particular firm depends upon the action of the
other competitors (just like prisoner’s dilemma game).
A firm must consider its rivals’ behavior to determine its own best policy or
strategy. Consider for instance:
• BMW, Jaguar, Mercedes. They must consider pricing, styling
• Sony PlayStation vs. xBox. They must consider pricing, features, release
dates.
How does this equilibrium change with the number of firms and the type of
actions firms may take?
Generally, oligopoly models predict that prices decrease with the number of
firms, but the magnitude of the price decrease varies greatly depending on
the assumptions.
Oligopoly models and their different assumptions
6
Models assume that firms focus their conjectures on:
• Price—that is, the announce price and sell what people will
buy at that price. OR
• Quantity—that is, the offer a quantity and take whatever price
they can get in the market to absorb that quantity.
Models assume something about timing:
• Static—firms move simultaneously and the game is over in the
blink of an eye; like deciding which way to move when two
people are walking into each other on the sidewalk. OR
• Dynamic–firms move sequentially like in chess; models must
assume who goes first.
Basic Cournot model for two-firms: assumptions
7
A possible price that firm A
might consider
Two firms in a market for a homogeneous
product (spring water)
Price
The market demand
schedule
Firms make output decisions simultaneously
instead of choosing prices.
PA
Each firm independently attempts to
maximize profits by choosing its output
based on its conjecture about the other
firm’s choice
Linear market demand and constant
marginal cost as shown.
Marginal revenue
D(P)
MC
D(PA )
Q
The quantity firm A would sell if firm B supplied
nothing.
Firm A’s decision based on its conjecture about
how much firm B will offer
8
Price
If Firm A believes Firm B will produce
q1B ,what is Firm A’s optimal quantity?
If Firm B produces q1B , Firm A will be
facing a “residual demand”
dA(qB)=D(p)- q1B
Market demand
D(P)
MC
Residual demand for
Firm A if Firm B sells q1B
q1B
Q
Firm A’s profit-maximizing output given firm B’s
output decision
9
Firm A will set marginal revenue
equal to marginal cost, given
residual demand
Price
Residual demand for
Firm A when Firm B
produces q1B
D(P)
If Firm B produces q1B then Firm
A’s profit maximizing output is
q1A
MC
q1A
MR for Firm
A given its
residual
demand
q1B
Q
Firm A’s decision on how much to supply varies
with its conjecture about firm B’s supply
10
Note that when qB=0, the
residual demand for Firm A
equals the market demand
D(P)
Price
Residual demand for
Firm A when Firm B
produces q1B
Hence, the optimal quantity
chosen by Firm A is that of a
monopolist: qMA
MC
q1A
MR for Firm A
given its residual
demand
q1B
Q
The “best response curve” summarizes A’s best
moves for each of B’s choices
11
For each value of qB, Firm A has a Best Response based on its
maximizing profits rule.
We can write down a schedule of these “best responses” for Firm
A for every possible output by Firm B. This is called Firm A’s
“Reaction Function” or “Best Response Function”.
The reaction function is key for analyzing the equilibrium decisions
of oligopoly firms.
The reaction function is linear when demand Is
linear
12
For a linear demand function and constant marginal cost, the
reaction function will also be linear.
qA
Firm A produces the monopoly level when
firm B produces nothing
Firm A’s Reaction Function
qM A
q1A
Firm A supplies nothing to the market if Firm B
supplies the entire market (by pricing at
marginal cost—i.e., the competitive level)
since it can’t make any profit.
q2A
q1B
q2B
qC
qB
Firm B also has a reaction function based on a
similar analysis
13
Firm B has a similar reaction
function that shows its best
response, given what Firm A
chooses.
Under the assumption that both
firms have the same marginal
cost Firm B’s reaction function
will be identical to Firm A’s.
qA
qC
Firm B’s
Reaction
Function
qM
Firm A’s
Reaction
Function
qM
Note Firm A and Firm B’s reaction functions are being drawn from different
orientations (i.e. B on the horizontal axis is looking at what A on the vertical axis is
doing; while A on the vertical axis is looking at what B on the horizontal axis is
doing.
qC
qB
The Cournot equilibrium occurs where the reaction
functions cross
14
The “equilibrium” is at the intersection
of the two reaction functions and
where:
•Each firm has chosen the profitmaximizing quantity given their
conjecture about what the other
firm is doing (so the equilibrium is
on the reaction functions);
•Each conjecture is right in that
each firm correctly anticipates
what the other does.
Proof: At any other point on the
reaction functions at least one firm is
wrongly anticipating what the other
will do.
qA
qCA
Verify for the Cournot output it is less
than the competitive level but
greater than the monopoly level.
Firm B’s Reaction
Function
Equilibrium
qM A
Firm A’s
Reaction
Function
qCOURNOTA
qCOURNOTB
qM B
Total output = 2 x qCOURNOTA,B = qCOURNOTA +qCOURNOT B
qCB
With Cournot oligopoly, total price is more than
with competition but less than with monopoly
15
In Cournot equilibrium, market
price is lower than what a
monopolist would charge but
higher than the competitive one.
P
D(P)
PM
Deadweight loss is also lower than
that in the monopoly case in the
same market, but still positive.
PCOURNOT
MONOPOLY
COURNOT
COMPETITION
MC
qMA,B Q COURNOT
qC
Q
Introduction to the Bertrand model
16
Forty-five years after the publication of Cournot’s book, Joseph
Bertrand (1874-1900) observed that Cournot’s results depended
on the assumption that firms compete over quantities. [ See
Bertrand, J. "Theorie Mathematique de la Richesse Sociale,"
Journal des Savants, 67, 1883, pp. 499-508]
Bertrand considers what happens if the firms’ “strategic variable”
consists of prices instead of quantities. (Do you think firms are more
likely to play price or quantity; does it depend on the features of
the industry?)
Bertrand’s model adopts the same assumptions as Cournot theory
except the strategic variable is price instead of quantity.
Firm A’s decision based on its conjecture about
firm B’s price
17
Products are perfect substitutes:
Whichever firm charges the lowest
price gets all the sales.
If price set by Firm A (PA) is lower than
price set by Firm B (PB), Firm A’s
demand will be D(PA)—the market
demand—whereas Firm B’s demand
will be zero. And vice versa.
If both Firms set the same price P= PA=
PB then each Firm will get half of the
demand: ½ D(P) (assumes customers
choose randomly since firms are
identical).
P
Firm B charges a higher
price but gets zero
demand
PB
PA
D(P)
QA =D(PA < PB)
Q
The Best Strategy with Bertrand Competition
18
If Firm A conjectures Firm B will set monopoly price its best price is slightly
below that  then, it gets all the monopoly profits for itself.
If Firm A conjectures that Firm B will set price between competitive and
monopoly price, its best price is again slightly below  It doesn’t get all
the monopoly profits but at least it gets all the profits available at this
supra-competitive price.
If Firm A conjectures that Firm B will set price at competitive level its best
price is also at the competitive level (equal to marginal cost) It loses
money at a lower price and makes no sales at a higher price.
Firm B is symmetric to Firm A and behaves exactly in the same way.
Equilibrium with Bertrand competition
19
The equilibrium is where price equals marginal cost (the
competitive level).
At any higher price the conjectures are inconsistent. Whatever
price a firm expects, the other one will undercut it to get the
whole market and the entire profits.
At the competitive price firms cannot cut prices any more
because they will lose money (does predatory pricing make
sense here?). And they cannot raise prices either because they
will lose all sales.
So at P = MC conjectures are consistent with each other: if Firm A
charges the competitive price, Firm B will too, and vice versa.
Bertrand model with product differentiation
20
As the number of competitors goes from one to two, the
equilibrium price goes from the monopoly level to the perfect
competition price.
The Bertrand model assumes both firms sell identical products.
With slightly different products undercutting the rival’s price the
model does not guarantee a firm gets the entire demand.
With differentiated products equilibrium price is above marginal
cost.
Differentiated-market Bertrand accords with reality and this
model is extensively used in econometric studies of markets and
in merger analysis.
Cournot and Bertrand can both be restated as
games
21
The Cournot and Bertrand equilibria are Nash Equilibria in noncooperative games.
Bertrand is an example of a prisoner’s dilemma game where the
players independently choose the worst possible outcome.
Cournot is an example where the players in the end could have
done better or could have done worse.
Oligopoly theory and the embarrassment of
riches
22
The vastly different results obtained from Cournot and Bertrand
point to a fundamental problem with oligopoly theory:
A priori almost any outcome between monopoly and
competition for the two firms combined seems plausible.
And it is possible to find assumptions that produce almost any
equilibrium.
Economists have lost some of their initial enthusiasm for game
theory (it dominated industrial organization in the1980s and 1990s)
because it does not yield robust results.
23
Dynamic Games of Competition
Dynamic Games
24
Consider decision to enter and respond to entry:
Entrant gets 4, Incumbent 5
Incumbent
Entrant
Enter
Stay Out
Accomodate
Fight
(4,5)
(-1,0)
(0,10)
(0,10)
Dynamic Equilibria and Credible Threats for the
Entry Game
25
There are two possible equilibrium strategies:
• Enter-Accommodate
• Stay out-Fight
But one of these isn’t credible:
• The incumbent can play its “fight” strategy and brag that it
will demolish the entrant.
• But what if the entrant comes in (by mistake for example)?
• Once he is in, the incumbent is better off accommodating (is
there an argument that it should fight nonetheless?)
• Key principle: threat must be credible to be effective.
Dynamic Games and Game Trees
26
Dynamic games are represented by game trees (“extensive form
of a game”) that shows time-path of strategies:
Entrant
Stay out
Enter
Incumbent
0
10
Fight
Accommodate
-1
4
0
5
Solving the Game: Backward Induction
27
Start with what is optimal in the “end game” and then figure out
what the optimal strategy is in the previous sub-games (this is
known as “backward induction”—a very powerful technique in
dynamic optimization theory).
Each player plays its best strategy in the sub-game knowing what
has gone on before. This is known as the sub-game perfect Nash
equilibrium.
Nash Equilibrium for the Entry Game
28
Post-entry game: equilibrium is to accommodate.
Pre-entry game: given that post-entry equilibrium is to
accommodate, optimal strategy is to enter.
Equilibrium: Enter, Accommodate
Entrant
Stay out
Enter
Incumbent
0
10
Fight
Accommodate
-1
4
0
5
Making Credible Commitments
29
Strategy analysis often considers whether players can make
binding commitments that force them to undertake strategies
that are ex post unprofitable but ex ante optimal.
For the entry game the incumbent could have “meeting
competition clauses” or advertise “Our prices can’t be beat. We
won’t be undersold.”
Next week: Makeup Lecture 6.2
30
Part 1
Part 2
Transaction
Costs
Welfare and
Efficiency
Opportunistic
Behavior
Market
Failures
Theory of the
Firm
Economics of
Remedies
Antitrust,
Welfare and
Market Failure