### Lecture 3

Lecture 3: Oligopoly and Strategic Behavior
Few Firms in the Market: Each aware of others’ actions
Each firm in the industry has market power
Entry is Feasible, although incumbent(s) may try to deter it.
Examples: Airlines, Telecommunications, Search
Engines, Automobiles, Microprocessors
Measuring market concentration:
concentration indices
Ci = combined market share of i largest firms, eg, C4.
H = Herfindahl index, aka HHI.
H =  si2
both of these vary between 0 (many, many firms) and 1 (monopoly).
Example: 4 firms in the market: S1=.50, S2=.25, S3=.15, S4=.10
C3 = .90,
HHI= .52+.252+.152 + .102 =.345
Market structure and performance
Nature of comp.
Value of H
Intensity of price comp.
perfect
below .2
fierce
oligopoly
.2 to .6
varies*
monopoly
.6 or above
light
*“Firms must understand the nature of markets in which they
compete. There are reasons why, for example, even firms in
an industry such as pharmaceuticals have, by economywide
standards, impressive profitability, while top firms in the
airline industry seem to achieve low rates of profitability even
in the best of times.” (BDS, p.7)
In an oligopoly, degree of market power depends on:
Demand Elasticity
Market Concentration
Collusive Behavior
The “five forces framework” (Michael Porter, Competitive
Strategy, NY, Free Press, 1980)
Degree of market power depends primarily on rivalry within
the industry, but also takes into account, vertical structure, the
threat of entry, and threat of substitute products.
Quantity (Cournot) Competition
Assume Homogeneous Products: MC=10 for both firms
(Results are qualitatively similar with differentiated products)
Demand: P=70-Q= 70- (q1+q2), since Q= q1+q2, where
Q=total quantity.
p1= Pq1 – TC1= (70-q1-q2) q1 -10q1
p1 =60q1 – q12 – q2q1
dp1/dq1=60-2q1-q2 =0 or
q1=(60-q2)/2 (Reaction function of firm 1)
Similarly, p2 =60q2 – q22 – q1q2
q2=(60-q1)/2 (Reaction function of firm 2)
Reaction function of firm 1
q2
Reaction function of firm 2
q1
Solve for the Nash Equilibrium Quantities
Reaction functions intersect at q1= q2=20.
Nash equilibrium is (q1*=20, q2*=20). P=30
Computing Profits: p1= p2 = (P-MC)q= (30-10)20=400.
What would a monopoly do?
MR=MC implies that 70-2Q=10, or Q=30.
P=40 and total profits are 900.
If each firm produced q=15, each firm would earn 450.
Prices are higher and total quantity is lower under
monopoly.
Suppose that there were three firms. Total quantity would
exceed 40 and the price and the profits would fall.
As the number of firms gets very large, “Cournot” model
approaches perfect competition. (Work out details!)
Oligopoly Models and Repeated Interaction:
Example
Let firm 1=SA, firm 2=Rest of the Cartel RC.
Product is oil
Suppose that the strategies of both SA and RC are limited to
either producing 20 million barrels or 15 million barrels.
If one firm produces 20 million barrels and the other firm
produces 15 million barrels, P=35 and the firm producing 20
million barrels earns 500, while the firm producing 15 million
barrels earns 375.
A one shot game
Rest of Cartel’s
Output
15
450
Saudi Arabia’s Output
15
450
500
500
375
375
20
20
400
400
Unique Nash equilibrium of one shot game is (20,20)
Repeated Games
Suppose that each firm adopts the following
Tit for Tat “trigger” strategy:
I will produce at the “cooperative” level as long as my
competitor did so if the previous period. If, however, my
competitor deviates from that level, I will produce 20 million
barrels forever. (Punishment threats must be credible to be
effective.)
Each player must determine whether it is worthwhile to deviate
from the cooperative output level. Such a deviation results in a
short term gain. But there are long term losses. Hence there is a
tradeoff which depends, in part, on the discount rate.
Cooperation yields the following payoff:
450+ 450/(1+r) + 450/(1+r)2 +…. = 450(r +1)/r
Deviation yields the following payoff
500+ 400/(1+r) + 400/(1+r)2 +….= 500+ 400/r
Cooperation can be sustained if:
r<(450-400)/(500-450)=1,
that is if the discount rate is less than 100%.
In general cooperation can be sustained if
r<(cartel profit – one shot eq. Profit)/(deviation profit - cartel profit).
Without repetition of play, players are less likely to cooperate
Repetition can create much stronger incentives to cooperate
Trading off the gains from being non-cooperative today
with the last future cooperation
Tradeoff of SR gains vs. LR losses means that the
discount rate matters