Transcript pptx - Cornell

Oligopoly
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Oligopoly (Competition Among A Few):
Structure
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In an oligopoly there are very few sellers of the good.
The product may be differentiated among the sellers
(e.g. automobiles) or homogeneous (e.g. gasoline).
Entry is often limited either by legal restrictions (e.g.
banking in most of the world) or by a very large
minimum efficient scale (e.g. overnight mail service)
or by strategic behavior.
Sill assuming complete and full information.
Oligopoly: Conduct
Harder to model! (Compared to perfect
competition and monopoly and monopolistic
competition.)
 In an oligopoly
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– firms know that there are only a few large
competitors.
– competitors take account of the effects of their
actions on the market.
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To predict the outcome of such a market,
economists frequently use game theory
methods.
Game Theory: Setup
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List of players: all the players are specified in advance.
List of actions: all the actions each player can take are
spelled out.
Rules of play: who moves and when is spelled out.
Information structure: who knows what and when is
spelled out.
Strategies: the set of actions players can use.
Payoffs: the amount each player gets for every possible
combination of the players’ strategies.
Solution or equilibrium concept: a way you reason that
players select strategies to play, and then consequently
how you predict the outcome of the game.
Solution Concept:
Dominant Strategy Equilibrium
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A Dominant Strategy Equilibrium of a game is a
set of strategies for all players, such that, for each
player his payoff from playing his dominant
strategy is at least as large as his payoff would be
by playing any other strategy, no matter what his
rivals choose as their strategies.
Solution Concept:
Nash Equilibrium
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Named after John Nash - a Nobel
Prize winner in Economics.
Did you see A Beautiful Mind?
A Nash Non-cooperative
Equilibrium of a game is a set of
strategies for all players, such that,
when played simultaneously, have
the property that no player can
improve his payoff by playing a
different strategy, given the
strategies the others are playing.
Each player maximizes his or her
payoff under the assumption that all
other players will do likewise.
Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities
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Pioneered by Antoine Augustin
Cournot, circa 1838.
Duopoly  an oligopoly of 2 firms.
Firms selling identical spring water.
Firms have identical cost functions.
Firms decide how many units to put
on the market; q1 and q2.
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Market then determines the price:
PD = f(Q) where Q=q1+q2.
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So…,GIVEN what your rival is putting
on the market, the more you put on
the market, the lower the price for
both of you, and vice versa.
Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities
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Firm i’s strategic choice variable = qi ,that is, its output
level.
Firm i’s conjecture about its rival when deciding his qi is
NASH
– meaning firm i figures out a best reaction to firm j’s strategic
choice.
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So, in this Cournot-Nash game you would get the
following:
– BRF1: Firm 1’s Best Response Function
» tells what quantity firm 1 should put on the market GIVEN firm 2’s
quantity.
– BRF2: Firm 2’s Best Response Function
» tells what quantity firm 2 should put on the market GIVEN firm 1’s
quantity.
Cournot-Nash Duopoly: A NonCooperative Outcome in Quantities
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When firm 1’s best response to firm 2 is
simultaneously firm 2’s best response to firm 1,
we have a Nash equilibrium in quantities:
q1CN and q2CN.
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The full Cournot-Nash(CN) Equilibrium is then:
–
–
–
–
QCN = q1CN + q2CN
Get PCN from plugging QCN into demand: PD = f(QCN)
Get profit for each firm: P1CN and P2CN
Get joint profit: PjointCN= P1CN + P2CN
Properties of the CournotNash Equilibrium for Duopoly
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Cournot Nash compared to simple monopoly(SM) and to
perfect competition(*).
Q* > QCN > QSM
P* < PCN < PSM
PSM > PJointCN > PJoint*
Deadweight loss with CN is less than for a simple
monopoly in the same market but still positive, thus
greater than the deadweight loss from a competitive
market.
Extensions to the model?
– More than two firms? Can do.
– Different cost structures? Can do.
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Assume: PD=12-2Q, Q=q1+q2, tc1=tc2=0  mc1=mc2=0
Simple Monopolymr=12-4Q & set mr=mc, so Qsm=3, Psm=$6, Profitsm=$18
Perfect Competition  Set PD=mc and so Q*=6 and P*=0, Profit =$0
$
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14
12
10
8
6
4
2
0
-2 0
-4
-6
-8
-10
Demand
MC
MR
1
2
3
4
5
Q
6
7
8
9
The Cournot-Nash Reaction
Functions
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Consider firm 2’s reactions to firm 1’s quantities.
Suppose q1=0. Then firm 2 would do what a
monopolist would do, and q2=3.
Suppose q1=6. Then firm 2 would see there was no
room for it and select q2=0.
Between q1=0 and q1=6, there is a “best response”
from firm 2’s point of view, which lies on the red
straight line.
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q2
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q1
Consider firm 1’s reactions to
firm 2’s quantities.
Suppose q2=0. Then firm 1
would do what a monopolist
would do, and q1=3.
Suppose q2=6. Then firm 1
would see there was no room
for it and select q1=0.
Between q2=0 and q2=6,
there is a “best response”
from firm 1’s point of view,
which lies on the blue straight
line.
The Cournot-Nash
equilibrium is where the blue
and red intersect at q1=q2=2.
So, QCN=4 and PCN=$4.
Each firm gets profit=$8.
Joint profit = $16.
Demand
Demand
MC
MR
$
14
12
10
8
6
4
2
P*= 0
-2 0
-4
-6
-8
-10
1
2
3
4
5
6
7
Marginal revenue
Q
8
9
Bertrand-Nash Duopoly: An Alternative
Non-cooperative Outcome
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Pioneered by Joseph Louis
Francois Bertrand, circa 1883.
Duopoly  an oligopoly of 2 firms.
Firms selling identical spring water.
Firms have identical cost functions.
Firms decided what price to post on
the market.
What each firm sells depends on
their own price along with their
rival’s price:
q1D = g(P1 , P2) and
q2D = h(P1 , P2)
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If P1 < P2 everyone buys from firm 1
If P1 > P2 everyone buys from firm 2
Bertrand-Nash Duopoly: A
Non-cooperative Outcome
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Firm i’s strategic choice variable = Pi
Firm i’s conjecture about rival when deciding his Pi is
NASH
– meaning firm i figures out a best reaction to firm j’s strategic
choice

So, in this Bertrand-Nash game you would get the
following:
– BRF1: Firm 1’s Best Response Function
» tells what price firm 1 should choose GIVEN firm 2’s price
– BRF2: Firm 2’s Best Response Function
» tells what price firm 2 should choose GIVEN firm 1’s price
Bertrand-Nash Duopoly: A
Non-cooperative Outcome
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When firm 1’s best response to firm 2 is simultaneously
firm 2’s best response to firm 1, we have a Nash
equilibrium in prices: P1BN and P2BN
The full Bertrand-Nash(BN) Equilibrium is then:
– PBN = P1BN = P2BN
– Firm 1 and Firm 2 split the market in any way provided that:
q1BN + q2BN = QD(PBN)
– Get profit for each firm: P1BN and P2BN
– Get joint profit: PjointBN = P1BN + P2BN
Properties of the BertrandNash Equilibrium for Duopoly
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Bertrand-Nash Equilibrium compared to simple monopoly
and to perfect competition
Q* = QBN > QSM
P* = PBN < PSM
PSM > PJointBN = PJoint*
Deadweight loss with BN is zero!
Bertrand  all you need is one competitor to get
competitive results!!
Extensions to the model?
Duopoly Results as N Changes
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Bertrand compared to Cournot.
– When N=1 then Cournot = Bertrand = Simple Monopoly
– When N>1 then...
» Bertrand=Perfect Competition
» Cournot is in between Perfect Competition and Monopoly
– When N gets large enough, then...
» Cournot = Bertrand =Perfect Competition
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Results have different implications for anti-trust action.
– Should Coke be allowed to merge with Dr. Pepper? Should Pepsi be
allowed to merge with 7-Up? Good questions.
– Should Chrysler be allowed to merge with Fiat?
– How about GE being able to sell NBC Universal to Comcast?
– How about US Airways and United?
Edward Chamberlin:
A Cooperative Oligopoly Outcome (Collusion)
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circa 1930’s
The duopolists can do better than the Nash Non-Cooperative
Equilibrium – Bertrand or Cournot.
So far, because the equilibrium is non-cooperative, we have ruled out
the possibility of collusion between the two firms.
Collusion means that the firms explicitly and/or implicitly cooperate in
choosing a market output and the division of output between them.
(Note, if they set the output level, then the market sets the price.)
If the duopolists collude and divide up the market privately, they can
produce the monopoly quantity and divide the monopoly economic
profits.
Since the monopoly economic profits are more than the sum of the
duopoly profits, the duopolists are better off if they collude.
When we allow the possibility of collusion the game can turn out
differently.
No longer a NONcooperative game.
Chamberlinian Collusion With A Duopolymimic a multi-plant monopoly
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With only a couple/few
identical firms, and
homogeneous output, this
might be expected.
Cournot-Nash Joint
Profit
V1
V2
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However, when firms have different
cost structures…
X1
Cournot-Nash
Joint Profit
X2
X1=6, X2=4,
sum=10
V1=5, V2=5,
sum=10
“Collusive
Monopoly”
Joint Profit
W1=11,
W2=11,
sum=22
W1
W2
“Collusive
Monopoly” Joint
Profit
Y1
Y2
Y1=19, Y2=3,
sum=22