ECON 2005 Duopoly Market Discussion
Description
Consider a duopoly market, where two rms sell di¤erentiated products,which are imperfect substitutes. The market can be modelled as a staticprice competition game.
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Topic 1 Welfare Economics
of Market Power
?
?
DefinitionMarket power is the ability to
profitably raise price above marginal cost
(Church-Ware (2000), ch1, pp.10)
Firm behaviour in terms of profit
maximisation
max ?=
(q) R (q) ? C (q)
MP
=
( q ) MR ( q ) ? MC ( q )
( )
( )
MR q* = MC q*
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1
Perfect Competition
(CW, ch2.1, pp. 21)
?
?
There are many firmspricetakers
Supply (single firm)
R ( q ) = pq
?
?
MR ( q ) = p
( )
p = MC q*
Price reflects (marginal) cost
Supply (market)
N
Q s ( p ) = ? Si ( p )
i =1
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2
?
Market equilibrium
( )
( )
Q s Pc = Q D Pc
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3
Efficiency (PC)
?
Gains from trade
?
?
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Consumer surplus
Producer surplus
4
?
Gains from trade
?
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Total surplus
5
Market Power
(CW, ch2.4, pp. 29)
?
?
RecapMarket powerthe ability
to profitably raise price above
marginal cost
Restrictions on market power:
Supply side substitution
? Demand side substitution
?
?
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Firms with market powers are price
makers
6
Market Power and
Pricing
?
Monopoly pricing
=
? (Q ) P (Q ) Q ? C (Q )
MR=
(Q ) P (Q ) +
( )+
P Q
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m
dP ( Q )
( )Q
dP Q m
dQ
dQ
m
Q
( )
=
MC Q m
7
?
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MR for monopolist
8
?
Inefficiency of monopoly pricing
deadweight-loss (DWL)
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9
?
Inefficiency of monopoly pricing
(example)
Linear demand: P(Q)=A-bQ
Marginal cost: (constant)
c
MR=
( Q ) P ( Q ) + ??dP ( Q ) / dQ ?? Q = A ? 2bQ
2
A ? c)
(
A?c
A+c
m
m
m
Q =
? =
P =
2b
4b
2
A ? c)
(
s
Q =
b
2
Pm ? c Qs ? Qm
A ? c)
(
DWL =
=
2
8b
(
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)(
)
10
Determinants of Market
Power
?
Price elasticity of demand
%?Q
dQ P
dQ dP
?=
=? /
=?
%?P
Q P
dP Q
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11
?
Measurement of market power
( )
( )
MR Q = MC Q
m
?
( )
( )=1
P m ? MC Q m
Pm
?
Long-run elasticity of demand
?
?
?
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( )
Lerner index (Mark-up)
L=
?
m
? dP Q m Q m ?
m
?
? P m ?1 +
=
MC
Q
?
dQ P m ?
?
?
Consumer response
New entrants
New technology
12
Benefits of Monopoly
(CW, ch4.5, pp. 148)
?
Scale Economies (Williamson
1968)
A merger into a monopoly may
reduce industry-wide costs
? The cost savings may compensate
the inefficiency due to monopoly
pricing
?
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13
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14
?
Innovation and Research and
Development (Schumpeter 1934,
1965)
Market power allows a firm to profit
from innovationa necessary
incentive for Research and
Development (R&D)
? R&D are the engine of
technological progress and
economic growth
?
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15
Market Power and
Public Policy
?
?
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Regulation
Antitrust laws
16
Topic 2 Introduction to
Competition Policy
Purpose: to protect and promote
competition
Legal power for competition authority
to investigate and intervene
Possible punishment for illegal
anticompetitive behaviour
?
?
?
i.
ii.
iii.
iv.
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Fines
Imprisonment
Cease-and-desist orders
Divestiture of assets and dissolution of
organisation
1
Policy Areas
?
Monopoly policy
?
?
?
Restrictive trade practices policy
?
?
?
?
E.g., price-fixing agreement
Predatory pricing
Vertical restraint (not necessarily
anticompetitive)
Merger (control) policy
?
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No outright prohibition
Control abuse of dominant position
Deals with substantial lessening of
competition
2
Objectives and
Approaches
?
?
Economic rationale: to enhance
efficiency (total surplus)
Weighing anticompetitive effect
against efficiency gain
?
?
?
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Consumer protection?
Restraints that are per se illegal
(e.g., cartel)
Restraints that are subject to rule
of reason (e.g., some vertical
restraints )
3
Legal Framework – US
?
Antitrust statutes
?
?
Sherman Act 1890
Clayton Act 1914
?
?
?
?
FTC Act 1914
Enforcement
?
?
?
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Robinson-Patman Act 1936
Celler-Kefauver Antimerger Act 1950
Department of Justice: Antitrust Division
Federal Trade Commission (FTC)
Private enforcement
4
Sherman Act 1890
?
?
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Section 1 prohibits concerted
action that leads to, or is intended
to lead to, restraint of trade.
Section 2 deals with unilateral
behaviour to monopolise an
industry
5
Clayton Act 1914
?
?
?
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Augments Sherman Act
Deals with 4 specific practices:
(i) tie-in, (ii) exclusive dealing, (iii)
mergers and (iv) interlocking
directorates
Allows injured party to recover
treble damages (three times actual
damages) plus attorneys fees
6
Legal Framework EU
(A source of UK law pre-Brexit
and during Brexit transition period)
?
Antitrust statutes
?
?
?
?
Enforcement
?
?
?
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Articles 81 and 82 of the EC Treaty
Regulation on implementation rules on
competition in Articles 81 and 82 of the
EC Treaty
EC Merger regulation
European Commission DirectorateGeneral (VI) of Competition
Court of First Instance (CFI)
National Competition Authorities (NCA)
can also enforce Articles 81 and 82 of EC
Treaty (since 2003)
7
EC Competition Law
?
Article 81 of EC Treaty prohibits anticompetitive agreements which
?
?
?
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Affect trade between Member States,
And prevent, restrict or distort
competition in the Single Market.
Article 82 of EC Treaty prohibits the
abuse of a dominant position if it affects
trade between member states.
8
Legal Framework – UK
?
Antitrust statutes
?
?
?
?
?
Enforcement
?
?
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Competition Act 1998
Enterprise Act 2002
Articles 81 and 82 of EC Treaty (since
2003, Modernisation Regulation)
Enterprise and Regulatory Reform Act
2013
Competition and Markets Authority (CMA)
– merging former Office of Fair Trading
(OFT) and Competition Commission (CC)
Competition Appeal Tribunal (CAT)
9
Competition Act 1998
?
?
Prohibits agreements and
practices considered to have a
damaging effect on competition
Chapter 1: agreements
?
?
Chapter 2: practices abuse of
dominant position
?
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E.g., price-fixing
E.g., supplementary conditions in
contracts
10
Enterprise Act 2002
?
?
?
?
30/01/2020
Replaces the Fair Trading Act 1973
Part 3 deals with mergers
Part 4 deals adverse effects on
competition (including monopoly)
Part 6 deals with cartel offence
11
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12
Topic 3 Game Theory I
?
Why game theory?
?
?
?
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Multiple person decision problem
in a game-theoretic situation
Payoff Interdependency
Optimal choice by an agent
depends on the actions of others
No persons decision problem
can be solved in isolation
1
?
Game-theoretic situation vs.
decision-theoretic situation
?
Perfectly competitive markets and
monopolies are decision-theoretic
situations
? There
is no interaction between
decision makers
?
Oligopolies are game-theoretic
situations
? Firms
need to reason strategically,
i.e., form expectations about
others decisions when deciding
own course of actions.
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2
?
Non-cooperative game theory
provides a set of language and
tools to
Model the payoff-interdependence
situation
? Predict the outcome of
interdependent decision making
?
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3
The Basic Elements of a
Game
1.
2.
Players: identity of decision markers
Rules
a)
b)
c)
3.
4.
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Timing of moves
Actions available at each move
Information available at each move
Outcomes: all possible combinations of
actions
Payoffs: players preferences over the
outcomes
4
Types of Games
1.
2.
3.
4.
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Static games of complete
information
Dynamic games of complete
information
Static games of incomplete
information
Dynamic games of incomplete
information
5
Equilibrium Concepts and
Fundamental Assumptions
?
?
An equilibrium concept is a
solution to a game
Two fundamental assumptions
1.
2.
Rationality: payoff maximisation
Common knowledge
All players know
?
?
?
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their opponents are rational
the structure of the game
All players know that all players
know?
6
Static Games with
Complete Information
?
Normal form representation
1. Players 1,2,?,I
2.
3.
?
Two-player with finite action set
?
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A set of actions for each player Si
A payoff function for each player ?i(s)
Payoff matrix
7
06/02/2020
C1
C2
C3
R1
4,3
5,1
6,4
R2
2,1
3,4
3,6
R3
3,0
4,6
2,8
8
C1
C2
C3
R1
4,3
5,1
6,4
R2
2,1
3,4
3,6
R3
3,0
4,6
2,8
R1 is a strictly dominant
strategy for player 1
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9
C1
C2
C3
R1
4,3
5,1
6,4
R2
2,1
3,4
3,6
R3
3,0
4,6
2,8
C3 is a strictly dominant
strategy for player 2
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10
C1
C2
C3
R1
4,3
5,1
6,4
R2
2,1
3,4
3,6
R3
3,0
4,6
2,8
(R1,C3) is the predicted
outcome of the game
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11
?
The Prisoners Dilemma
Rat
Clam
Rat
-3,-3
0,-5
Clam
-5,0
-1-1
Underline strictly dominant strategies
(Rat,Rat) is the predicted outcome
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12
?Iterative elimination of strictly
dominated strategies
06/02/2020
C1
C2
C3
R1
4,3
5,1
6,2
R2
2,1
3,4
3,6
R3
3,0
9,6
2,8
13
?Iterative elimination of strictly
dominated strategies
C1
C2
C3
R1
4,3
5,1
6,2
R3
3,0
9,6
2,8
Eliminate R2 (strictly dominated by R1)
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14
?Iterative elimination of strictly
dominated strategies
C1
C3
R1
4,3
6,2
R3
3,0
2,8
Eliminate C2 (strictly dominated by C3)
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15
?Iterative elimination of strictly
dominated strategies
R1
C1
C3
4,3
6,2
Eliminate R3 (strictly dominated by R1)
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16
?Iterative elimination of strictly
dominated strategies
C1
R1
4,3
Eliminate C3 (strictly dominated by C1)
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17
L
M
R
U
2,0
3,5
4,4
D
0,3
2,1
5,2
There is no strictly dominated strategy
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18
L
M
R
U
2,0
3,5
4,4
D
0,3
2,1
5,2
U is the best response to L and M, D is the best response to R
L is the best response to D, M is the best response to U
R is never a best response
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19
L
M
U
2,0
3,5
D
0,3
2,1
U is the best response to L and M
L is the best response to D, M is the best response to U
D is never a best response
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20
U
L
M
2,0
3,5
M is the best response to U
L is never a best response
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21
M
U
3,5
Iterative elimination of never-best responses gives rise to the set
of rationalisable strategies
(U,M) is the predicted outcome of the game
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22
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
There is no strictly dominated strategy
06/02/2020
23
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
06/02/2020
24
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
06/02/2020
25
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
C4 is never a best response
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26
C1
C2
C3
R1
0,7
2,5
7,0
R2
5,2
3,3
5,2
R3
7,0
2,5
0,7
R4
6,6
2,2
4,4
R4 is never a best response
06/02/2020
27
C1
C2
C3
R1
0,7
2,5
7,0
R2
5,2
3,3
5,2
R3
7,0
2,5
0,7
Iterative elimination of never-best
responses
The set of rationalisable strategies has 9
possible outcomes
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28
Nash Equilibrium
?
Nash equilibrium is a strategy
profile such that
every players strategy is a best
response
? to the strategies of all other
players.
?
?
06/02/2020
In a Nash equilibrium no player
can profitably deviate unilaterally
29
Find the Nash equilibrium for the following
game:
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
06/02/2020
30
Find the Nash equilibrium for the following
game:
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
06/02/2020
31
Find the Nash equilibrium for the following
game:
C1
C2
C3
C4
R1
0,7
2,5
7,0
6,6
R2
5,2
3,3
5,2
2,2
R3
7,0
2,5
0,7
4,4
R4
6,6
2,2
4,4
10,3
Underline all best responses
In a Nash equilibrium both players play
best responses
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32
Find the Nash equilibrium for the following
game The Battle of Sexes:
Football
Ballet
Football
3,1
0,0
Ballet
0,0
1,3
Underline all best responses
06/02/2020
33
Find the Nash equilibrium for the following
game The Battle of Sexes:
Football
Ballet
Football
3,1
0,0
Ballet
0,0
1,3
Underline all best responses
06/02/2020
34
Find the Nash equilibrium for the following
game The Battle of Sexes:
Football
Ballet
Football
3,1
0,0
Ballet
0,0
1,3
Underline all best responses
In Nash equilibria both players play best
responses
06/02/2020
35
?
Find the Nash Equilibrium for the
Prisoners Dilemma Game
Rat
Clam
Rat
-3,-3
0,-5
Clam
-5,0
-1,-1
Underline all the best responses
(Rat,Rat) is the Nash equilibrium
06/02/2020
36
?
?
06/02/2020
Nash equilibrium is the most
commonly used equilibrium
concept in Industrial Economics
All equilibrium concepts used in
the rest of this course will be based
on Nash equilibrium
37
Topic 4 Classic Models of
Oligopoly
?
?
?
?
?
?
13/02/2020
An oligopoly is a market featured by
competition among a small number of
suppliers
Static oligopoly models timeless
competition among the few
Strategic variables: quantity vs. price
Payoff interdependence – strategic
interaction
Equilibrium analysis (Nash)
Welfare of oligopoly vs. perfect
competition and monopoly
1
Cournot Game
?
?
?
Number of firms: 2 duopoly
Homogenous product, e.g., spring
water
Strategic variable: output level
Cournot (quantity) competition
(price is set automatically by market to
equate demand and supply)
?
?
13/02/2020
Firms compete only once and move
simultaneously
Payoffs: profits
2
Profit Maximisation and
Best Response Functions
?
?
Profit of firm 1:
?1 = P(q1+q2)q1 – C(q1)
Residual demand
P1(q2a) = P(q1+q2a) when q2 = q2a
? P1(q2b) = P(q1+q2b) when q2 = q2b
?
13/02/2020
3
Residual Demand
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4
Profit maximising: Firm 1 acts as a
monopolist on its residual demand curve
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5
?
Marginal revenue:
dP ( q1 + q2 )
MR1 ( q1 , q2 )= P ( q1 + q2 ) +
q1
dq1
?
Profit maximisation
P ( q1* + q2 ) +
?
13/02/2020
dP ( q1* + q2 )
dq1
q1* =
MC1 ( q1* )
Best response functions:
? q1 = R1(q2)
? Similarly, q2 = R2(q1)
6
Cournot (Nash) equilibrium:
q1c = R1(q2c), q2c = R2(q1c)
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7
An Example: Linear Demand and
Constant Marginal Cost
?
?
?
?
?
13/02/2020
Demand: P(Q)=A-bQ, (Q = q1+q2)
Marginal cost: c
Residual demand (firm 1):
P(q1+q2)=(A-bq2)-bq1
Marginal revenue:
MR1(q1,q2)= (A-bq2)-2bq1
Profit maximisation
(A-bq2)-2bq1 = c
8
?
Best response functions:
A ? bq1 ? c
q2 =
2b
A ? bq2 ? c
q1 =
2b
?
Cournot-Nash equilibrium quantities:
A?c
q= q=
3b
c
1
?
c
2
Market output and price:
A + 2c
? A?c ? c
c
Q = q + q = 2?
A bQ =
? P =?
3
? 3b ?
c
?
c
1
c
2
Profits:
?= ?=
c
1
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c
2
( A ? c)
2
9b
9
Properties of Cournot
Equilibrium
?
Marginal product rule:
(
)
P q +q +
(
13/02/2020
c
1
)
c
2
(
dP q1c + q2c
dQ
( )= ? (
)q
c
1
P q1c + q2c ? MC1 q1c
dP q1c + q2c
P q1c + q2c
dQ
(
)
( )
=
MC1 q1c
)
q1c
Q
P q1c + q2c Q
(
)
10
?
Lerner index
Li =
(
)
( )=s
P qic + q cj ? MCi qic
(
P qic + q cj
)
i
?
where i,j=1,2, i?j, si=qic/Qc is firm
is market share, ? is elasticity of
market demand
13/02/2020
11
?
Market power
1.
2.
3.
4.
5.
13/02/2020
Cournot duopolists exercise market
power
Market power is limited by elasticity of
market demand
Cournot markups are smaller than
monopoly markup since si qm /2
?Collusion (M) is not NE,
and is not sustainable
13/02/2020
21
Free Entry Cournot
Equilibrium
?Positive profits would attract
entry until they are dissipated
entirely
?Consider positive fixed cost and
economies of scale
?NE in quantity: MR(qc)=MC(qc)
?Zero-profit condition: Pc=AC(qc)
13/02/2020
22
Example: Free-Entry Cournot Equilibrium with
Linear Demand, N firms and Constant MC
?
?
?
?
?
?
Demand: P(Q) = A – bQ, where Q =? qi
Costs: Ci = cqi + f
Profit in equilibrium:
?c=[(A-c)/(N+1)]2/b
Zero-profit condition:
[(A-c)/(N+1)]2/b = f
Equilibrium number of firms:
Nc = (A-c)/(bf)1/2 1
Comparative statics:
f?
?
Nc ?
?
Pc ?
?
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?c ?
23
Bertrand Competition
?
?
A critique on the Cournot model:
In reality firms choose prices rather than
quantities
Bertrand model
?
?
?
?
?
13/02/2020
Two firms compete in prices once
Homogeneous product, e.g., spring water
Constant marginal cost: c
Market demand: D(p)
Payoffs: profits
24
?
Residual demand:
? D ( p1 ) if p1 < p2
?
?1
=
D1 ( p1 , p2 ) ?=
D ( p1 ) if p1 p2
?2
if p1 > p2
?? 0
?
Profit function:
? ( p1 ? c ) D ( p1 ) if
?
?1
? 1 ( p1 , p2 ) =
? ( p1 ? c ) D ( p1 ) if
?2
0
if
??
13/02/2020
p1 < p2
p1 =
p2
p1 > p2
25
The Bertrand Paradox
?
Find the Nash equilibrium
– consider the following 4 cases:
1.
2.
3.
4.
13/02/2020
p1 > p2 > c. Not an NE. Firm 1 is not
playing best response: can profitably
deviate by setting p1 = p2 – ?, where ??0.
p1 > p2 = c. Not an NE. Firm 2 is not
playing best response: can profitably
deviate by setting p2 = p1 – ?, where ??0.
p1 = p2 > c. Not an NE. Either firm can
profitably deviate by slightly
undercutting rivals price.
p1 = p2 = c is the NE. No firm can
profitably deviate.
26
?
Paradoxical predictions:
1.
2.
?
But how robust are the results?
?
?
13/02/2020
Two firms are enough to
eliminate market power
Competition between two firms
completely dissipates profits
Products may be differentiated
There maybe capacity constraints
27
Product Differentiation
?
?
Consider two firms products are
imperfect substitutes, e.g., mineral water
and coke
There is interdependence in demand:
q1(p1,p2) ? as p1? or p2 ?
q2(p1,p2) ? as p2? or p1 ?
?
Example:
q1(p1,p2) = A- p1+0.5 p2
q2(p1,p2) = A- p2+0.5 p1
C(q) = cq, i.e. MC = c, where cc
Similarly, R2(p1)= (A + c + 0.5p1)/2>c
13/02/2020
30
Bertrand equilibrium with product differentiation
p1B>c, p2B>c
13/02/2020
31
Cournot vs. Bertrand
?
?
The predictions of Cournot and Bertrand games are
very different.
But which is correct?
Kreps-Scheinkerman (1983) suggests Cournot
game can be seen as a shorthand description of a
two-stage game where firms first invest in capacity
then compete over prices.
?
?
13/02/2020
Cournot model is appropriate when firms are
capacity constrained and the investment in capacity
takes time, e.g., hotel rooms, restraint seats, etc.
Bertrand model may be relevant when there are
constant returns to scale and no capacity constraints.
32
Topic 5
The Theory of the Market
– Market Definition and
Assessment of Market Power
25/02/2020
1
The Du Pont – Cellophane
Monopolisation Case 1947
?
?
?
25/02/2020
From 1933 -1950, Du Ponts average share was
76% in the market for cellophane a transparent,
heat-sealable, printable, tough wrapping material
The court was to judge whether Du Pont was
liable for monopolising the market for cellophane,
which was the case brought by the DOJ in 1947
against Du Pont
The courts rulings cleared Du Pont from the
allegation of monopolisation on the ground that
cellophane was not the relevant market. Instead
it was determined that the relevant market was
flexible packaging materials of which Du Ponts
sales of cellophane did not exceed 18%
2
Market Definition
?
?
Many antitrust cases were won on the
battles of definition of markets, e.g., the
Cellophane case
The concepts of a market
?
?
?
The two dimensions of a market
?
?
25/02/2020
Economic markets
Antitrust markets
Product dimension: the set of products
Geographic dimension: the geographic
region
3
Economic Markets
?
?
?
An economic market consists of a set of
products, a set of buyers, a set of sellers,
and a geographic region in which the buyers
and sellers interact and determine the prices
for each product
A market can be defined if there is a
marked gap in the chain of substitutes
between products included in the industry
and those excluded, while at the same time
products included are close substitutes
The marked gap may not always exist
?
25/02/2020
The theoretical distinction between supply
and demand side substitutions may become
blur in practice, e.g., (almost) all goods are
differentiated
4
Antitrust Markets
?
?
?
The problem of arbitrariness of the market definition
The concept of an antitrust market 1982 DOJ Merger
Guidelines
The hypothetical monopoly test:
A market is defined as a product or group of products and a
geographic area in which it is produced or sold such that
a hypothetical profit-maximising firm (not subject to price
regulation, that was the only present and future producer or
seller of the those products in the area)
likely would impose at least a small but significant and
nontransitory increase in price (SSNIP, say, 5-10%),
assuming the terms of sale of all other producers are held
constant.
A relevant market is a group of products and a geographic area
that is no bigger than necessary to satisfy this test.
25/02/2020
5
Antitrust Markets:
The Assessment of Market
Power
?
Market power and antitrust
In economics, market power is
defined as the ability to profitably
raise price above marginal cost
? The antitrust law is not only
concerned about the pricing power,
but also about the exclusionary
power
? Constraints to market power:
? Demand side substitution
? Supply side substitution
? Entry
?
25/02/2020
6
?
Market power and market shares
?
Using market share as a proxy of
market power requires appropriate
definition of markets
Too narrow definition
? Too broad definition
?
?
Define antitrust market such that
market shares provide useful
information about market power
The measures of market
concentration, e.g., HHI
? High market shares are a necessary,
but not sufficient condition for finding
market power
?
25/02/2020
7
Topic 6 Horizontal Mergers
25/02/2020
1
An Equilibrium Analysis of
Horizontal Mergers
?
Example: Merger of Cournot Duopolists
?
?
?
?
25/02/2020
Demand function: P = 1 – Q
Cost function: C = 0.1q
Cournot equilibrium:
q1 = q2 = (1-0.1)/3 = 0.3
PD = 1-2(0.3) = 0.4
The merger gives rise to the monopoly
equilibrium:
QM = (1-0.1)/2 = 0.45
PM = 1-0.45 = 0.55
2
Loss of surplus:
?
Triangle: (0.6-0.45)(0.55-0.4)/2 = 0.01125
?
Rectangle: (0.6-0.45)(0.4-0.1) = 0.045
?
Total: 0.05625
25/02/2020
3
?
Price versus efficiency: The
Williamson trade off
MC decreases after merger
Net welfare change = B – A
The efficiencies defence
MCD
MCM
25/02/2020
4
?
The use of the Herfindahl index in
merger analysis
?
Recall
N
H = ?s
i =1
?
25/02/2020
2
i
( )
? P c ? MCi qic ? H
?=
si ?
?
c
? ?
P
i =1 ?
?
?
N
Antitrust convention: multiply H
by 10000, so
? For perfect competition: H=0
? For monopoly: H=10000
5
?
Consider a merger of 2 of 5 equalsized firms
? Initial
value of H is 1/5(10000)=2000
? After the merger,
H=[(2/5)2+3(1/5)2](10000)=2800
? H=800,
indicating an unacceptable
increase of market power
25/02/2020
6
Equilibrium with Nonmerging Firms
?
?
?
?
25/02/2020
Consider 3 equal-sized firms, two of which merge
The Herfindahl approach would start with
H=1/3(10000)=3333, then change to
H=((2/3)2+(1/3)2)10000=5555 after the merger
The equilibrium approach would suggest, in
stead, that H=1/2(10000)=5000 after the merger
The Herfindahl approach would overestimate the
change in H, but indicate the sign of welfare
change correctly
7
Coordinated Effects of Mergers
?
Necessary conditions for successful
collusion:
1.
2.
3.
?
25/02/2020
A collusive arrangement to restrict
output so as to raise price
Means to detect deviation from the
collusive arrangement
The ability to punish cheaters
The increase in concentration as a
consequence of a horizontal merger
may enhance the probability of
successful collusion
8
Entry
?
?
25/02/2020
The high price, hence, high
profitability that follows a merger is
likely to attract new entry
The effect of a merger crucially
depends on the existence and the
height of barriers to entry
9
Mergers: The Antitrust Framework
?
?
?
25/02/2020
Merger guidelines
? US: 1982 Merger Guidelines
? UK: Enterprise Act 2002 Merger Guidelines
? EU: Merger Regulation (May 2004)
Market definition
? Relevant antitrust market
? Hypothetical monopolist test
Market structure and concentration
? Post merger HHI >1800 as highly
concentrated, then a merger with ?HHI > 50
may give rise to potential competition
concerns
? post merger HHI > 1000 as concentrated,
then a merger with ?HHI > 100 may give rise
to potential competition concerns
10
?
?
?
?
?
25/02/2020
Substantial lessening of competition test
? Non-coordinated (unilateral) effects
? Coordinated effects
Entry and product repositioning
? Barriers to entry
? Scale of entry
? Timeliness and sustainability of entry
? Supply side substitutability and imports
Countervailing buyer power
Failing firm defence
Efficiencies
? A bias toward consumers benefits
? Efficiencies that increase rivalry
? Efficiencies that lessen competition but still
increase consumer benefits
11
Topic 7 Game Theory II
?
1.
2.
3.
4.
5.
02/03/2020
Extensive form representation
Identity and number of players
Timing of moves by each player
Choice of actions at each move
Information about history of the
game
Payoffs over all possible
outcomes
1
Game Tree
1.
2.
3.
4.
02/03/2020
Decision Nodes: A
players turn to
move
Branches: actions
available at each
move
Terminal Nodes:
payoffs
Information Sets:
knowledge about
the history of the
play of the game at
each move
2
Game Tree
1.
2.
3.
4.
02/03/2020
Decision Nodes: A
players turn to
move
Branches: actions
available at each
move
Terminal Nodes:
payoffs
Information Sets:
knowledge about
the history of the
play of the game at
each move
3
Game Tree
?
?
02/03/2020
This is an
extensive form
representation of
the prisoners
dilemma game
This is an
example of
game of
imperfect
information
4
Game Tree
Game of perfect
information
02/03/2020
Game of imperfect
information
5
Strategies vs. Actions
?
?
In static game, a strategy and an
action are the same thing
But in a dynamic game, they are
different
?
?
02/03/2020
A strategy specifies an action for
a player to take at each of her
decision node, even if it is not
reached in the actual play of the
game
A strategy is a complete
contingent plan
6
An Example
Player 2s strategies:
1.
If player 1 plays u, then play U.
If player 1 plays d then play U.
Denote by (U,U)
2.
If player 1 plays u, then play U.
If player 1 plays d then play D.
Denote by (U,D)
3.
If player 1 plays u, then play D.
If player 1 plays d then play U.
Denote by (D,U)
4.
If player 1 plays u, then play D.
If player 1 plays d then play D.
Denote by (D,D)
02/03/2020
Normal Form
(U,U)
(U,D)
(D,U)
(D,D)
u
5,2
5,2
1,0
1,0
d
4,4
6,0
4,4
6,0
7
Nash Equilibria
(U,U) (U,D) (D,U) (D,D)
u
5,2
5,2
1,0
1,0
d
4,4
6,0
4,4
6,0
?Underline all best responses
?In a Nash equilibrium all player play
their best responses
?Nash equilibria: (u,(U,U)) and (d,(D,U))
02/03/2020
8
Noncredible Threat
?
(d,(D,U))
02/03/2020
9
Subgame Perfect
Nash Equilibirum
?
A subgame is smaller
game embedded in the
complete game
?
?
02/03/2020
Starting from some point
in the original game and
including all subsequent
nodes and branches
Not cutting any
information sets
10
Subgame Perfect
Nash Equilibirum
(u,(U,U))
?
02/03/2020
A Subgame perfect
Nash equilibrium
(SPNE) is a strategy
profile that the
strategies in every
subgame are a Nash
equilibrium
SPNE
(d,(D,U))
Not SPNE
11
Find SPNE of Finite Game
by Backward Induction
02/03/2020
12
Exercise: Centipede Game
02/03/2020
13
Two Stage Games
02/03/2020
U
D
u2
3,3
0,5
d2
5,0
1,1
U
D
u2
3,3
2,2
d2
2,2
1,1
14
Games of Almost
Perfect Information
?
A repeated game consists of a
static game that is repeated
1.
2.
?
02/03/2020
Finitely Repeated Games
Infinitely Repeated Games
(supergames)
Players know the entire history of
the play of the game except for
the actions of their opponents in
the current stage.
15
Finitely Repeated Games
Example: Twice-repeated Prisoners Dilemma Game
02/03/2020
Clam
Rat
Clam
3,3
0,5
Rat
5,0
1,1
Clam
Rat
Clam
4,4
1,6
Rat
6,1
2,2
16
?
Conclusion: SPNE for twicerepeated Prisoners Dilemma
game is
Playing Nash equilibrium (R,R) in
each stage
?
The result can be extended to
T-times repeated games
?
02/03/2020
Using backward induction
works as long as T is finite
17
Infinitely Repeated Games
?
Interpret stages as time periods
Discount of payoffs
? Discount factor (?) and discount
rate (r)
? = 1/(1+r)
? Present value of payoff
Vi=? ?t=1 ? t-1?i(t)
?
02/03/2020
18
SPNE of Infinitely Repeated Games
?
?
Backward induction does not work in
supergames
Example: infinitely repeated Prisoners
Dilemma game
?
Playing (Rat,Rat) in each period
?
?
?
?
But can they do better?
?
02/03/2020
It is a Nash equilibrium
It is also a N.E. in each subgame
Therefore, it is a SPNE
E.g., can they possibly sustain the
cooperative outcome (Clam,Clam)?
19
?
?
?
Consider both playing the trigger strategy:
Play Clam in first period (t=1). Thereafter play
Clam at all t as long as no one has ever played
Rat; otherwise play Rat forever.
Is this a SPNE?
I.e., does this give rise to a N.E. in all
subgames?
There are two types of subgames:
1.
2.
02/03/2020
Both have always played Clam in the history
At least one has played Rat on at least one
occasion in the history
20
1.
?
?
?
02/03/2020
When both have always played Clam in the history
Given the opponent is playing the trigger strategy,
the payoff from also doing so and playing Clam is:
VC = ? ?t=1 ? t-13
= 3/(1- ?)
The payoff from deviation and playing Rat is:
VR = 5+? ?t=2 ? t-11
= 5+ ? /(1- ?)
The strategies are Nash if VC ? VR,
i.e.,
3/(1- ?) ? 5+ ? /(1- ?)
or
? ? 1/2
21
2.
?
?
02/03/2020
When at least one has played Rat on at least one
occasion in the history
Given the opponent is playing the trigger strategy,
hence, will play Rat forever, the best response is to
play Rat forever, consistent with the trigger strategy
The strategies are Nash
22
?
Conclusion
1.
2.
02/03/2020
Both playing the trigger strategy is
a SPNE if the players value the
future sufficiently (? ? 1/2)
In the infinitely repeated Prisoners
Dilemma game, it is possible to
sustain the cooperative outcome
(Clam, Clam)
23
Topic 8 Dynamic Models of
Oligopoly and Collusion
?
?
?
?
09/03/2020
Collusion – Concerted actions
among oligopolists
The gain from collusion
Reaching an agreement
Sustainability of collusion
? The supergame approach
1
The Gain from Collusion
?
09/03/2020
Profit Possibility Frontier (PPF)
2
?
09/03/2020
Constant unit costs and PPF
3
Reaching An Agreement
?
?
?
?
09/03/2020
Room for market power to grow
Division of the gain of collusion
Explicit (cartel) vs. tacit
agreements
Way of communication and
coordination
4
Sustainability of Collusion
09/03/2020
?
The classic oligopoly models predict that
firms have incentives to cheat on a
collusive agreement
?
The analysis relies on a static
framework
?
There are critiques on the classic
oligopoly models:
5
The oligopolist interaction is repeated
over and over, hence the firms should
recognise their mutual
interdependence and maximise joint
profits (Chamberlin 1933)
? Theory of oligopoly should address
the oligopolists problem: how to
police or enforce a collusive
agreement
?
09/03/2020
6
?
The factors that affect the ability
to police an agreement
1.
2.
3.
09/03/2020
Detection
Speed of punishment
Strength of punishment
7
?
Dynamic games
Firms can react to cheating
behaviour in a multi-period
situation
? Punishment (retaliation) to
cheaters can be devised
? The questions then turn to be:
?
1) Is
the threat of punishment credible?
2) Is the punishment harsh enough?
09/03/2020
8
Supergames
?
?
?
09/03/2020
Infinitely repeated Bertand duopoly game with
discount factor (?)
Payoff: Vi=? ?t=1? t-1?i(pi(t),pj(t))
Notations:
Monopoly price: pm
Monopoly profit: ?m
Bertrand price of firm i: piB = mc (marginal cost)
Bertrand profit of firm i : ?iB = 0
Collusive price of firm i: pi* = pm
Collusive profit of firm i: ?i* = ?m/2
Deviation price of firm i : pid = pm ? ? (??0)
Deviation profit of firm i : ?id = ?m
9
?
Consider the grim trigger strategy:
?
?
?
Collusion can be supported by the trigger
strategy as a SPNE if
1.
2.
09/03/2020
Play the collusive price in each period if
all other firms have done so in the past
(Collusion)
If any firm has ever deviated from playing
its collusive price, play the Bertrand price
(Punishment)
The punishment is credible
No firm wants to deviate from the
collusion
10
Subgame Perfection
1.
2.
The threat is credible: it is a Nash equilibrium in subgames
where some firm has cheated in the past
The incentive to deviate from the collusive output
?
Payoff from a deviation (given no firm has deviated
before ?) is:
Vid= ?id +? ?t= ? +1? t-??iB
= ?m
?
Payoff from continuing to cooperate is:
Vi*= ? ?t= ? ? t-??i*
= ? i * /(1-?) = ? m /(2(1-?))
?
Deviation is not profitable if Vi* ? Vid, i.e.,
or
09/03/2020
? m /(2(1-?)) ? ?m
? ? 1/2
11
Some Factors that Influence the
Sustainability of Collusion
?
Public prices
?
?
?
09/03/2020
Detection will be easier if firms
can observe prices or output of
rivals
Secret price discount makes
detection difficult
Uncertainty of demand conditions
12
?
Number of competito
