Regulation and Antitrust Collusion and horizontal agreements Christine Zulehner Summer term 2011

Regulation and Antitrust
Collusion and horizontal agreements
Christine Zulehner
Department of Economics
Johannes Kepler University Linz
Summer term 2011
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Adam Smith (1776) already noticed that
people of the same trade seldom meet together, even for merriment
and diversion, but the conversation ends in a conspiracy against the
public, or in same contrivance to raise prices ....
Illustration: newspaper industry in Detroit
in 1989, Detroit Free Press and Detroit News were allowed to merge
although they formed a monopoly as Free Press was about to fail
the two papers further appeared as two entities, but the firm merged
on all other aspects like cost, setting rates, advertising and so on.
firm acted as a monopoly and we observed a change in profits: each
lost about 10 Mill. a year, afterwards profits were high as 150 Mill
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Incentive to collude
Linear demand: p = a − b ∗ q and constant marginal cost: MC = c
maximize: π = (p − c) ∗ q = (a − bq − c) ∗ q
FOC: dπ
dq = a − 2b ∗ q − c = 0 → q = 2b and p =
πM =
Cartel of two firms i = 1, 2: πiCartel =
Cournot competition among two firms i = 1, 2
maximize π1 = (a − b ∗ (qi − q2 ) − c) ∗ q1
FOC: dπ
dq = a − 2b ∗ q1 − b ∗ q2 − c = 0
3b = q2 ,
→ q1 =
and p =
Price competition among two firms i = 1, 2: πiBertrand = 0
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Collusion and cartels
Collusion theory
Factors that facilitate collusion
Policies against collusion
Calculation of cartel damages
chapter 4 in Motta (2004): Competition policy: Theory and practice
chapter 7 in Davis and Garces (2010): Quantitative techniques for
competition and antitrust analysis
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Collusion and cartels
What is collusion?
since total industry profits in oligopoly are always lower than monopoly
profits, firms will attempt to establish agreements among each other to
eliminate competition
What is a cartel?
institutional form of collusion
attempt to enforce market discipline and reduce competition between a
group of suppliers
cartel members agree to coordinate their actions (prices fixing, quotas,
consumer allocation, bid rigging)
prevent excessive competition between the cartel members
secret agreements, because cartels illegal in the US and EU
Tacit collusion: mutual understanding without explicit agreement
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Incentives to cheat
Main problem with cartel agreements as well as tacit collusion
temptation to cheat on competitors
if all other firms stick to the agreement, you can increase profits by
deviating and stealing your rivals’ business (undercutting, violating
territories, etc)
comparable to a Prisoner’s dilemma
To sustain collusion, cartel must be able to
detect deviators: can you give an answer to a question like “Have prices
decreased as someone deviated or as demand decreased?”
punish the deviator(s): which strategies are possible?
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The diamond cartel
De Beers established in South Africa in 1888 by Cecil Rhodes
owned all diamond mines in South Africa
had joint ventures in Namibia, Botswana, Tanzania
controlled diamond trade (mines → cutters and polishers) through
“Central Selling Organization” (CSO), processing about 80% of world
CSO’s services for the industry
expertise in classifying diamonds
stabilizing prices (through stocks of diamonds)
advertising diamonds
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The diamond cartel cont’d
Huge temptation for mining companies to bypass CSO and earn high
margins themselves
In 1981, President Mobutu announced that Zaire (world’s largest supplier of
industrial diamonds) would no longer sell diamonds through the CSO
Two months later, about 1 million carats of industrial diamonds flooded the
market, price fell from $3 to less than $1.80 per carat
Supply of these diamonds unknown, but very likely retaliation by De Beers
In 1983, Zaire renewed contract with De Beers, at less (!) favorable terms
than before
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The law
Cartel laws make cartels nowadays illegal in the US and Europe
US: jail sentences (DRAM cartel)
exception in the US: export cartels
exception in Austria: “Bagatellkartelle”
Cartels have always been with us and still are
Some are explicit and difficult to prevent (OPEC)
Other less explicit attempts to control competition
Authorities continually search for cartels
improving methods detecting cartels like price screening
leniency programs
have been successful in recent years (nearly $1 billion in fines in 1999)
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The vitamin cartel
EC has found that 13 European and non-European companies participated
in cartels aimed at eliminating competition in the vitamin A, E, B1, B2, B5,
B6, C, D3, Biotin (H), Folic Acid (M), Beta Carotene and carotinoid
A striking feature of this complex of infringements was the central role
played by Hoffmann-La Roche and BASF, the two main vitamin producers,
in virtually each and every cartel, whilst other players were involved in only a
limited number of vitamin products → severity of punishment
Hoffman-La Roche AG
Aventis SA
Solvay Pharmaceuticals
Merck KgaA
Daiichi Pharmaceuticals Co Ltd
Eisai Co Ltd
Takeda Chemical Industries Ltd
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Fines in mill A
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Collusion theory
Noncooperative collusion in a static model vs. repeated games
dominant firm model
dynamic strategies
Factors that facilitate collusion
market structure
price transparency and exchange of information
pricing rules (facilitating practices)
Further reading
imperfect information and non-cooperative collusion (Greene and
Porter 1984)
price wars during booms (Rotemberger and Saloner 1986)
impact of cyclical demand movements on collusive behavior
(Haltiwanger and Harrington 1986)
collusion with capacity constraints (Fabra 2006)
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Noncooperative collusion in a static model
N firms produce a homogenous product
let the inverse demand function be linear
p = a − bQ with Q =
i =1 qi
constant average and marginal cost
c(qi ) = c
F of the N firms form the fringe
each firm in the fringe acts as a Cournot quantity setting oligopolist
it maximizes its own profit taking the the output of the other firms as
the remaining K firms restrict output and maximize joint profits taking the
behavior of the fringe into account
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Noncooperative collusion in a static model
profit maximization
maxπj = pqj − cqj = (a − bQ)qj − cqj
FOC: ∂qjj = (a − bQ) − bqj − cqj = 0
→ 2bqj = a − c − bQK − bQF −j
each fringe firm selects output along a best-response curve
qj = 12 (S − QK − bQF −j )
with S = a−c
k=1 qk the output of the restrictive group
b and QK =
QF −j is the combined output of all fringe firms except firm j
in equilibrium all fringe firms produce the same output
QF −j = (F − 1)qj
qj = 12 (S − QK − bQF −j )
qj = S−Q
F −1 and QF = F F +1
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Noncooperative collusion in a static model
residual demand function the restrictive group is facing
p = a − b(QK − QF )
p = c + F +1
(S − QK )
profit maximization
maxπk = pqk − cqk
given residual demand, the profit maximizing per firm and total output are
qk =
1 1
K 2S
and QK = 12 S
the output restricting group acts as Stackelberg leader
qf =
1 1
F +1 2 S
and p = c +
1 1
F +1 2 bS
profits per firm of firms inside and outside the restrictive group
πk (F , K ) =
K (F +1) 2 S
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and πf (F ) =
(F +1)2 ( 2 S)
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Noncooperative collusion in a static model
questions: is this a stable situation? is there an incentive to deviate?
assume first, all firms restrict output
such a situation is stable if
πk (0, N) ≥ πf (1) → N ≤ 4
if there are four or less than four firms then output restriction is stable;
if there are more than four firms that restrict output, each firms share
of the monopoly profit is too small; each firms should defect and act as
an independent Cournot firm
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Noncooperative collusion in a static model
if the number of fringe firms is positive, the conditions for internal and
external stability can be rewritten as
F +1+
≤K ≤F +3+
F +1
necessary and sufficient condition for internal stability: no restricting
firm wants to deviate
necessary and sufficient condition for external stability: no fringe firm
wants to deviate
enough firms in the fringe so that fringe profits are not too great and
output restricting firms have no incentive to join the fringe
enough firms restricting output so that fringe firms do not want to join
the output restricting firms
since F and K are integers, this implies that if there are F firms in the
fringe, output restriction is stable only if output restriction is by groups
of F + 2 or F + 3 firms
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Noncooperative collusion in repeated games
static models omit an essential element of the cost of defecting from an
output restricting equilibrium
profit lost once rivals realize that the agreement is being violated
when firms deviate, the equilibrium output of all firms increases
other firms observe that and react by also deviating and producing more
whether output restriction is stable in a dynamic sense depends on a single
firm’s present value of short-term gains from output expansion
firms compare future discounted profits to short-run gains due to deviation
such a trade-off cannot be analyzed in a static game
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Cartel stability
in general, cartels are unstable
can we find mechanisms that give stable cartels?
violence is one possibility!
suppose that the firms interact over time
make cheating unprofitable: reward “good” behavior, punish “bad”
ingredients necessary to enforce collusion
timely detection of deviations from collusive actions
credible mechanism for the punishment of deviations
threat of punishment prevents firms from deviating
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Incentive to deviate
Cournot with two firms i = 1, 2
linear demand p = a − b ∗ (q1 + q2 ) and constant marginal cost c
maximize π1 = (a − b ∗ (q1 − q2 ) − c) ∗ q1
FOC: dπ
dq1 = a − 2b ∗ q1 − b ∗ q2 − c = 0
→ q1 = a−c
3b = q2 and p =
profits: π1 =
= π2
firm 1 sticks to the collusive agreement and firm 2 deviates by playing a best
profits of firm 1: π1collude =
profits of firm 2: π2deviate =
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> π1collude
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Repeated games
formalizing these ideas leads to repeated games
a firm’s strategy is conditional on previous strategies played by the firm
and its rivals
profits from cheating are taken into account
repeated games can become very complex
strategies are needed for every possible history
but some “rules of the game” reduce this complexity
Nash equilibrium reduces the strategy space considerably
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Finite vs. infinite games
number of periods played is known and finite
credibility of punishment strategies and possibility of cooperation
backward induction
Selten theorem: if a game with a unique Nash equilibrium is played
finitely many times, its solution is that Nash equilibrium played every
suppose the cartel expects to last indefinitely
equivalent to assuming that the last period is unknown
every period there is a finite probability that competition will continue
now there is no definite end period
so it is possible that the cartel can be sustained indefinitely
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Noncooperative collusion in a repeated game
Intuition: cartels solve the cheating problem by threatening to punish
deviators in the future
homogenous good duopoly
constant symmetric MC
in each period t = 1, 2, 3, . . . , firms simultaneously set prices
“repeated Bertrand game”
One possibility
Bertrand equilibrium (i.e. p1 = p2 = MC) in each period t = 1, 2, 3, . . .
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Noncooperative collusion in a repeated game cont’d
Another possibility
collusive equilibrium (p > MC)
Suppose firms play “grim trigger strategies”:
in the first period, both firms set pM (monopoly price), and share
profits πM equally.
in any of the following periods: firm sets pM if both firms set pM in
each preceding period
if instead one of the firms violated the collusive agreement (price below
pM in previous period), then both firms set p = MC forever
(“punishment” or “retaliation”)
Is this enough to keep firms from cheating?
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Noncooperative collusion in a repeated game cont’d
If both firms stick to the collusive agreement, each has expected discounted
profits as
0.5πM + 0.5δπM + 0.5δ 2 πM + . . . = 0.5πM 1−δ
where δ < 1 is the discount factor
If firm 1 deviates today:
undercut firm 2, make profits πM today
from tomorrow onwards, p = MC, and so π = 0
→ Is collusion better than deviation?
incentive constraint: 0.5πM 1−δ
≥ πM + 0
which holds whenever δ ≥ δ = 0.5
with δ ∗ the critical discount factor
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State games
assume there is a sequence of discrete time points
at each point in time firms play a static game
repeated game
example: Cournot
a strategy vector s ∗ ∈ S = (S1 , . . . , Sn ), the strategy set, is a
noncooperative equilibrium if each element of s ∗ maximizes the
corresponding player’s payoff taking other elements of s ∗ as given
πi (s ∗ ) = maxsi ∈Si πi (s1∗ , . . . , si∗−1 , si , si∗+1 , . . . , sn∗ ), i = 1, . . . , n
Friedman (1971) proofed the existence of an equilibrium
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Strategies in a state game
how does the firm react when, for example, another firm deviates from a
cartel behavior
strategies describe behavior of the firm
example: trigger strategies
let sncc be the strategy of the noncooperative collusion, i.e. firms
restrict their output
let snash be the strategy that gives the Nash outcome, in our example:
a trigger strategy is then
1: each player begins by playing his or her part of sncc and continues to
do as long as all other players do the same
2: revert to snash in the period following any defection from sncc and
continue to play snash forever
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Profits in each period and future discounted profits
πi ,nash < πi ,ncc < πi ,defect
such a condition holds, if the static game is Cournot, the demand function is
linear, marginal cost is constant and the same for all firms
and the sncc strategy means that each firm produces
noncooperative collusive output
PDVi ,ncc = απi ,ncc + α2 πi ,ncc + . . . =
of the
1−α πi ,ncc
with α the discount factor
PDVi ,defect = απi ,defect + α2 πi ,nash + . . . = απi ,defect +
1−α πi ,nash
compare discounted profits from the period of defection onwards
wlog we assume that this is the first period
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for a trigger strategy to be a noncooperative equilibrium, the payoff function
adhering to the trigger strategy must be at least as great as the payoff from
defection, i.e. PDVi ,ncc ≥ PDVi ,defect
PDVi ,ncc ≥ PDVi ,defect if α ≥
or using α =
πi ,defect −πi ,ncc
πi ,defect −πi ,nash
πi ,defect −πi ,ncc
πi ,defect −πi ,nash
this is always fulfilled, if r is sufficiently close to zero
or, α is sufficiently close to one, i.e. the future has the same importance as
the presence
if α is large enough, collusion can be sustained
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one can also show that the equilibrium is subgame perfect
the result is that the trigger strategy sustains output paths that allow each
player to earn more than with Cournot output
example of Folk Theorem
states that noncooperative behavior can sustain any strategy producing
individual profits larger than Nash profits, if r is sufficiently small
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Other strategies
trigger strategy: severe threat
as usual - people forget or they do not want to be that harsh
others know that, thus to stick to the Nash after defection might not
be credible
we search for strategies that are less grimm than trigger strategies
stick and carrot
tit for tat
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Coordination on the collusive price
Which collusive price? → problem of coordination
tacit collusion: costly experimentation to coordinate on a collusive
outcome, risk of triggering price wars
explicit collusion: firms coordinate on collusive outcome and avoid
problems due to shock adjustments
market sharing schemes: possible to adjust to cost and demand shocks
without triggering price wars
firms will try to talk in order to coordinate!
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Factors that facilitate collusion
Market structure
Price transparency and exchange of information
Pricing rules (facilitating practices)
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Market structure
Concentration: collusion is normally easier to maintain among few (and
similar) firms
n (1
+ δ + δ 2 + . . .) =
δ > 1 − n1
πM 1
n 1−δ
≥ πM + 0
Entry: if entry barriers are high, collusion is easier to sustain
Cross-ownership: reduces incentives to cheat, hence facilitates collusion
Regularity and frequency of orders: allow for easy detection and timely
punishment, hence facilitate collusion
Buyer Power: strong buyers can play off rivals against each other →
discourages collusion
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Market structure cont’d
Random shocks to demand: make it harder to detect deviation → discourage
Steady demand growth: makes punishment more effective → facilitates
Product homogeneity: has ambiguous effect on collusion
Symmetry: more equal distribution of assets facilitates collusion
Multi-market contacts: allow firms to leverage punishment into other
markets, hence facilitating collusion
Inventories and excess capacity: have ambiguous effect on collusion
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Price transparency and exchange of information
observability of firms’ actions facilitate enforcement
when prices are unobservable and demand is subject to shocks:
deviation is difficult to identify → collusion more difficult (possibly
involving temporary “price wars”)
information exchange of past/present prices and quantities: detailed info
likely pro-collusive
frequency auctions: simultaneous ascending auctions
code for a certain region = 02, then firms used a price like 1002 to
indicate their interest in this region
in Germany the auction design requested 10% increases when rasing
bids: Mannesmann signaled to share the market by bidding 18.8 mill
DM on blocks 1-5 and 20.0 mill DM on blocks 6-10 → why different
bids for equal products? as an answer, managers of T-Mobil increased
to 20.0 DM on the blocks 1-5
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Price transparency and exchange of information cont’d
public announcements
Telekom Austria cited in the newspapers:
“it would be satisfied with 2 out of the 12 blocks of frequencies on
offer”, but “it would bid for a 3rd block if one of its rivals did”
“collusive price” is often ambiguous (may need to be adjusted from time to
time) → exchange of information on future prices/quantities
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Pricing rules (facilitating practices)
Most favored nation (or most favored costumer) clause
engages a seller to apply to a buyer the same conditions offered (by the
same seller) to other buyers
engagement to not price discriminate → make it costly to give price
collusion: harder to deviate and costly to carry punishment
Meeting-competition clauses
if the buyer gets a better price from another seller, the current seller
would match the price
clause works as an information device and reduces incentive to deviate
Resale price maintenance
vertical price agreement → vertical restraints and vertical mergers
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Practice: What should be legal and what illegal?
Standards of proof: market data vs. hard evidence
Ex-ante Competition policies against collusion
Ex-post Competition policies against collusion
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Standards of proof: market data vs. hard evidence
Inferring collusion from data
price levels: what is a high prices? estimation price-cost margins
without cost data
evolution of prices: price parallelism is not a proof of collusion
(common shocks)
conclusion: econometric tests as complementary evidence, not proof of
collusion (results sensitive to different techniques used)
Hard evidence
communication on prices or coordination on facilitating practices
focus on observable elements verifiable in courts, to preserve legal
certainty: fax, e-mail, phone calls, video etc.
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Ex-ante competition policies against collusion
avoid formation of cartels
deterrence of collusion: close monitoring and high fines, possibly prison
sentences for managers (like US)
black list of facilitating practices might deter collusion and free resources for
cartel detection
private announcements of future prices/outputs
exchange of disaggregate current/past information
good auction design to avoid bid-rigging
merger control (joint dominance)
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Ex-post competition policies against collusion
surprise inspections (“Dawn Raids”)
to find hard evidence of collusion
leniency programmes
introduced in the US in 1978 (reformed in 1993), in EU in 1996
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Calculation of cartel damages
Main effects of a price fixing cartel
Methods to calculate “but for” prices
Pass on defense
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Main effects of a price fixing cartel
cartel overcharge harm: effect of higher prices on actual consumers
lost volume effect: effect of higher prices on lost consumers/loss of volume to
actual consumers
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How are profits of consumers affected?
decomposition of profits of purchasing firm
π = (p − c)q
Δπ = −qΔc + qΔp + (p − c)Δq
direct cost effect: overcharge times number of purchased quantity
pass on: depends on the extent to which the price increase caused by the
cartel is passed along the supply chain
output effect: reduced profits as a lower quantity is sold
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Distribution of cartel overcharges
in 93% of the cases, overcharge in % of the cartel price is above zero
small but significant proportion of cartels with no overcharge
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Involved parties
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Dynamic effects
market structure and market functioning
reduction in rivalry between firms can result in lower levels of
slowing down in the rate at which improvements in efficiency are
inefficient firms do not leave market
distortions in the downstream markets due to higher input costs
for example, the counterfactual price may have been even lower (and
hence the overcharge even higher) if the market had seen cost-reducing
innovations in the absence of the cartel
however, it may be difficult to demonstrate a causal link between the
infringement and the alleged longer-term harm
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Calculate the damages
calculation of the price-overcharge “rectangle”
period of time during which the conspiracy had an effect on prices
prices at which the conspirators sold their output
“but for” prices that would have prevailed in the market in the absence
of the conspiracy
also relevant: prices of (non-conspiring) competitors of the conspirators,
who might adjust their prices in the light of the conspirators’ prices
should include the “but for” prices of the non-conspiring competitors
the quantities sold by the conspirators during the period of the
the quantities sold by the non-conspiring competitors
calculation of the deadweight welfare loss “triangle” needs one further piece
of information
price-elasticity of demand for the product
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Methods to calculate “but for” prices
comparator based methods and models
before and after, yardstick
comparison of means, time series models, difference-in-difference
determinants of prices, forecasting
financial analysis based methods and models
cost based analysis
market structure based methods and models
theoretical/structural models
static vs. dynamic models
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Before and after
comparison of data on companies (or markets) involved in the antitrust
infringement in a particular period with data on the same companies (or
markets) in a period without the violation
before and during; during and after; before, during and after
pre-infringement data is not contaminated by the cartel
time after the cartel is obviously most recent, but the unwinding of the
cartel is perhaps not over
we would like to measure deviations from the long-run equilibrium path
appropriate when cartel period is rather short and the cartel does not induce
a change in the long-run equilibrium path
example: Grazer Fahrschulen
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Time series comparison
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cross-sectional comparator-based approach
similar markets with and without a cartel are compared
appropriate with local markets
however, where there is a risk that these comparable markets may also have
been cartelized, other methods should be considered
in combination with time series data: difference-in-difference
example: Lombard cartel
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Comparison of means or regression analysis
a comparison of means across regions or firms is applicable if there is a
treatment effect
treated and non-treated are otherwise the same, but for the treatment, i.e.,
the cartel
regression analysis can account for differences in observables
regions are not the similar, but differ in observable demand
characteristics like population density
Yi = α + βXi + δDi + i
similar considerations for firms
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Comparison of means or regression analysis
comparison over time
ARIMA models: price data is forecasted using only past observations of
cointegration and VEC models: it is possible to account for demand
and supply and other observables
infringement vs. non-infringement market in addition to period before
and during infringement
variations across firms and time are exploited
damage estimate = (period during)i - (period before)i minus (period
during)ni - (period before)ni
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Regression analysis: determinants of prices
Dummy variable approach
price = f(cartel, determinants like product characteristics)
data for different time periods or different regions
for the estimations all data is used
Residual approach
price = f(determinants)
different time periods or different regions
for the estimations data of non-cartel regime is used and predicted for
the cartel regime
implicit assumption: coefficients of the determinants are constant over
periods or regions
hedonic pricing: coefficients capture demand and supply factors
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Bid-rigging in procurement auctions
procurement auctions: lowest bid wins
mechanism to collude
division of the market
inflated bids
side payments
in any case, the expected winning bid will be higher
Porter and Zona (1999)
research question: how can we detect cartels?
application: detecting cartels in the Ohio school milk market
econometric approach
compare markets with collusion with control group: same time,
different regions
in which districts do firms submit bids?
how high are the submitted bids?
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Cost based approaches
average cost + competitive profit margin
estimation of competitive price based on past margins
cost: balance sheet data
profit margin: recover cost of capital to invest in the firm, includes risk
more applicable when parties involved are companies as opposed to
individual consumers
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Market structure based
based on an IO model the “but for” price is simulated
estimation of marginal cost, demand elasticity using data on prices and
various static oligopoly models
Bertrand competition
Cournot competition
Stackelberg model
Dominant firm model
dynamic considerations
output decisions of today influence a firm’s cost structure in the future
by learning effects
entry and exit in the industry
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Cournot model: competition in quantities
there are i = 1, . . . , n firms that maximize their profits πi
πi = p(q)qi − cqi
∂q qi
Lerner index:
+ p(q) − c = 0
with si =
= − ∂p(q)/p(q)
cartel overcharge
factual is a cartel, i.e., a monopoly with firms maximizing joint profits:
m = p(q)−c
counterfactual is an oligopoly with N firms: m(N − 1)/(N + 1)
the lost-volume effect triangle as a proportion of the overcharge rectangle is
equal to (N − 1)/2(N + 1)
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Relation b/w number of firms and lost volume effect
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Structural approach
Lerner index:
with si =
= − ∂p(q)/p(q)
rewrite: μ p(q)−c
p(q) = λ (elasticity adjusted Lerner index)
λ = 0 for perfect competition
λ = n1 for Cournot
λ = 1 for a cartel
estimation of marginal cost c using price and quantity data
inverse merger simulation that could also take changes in marginal cost into
if we also estimate λ, then we already now the extend of the cartel
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Moving from the factual/counterfactual to a final value
time period of the damage compared to the time period of the estimations
summation of losses over time, if the damages claim stretches over multiple
uprating and/or discounting cash flows to take into account the logic of
time value of money
interest from the time the damage occurred until the capital sum awarded is
actually paid
consider taxes
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Pass-on defense
under which circumstances is it plausible that the overcharge was passed on
to end-consumers
a distinction must be made between firm-specific and industry-wide
cost increases
what is the competitive environment
extend of pass-on
low pass-on: firm-specific cost increase, i.e., only the defendant is
concerned, and high degree of competition
high pass-on: under perfect competition, an overcharge that affects all
competitors in a downstream market (industry-wide) would be passed
on in full
medium pass-on: high concentration and industry-wide cost increases
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