Optimal Cartel Prices in Two Sided Markets
Federico Bo¤a1
Lapo Filistrucchi2
1 Free
2 University
University of Bolzano
of Florence and Tilburg University
July 4, 2015
CRESSE Conference 2015
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Research question
In a standard (one-sided) market when competing …rm produce
substitutable products, joint pro…ts maximization induces higher
prices than competition.
In a dynamic game, when joint pro…t maximization is not sustainable
as a cartel outcome, the "best" equilibrium for the …rms may involve
a lower than monopoly (but higher than competitive) price.
Does this property extend to two-sided markets?
The answer is no.
And it carries relevant welfare implications.
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A very well known result
Consider a standard dynamic game in a one-sided market involving
…rms selling substitute products.
Firms collude whenever it is rational for them to do so.
Suppose the aggregate pro…t-maximizing (i.e., monopoly) outcome is
not sustainable as an equilibrium behavior.
Then, the Pareto-optimal equilibrium from the viewpoint of …rms may
involve lowering the price below (or increase quantity above) their
monopoly level.
Under Nash reversion, this happens under a set of standard forms of
competition in the stage game (including Cournot and Bertrand, as
long as products are not perfect substitutes).
By lowering the cartel price (or increasing the cartel quantity), the gain
from unilateral deviation is decreased more than the decrease in the
bene…t from collusion.
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Two more results (the second one maybe less well known)
Consider a static game with …rms selling complement good. Then
monopoly price is below competitive price, or monopoly quantity is
above competitive quantity.
Positive externality from an increase in quantity not internalized under
competition.
Monopoly welfare superior to competition.
Prices are strategic substitutes and quantities are strategic
complements.
Consider now a dynamic (potentially collusive) game with
complements.
When the aggregate pro…t-maximizing (i.e., monopoly) outcome is not
sustainable as an equilibrium behavior, the Pareto-optimal equilibrium
from the viewpoint of …rms may involve increasing the price above (or
lowering quantity below) their monopoly level.
By increasing the cartel price (or reducing quantity), gain from
deviation is decreased more than the bene…t from collusion is
decreased.
Observe the similarity of the
pattern across the two cases:July 4, 2015
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Our own result
Consider …rms in two-sided markets selling two products that are
substitute (or at most independent) on both sides.
Under some conditions, in a dynamic game, colluding …rms behave as
…rms selling complements.
Intuitively, some form of complementarity in demand prevails, after
accounting for network e¤ects.
However, while with complement products collusion is bene…cial, in
"complementary" two-sided markets, collusion has interesting
distributional consequences.
It may end up decreasing aggregate welfare, in spite of a pricing
pattern suggestive of "bene…cial" collusion.
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Literature
Theory:
Rhumer (2011) (using Armstrong 2006 as a baseline). Collusion harder
to sustain under indirect network e¤ects. Incentives to deviate
increases (although even collusive pro…ts go up).
Antonielli and Filistrucchi (2011) collusion on prices and on the
editorial line.
AF build on Gabsewicz, Laussel and Sonnac (2001, EER, 2002, JPET,
2004, JEMS).
GLS & AF …nd that collusion on advertizing prices, competition on the
editorial line (i.e., political leaning) yields minimum political
di¤erentiation.
When instead collusion involves editorial line as well, political
di¤erentiation increases.
Reisinger, Ressner and Schmidtke (2009, JIE), analyze strategic
complementarity vs substitutability of advertizing quantity.
Advertising may increase with entry.
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Literature II
Empirical:
Gentzkow, Shapiro and Sinkinson (2014, AER), newspapers in the US
in 1924, Joint Operating Agreements increased political diversity
(binary)
Fan (2013, AER) - newspapers in the U.S., simulates mergers
accounting for Joint Operating Agreements (JOA)
Argentesi and Filistrucchi (2007, JAE) - newspapers in Italy, level of
prices compatible with collusion on cover price and competition on
advertising tari¤s.
Flath (2011, wp) - newspapers in Japan, resale price maintenance to
sustain collusion.
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A simple model
Based on Peitz and Valletti (IJIO, 2008).
Free-to-air television
Exogenously free (for expositional reasons, but see Calvano and Polo,
2014)
Two horizontally (and vertically) di¤erentiated channels, one per
broadcaster
Broadcasters choose advertising quantity
Viewers single-home, while advertisers may multi-home
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Readers’side I
Hotelling
Viewers uniformly located on a (0, 1) line. Political?
The market size is 1.
Channel 1 and 2 located at the two extremes of the line.
Readers bear a cost tV x when viewing a TV channel which is located
at distance x from their preferred location β.
Content is associated to advertizing.
Viewers dislike advertising, but they cannot avoid it, and incur a unit
disutility γ
Utility of a viewer R who decides to view channel i = 1, 2 and is
located at a distance x from the channel is:
uiV = k
γq1A
tV x
Viewers watch one (and only one) channel.
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Readers’side II
Demands on the viewers’side are given by:
qiV
=
γ qjA
qiA
2tV
+
1
_ i, j = 1, 2 : i 6= j
2
Note:
the allocation of viewers across the two channels is exclusively
determined by the amount of advertizing (as prices in normal markets);
channels also vertically di¤rentiated, in the eyes of viewers, due to
di¤erent levels of advertising;
vertical di¤erentiation is endogenous (while horizontal di¤erentiation is
exogenous).
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Advertizers’side
Advertizers can only sell to consumers who saw an ad and sell their
product to a share λ of those.
Advertizers’side has mass 1
Advertizers di¤er with respect to the quality of their product (uniformly
distributed).
Consumers perfectly informed on quality α.
Producers have constant (normalized to zero) MC and monopoly
power:
Able to extract the full surplus.
Advertizer advertizes in platform i if the expected pro…t from
advertizing αλqiV exceeds its cost piA
Demand:
piA
qiA = 1
λqiV
piA
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=
1
qiA λqiV
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Competition in advertizing quantities
Each broadcaster i = 1, 2 maximizes:
qiA λqiV qiA
max 1
q iA
Given qiV , it follows:
max 1
q iA
Note that:
0
qiA λ @
1
∂piA
=
∂qjA
γ qjA
qiA
2tV
1
1
+ A qiA
2
qiA λγqiA
>0
2tV
Pro…t supermodular in quantities (for qiA < 21 ):
∂2 π
=λ
∂qiA ∂qjA
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γ
2tV
Optimal cartel prices
1
2qiA > 0
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Some intuition
Products on the advertisers’side of the market are substitutes to each
other (here, in fact, independent) but will become complements once
network e¤ects have been taken into account.
Advertizing quantities are strategic complements.
Basically, advertizing quantities are prices paid by the readers.
As the price to the viewers is exogenously set to zero, pro…ts accrue
on the advertisers side only.
Firms will thus be competing in advertising quantities with complement
products as in a one-sided market.
Monopoly, by incentivizing the internalization of these strategic e¤ects,
leads to higher quantities, and lower prices, than competition.
Similarly to a one-sided market, when joint pro…t maximization is not
sustainable as a cartel outcome, sustainability of the cartel can be
obtained by pushing the collusive price towards the competitive level
(higher prices, lower quantities).
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Welfare
How about welfare?
Moving from (imperfect) competition to monopoly, advertising
quantities increase.
Viewers are worse o¤ because they view more ads.
The number of viewers declines (if aggregate demand is elastic)
Advertisers bene…t from higher advertising quantities but lose from
reaching fewer viewers.
Overall consumer welfare (viewers+advertisers) may rise or decline.
When moving from monopoly towards (imperfect) competition in order
to sustain collusion, the e¤ect is the opposite.
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Some further intuitions
Suppose viewers’prices were positive but exogenously …xed.
The main consequence would be that broacasters pro…ts would depend
not only on advertising revenues but also on viewers revenues.
By setting advertising quantity broacasters would a¤ect also viewers
quantity and thus viewers revenues.
Advertising quantities will play a similar role to viewers prices on the
viewers’side of the market.
When broacasters set advertising quantities, they would not only
compete in complement products on the advertising side of the
market, as in the simple model above, but would also be competing
with substitute products on the viewers’side of the market.
In both cases, quantities will be strategic complements.
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A linear duopoly
qiR
= R
γR piR + γRC pjR
λA qiA + λAC qjA
qjR
= R
γR pjR + γRC piR
λA qjA + λAC qiA
qiA
= A
γA piA + γAC pjA + λR qiR
λRC qjR
qjA
= A
γA pjA + γAC piA + λR qjR
λRC qiR
γAC , γRC , γA , γR , λAC , λR , λA , λRC > 0
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Conditions for "complementarity"
"Complementarity" arises if:
∂π D
i
∂b
qjR
=
,R
,A
∂π D
∂π D
i
i
+
=
∂b
qjR
∂b
qjR
| {z } | {z }
70
<0
=
γRC
2
( γR )
|
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{z
<0
qR
2 i
R
γC
}
λRC
+
|
Optimal cartel prices
γA
λR
2
γAC
2
( γA )
{z
?
γAC
qiA
}
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Intuition behind the conditions
If
,A
∂π D
i
R
∂b
qj
< 0 (i.e., ratio between own and rival’s e¤ect on advertising
quantity is larger for advertising prices than for newspaper quantities)
then
∂π D
i
∂b
q jR
< 0.
Interpretation: (endogenous) vertical product di¤erentiation to be
more important than horizontal product di¤erentiation (within a side)
Diversion ratio due to the network e¤ect must be bigger than the
diversion ratio due to the price change.
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Which side moves where?
In simple model above, ad quantities were the only instrument.
When moving from competition to monopoly, …rms act on them.
Given strategic complementarity, ad quantities increase.
In a richer model, when …rms set quantities on both sides, they have
two instruments: ad quantities and viewers quantities.
There are in general four e¤ects:
1
2
3
4
within
within
across
across
side e¤ects of viewers quantities
side e¤ects of advertising quantities
sides e¤ects of viewers quantities
sides e¤ects of ad quantities
E¤ects (1), (2) and (3) feature substitute products (hence quantities
are strategic substitutes), e¤ect (4) complement products (hence,
quantitites are strategic complements)
Ad quantities will increase if (4) is large enough (strategic
complementarity of ad quantities prevails)
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Conclusion
Presented a simple model where revenues derived only from
advertisers and advertising demand is nonlinear in viewers
Presented a richer model where revenues derived from both
advertisers and viewers and demands on both sides are linear in both
prices and quantities on the other side
To do: many things...
but at least a discussion of linearity versus non linearity;
and many examples
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