More work is needed on formulating tractable models of multi-homing demand, and
integrating them with endogenous multi-homing by advertisers. Various models of
multi-homing demand per se have indeed been formulated, such as
Kim and Serfes
(2006)
, and Anderson et al. (2015 forthcoming), based on the Hotelling (1929) spatial
model.
Anderson and Neven (1989) use a Hotelling-based model to describe consumers
mixing between products (called “roll-your-own” preferences by
Richardson, 2006).
52
There is also the random utility discrete-choice model of Gentzkow (2007).
While the work by
Anderson et al. (2013b) described above does integrate partial
multi-homing on both sides of the market, the model is not very tractable, and does
not readily extend (for example, to more platforms). That model can also usefully be ana-
lyzed with the alternative equilibrium concept of observable ad levels (in that vein,
repeated interaction and long-term reputation effects could be usefully addressed, and
the details ought to be fleshed out).
There is therefore still a need for tractable and workable approaches to break out the
two-sided interaction when both sides are partially multi-homing.
53
Indeed, one path is
to develop the time-use model in
Anderson and Peitz (2015): the model of ad congestion
they engage is one way to deliver such interaction.
Other questions, in addition to the anti-trust treatment for such markets (see
Chapter 6, this volume), include the effects of multi-homing on the other dimensions
of competition, such as content provision. As discussed in the next section, content pro-
vision is impacted by multi-homing because of the desirability of attracting exclusive (i.e.,
single-homing) consumers so that platforms strive to provide content valued by single-
homers to the exclusion of multi-homers.
2.5. EQUILIBRIUM GENRE CHOICES
In the broader perspective, program quality, type, and variety of offerings are paramount
to evaluating consumer satisfaction with media. The analysis so far has concentrated on
performance with respect to advertising choices while taking as given the program offer-
ings by platforms. Yet the types and numbers of choices provided in the market are argu-
ably at least as important to performance. We now explore these extra dimensions to
performance.
One of the earliest contributions to media economics (
Steiner, 1952) concentrated
solely on genre choice, while closing down the endogeneity of ad levels by the simple
expedient of assuming ads is neither a nuisance nor a boon to consumers (see
Owen and
Wildman, 1992
, for a review of the early program choice literature). We start at this
52
Variants of this have indeed been already deployed in the context of media economics—see, e.g., Gal-Or
and Dukes (2003)
, Gabszewicz et al. (2004), Richardson (2006), and Hoernig and Valletti (2007).
53
A theoretical analysis of this issue in the canonical two-sided market is Jeitschko and Tremblay (2015).
78
Handbook of Media Economics
point, and are able to draw on an extant literature on product differentiation with fixed
prices. We then expand the scope to consider the role of endogenous ad choices in a full
two-sided market context.
Steiner (1952) enunciated the duplication principle whereby media offerings tend to
concentrate (and double up) in genres with large consumer interest. Put succinctly by
example, if 70% of media consumers will only listen to country music, and 30% will only
listen to rock, and if there is only room for two radio stations (due to spectrum con-
straints), then the market equilibrium will have two country stations. A two-channel
monopolist will provide one channel catering to each type and so cover the full diversity
of tastes.
Beebe (1977) amended the setup to allow consumers to have second preferences, and
christened the Lowest Common Denominator outcome whereby a monopolist could
provide a low-tier program type that many types would listen to, while competition
could provide more specialist higher-tier programming. These themes are developed
more in
Chapter 1 (this volume) and implications for merger analysis are developed
in Chapter 6 (this volume). Of particular note is the implication that programming
choices are driven by advertisers’ desire to impress consumers of genres more likely to
buy the advertised products. Even if many consumers are interested in Nature programs,
their preferences are not given much weight in a market system with ad finance if they are
unlikely to respond to ads: sitcoms with ad-responsive viewers can instead attract multiple
(duplicative) offerings. The upshot is a first-degree market failure when preferences can-
not be expressed through the market by viewer willingness-to-pay. Of course, such
problems are likely to be largely mitigated in the modern context where product offerings
are many, and consumers who are unattractive to advertisers can find their market voice
through paying directly for content.
Steiner’s duplication principle finds its natural parallel in Hotelling’s (1929) principle
of minimum differentiation. However, while Steiner envisaged fixed “buckets” of
viewers, Hotelling’s model allowed for a continuum of types. The “fixed-price” version
of Hotelling’s model was extended to multiple outlets by
Eaton and Lipsey (1975), and
many subsequent authors elaborated upon the theme. One feature of such spatial models
of localized competition
54
is that there are multiple equilibria (for six or more outlets in
the linear market case) when a fixed number of outlets choose locations simultaneously,
and that different positions can earn different profits, so some locations are more profit-
able than others in equilibrium. This raises the question of how outlets might compete, in
a broader setting, to get the better locations, and also the question of equilibrium numbers
of firms under free entry. One way to tackle the problem is to consider sequential entry of
foresighted outlets that accounts for both the locations of subsequent entrants and the
54
The term localized competition refers to the idea that outlets compete directly only with neighboring
outlets in the underlying space of program characteristics.
79
Two-Sided Media Markets
possibility of deterring their entry. The problem is quite complex because an outlet must
consider the locations of future entrants, and how to use future entrants’ incentives to
their own advantage (see, for example,
Prescott and Visscher, 1977). Due to the fact that
entrants must fit between existing outlets (in their programming formats), the upshot can
be that outlets in the market can earn substantial pure profits in equilibrium (see, e.g.,
Archibald et al., 1986, for a forceful argument). The market may therefore involve a
far sparser coverage of product variety than would be suggested by models where outlets
are spaced so that all earn zero profit.
We now introduce ad nuisance into the spatial duopoly framework. We first treat SHCs,
and then allow for multi-homing.
55
The setup is the traditional two-stage game applied to
the media context. That is, we seek equilibria at which platforms first choose locations while
rationally anticipating the subsequent (second-stage) equilibrium in ad levels (and subscrip-
tion prices, when pertinent). The overarching principles governing equilibrium locations
balance two effects in the first-order conditions for best responses. First is the “direct” effect
of moving toward the rival. This is positive, and picks up the idea that with full prices
constant, consumer bases increase when moving inward. Notice that this is the only effect
in models with fixed prices, and is the driving force behind the Principle of Minimum
Differentiation noted above. The second effect is the “strategic effect” that moving in tends
to intensify competition by harshening the rival’s full price (in the pricing sub-game induced
by locations) and so hurts profit. This effect induces the desire to move away to relax com-
petition. A balance between the two effects characterizes an interior solution.
With these effects in mind, several results can be drawn off the shelf from existing
equilibrium models of spatial competition. First of all, there is a direct mathematical
equivalence between standard models of price competition and models of ad finance
when advertisers all have the same willingness-to-pay, v. To see this, notice that then
i’s profit is given by π
i
¼va
i
N
i
γa
i
;γa
j
: writing p
i
¼γa
i
, we have π
i
¼ v=γðÞp
i
N
i
p
i
; p
j
,
so that the profit is proportional to that in an equivalent pricing game. The solutions
are then those of the pricing game corresponding to the demand system induced by
the spatial structure that generates the demand N
i
(p
i
; p
j
). To take a central example, sup-
pose that consumers are located on the unit interval and consumer disutility (transport)
costs are quadratic functions of distance, as per the modification of
Hotelling’s (1929)
linear-cost model propounded by D’Aspremont et al. (1979). Then the location outcome
(at least when locations are restricted to the unit interval) are the extremes, giving rise to a
“maximum differentiation” result. This is because the strategic effect of relaxing compe-
tition dominates the direct effect for all interior locations for this disutility specification.
55
Gabszewicz et al. (2004) analyze the free-to-air TV model allowing consumers to mix between the pro-
grams of the two channels (as in
Anderson and Neven, 1989). Gabszewicz et al. (2004) assume that ad
nuisance is a time-weighted sum of ad nuisances to a power μ > 0 (i.e., the sum of a
0
μ
and a
1
μ
). When
μ <
ffiffiffi
2
p
, they find that platforms are at the extremes (the “normal” case would indeed fall in this range
because μ ¼1). It is only for higher μ that platforms move in.
80
Handbook of Media Economics
Taken literally, then, the prediction for genre choice is maximal variety difference
between competing platforms, opposite the minimum differentiation (or duplication à
la Steiner) predicted when there are no ad-nuisance costs. The inclusion of the nuisance
cost leads platforms to separate to avoid ruinous competition in the ad “price” paid by
consumers, and so to endogenously induce mutually compatible high levels of ads. Note
that the social optimum in this model is to locate at the quartiles, so the equilibrium is too
extreme.
When the advertiser demand is not perfectly elastic,
Peitz and Valletti (2008) show
that (with a concave revenue per viewer, R(a)) maximal differentiation still prevails
for high enough disutility (transport) rates. For lower rates, platforms move closer in
equilibrium as the direct effect kicks in. Likewise, lower ad-nuisance costs, γ, decrease
differentiation, although duplication (minimum differentiation) never arises for γ > 0,
for then ads and profits would be zero, which platforms avoid by differentiating.
We can also use the spatial analysis of
Section 2.2 to determine the equilibrium out-
come for a mixed-finance system (ads and subscription prices to consumers). Recall then
from
(2.2) that i’s profit is given by π
i
¼ s
i
+ Ra
s
ðÞðÞN
i
f
i
; f
j
, where a
s
solves R
0
a
s
ðÞ¼γ
and with f
i
¼s
i
+ γa
s
. This is therefore equivalent to a situation in the standard pricing
model where platforms have negative production costs, as we previously established.
Hence (modulo the caveat discussed next on non-negative subscription prices), the loca-
tion outcome is maximal differentiation with platforms setting ad levels to equate marginal
ad revenue per viewer to nuisance cost (
Peitz and Valletti, 2008).
Gabszewicz et al. (2001) engage the model above with a surprising twist by assuming
that platforms cannot feasibly set subscription prices below zero—if people were paid to
take newspapers, clearly they would walk off with stacks of them. This floor can change
the outcome quite dramatically. In their model, they assume no ad nuisance (γ ¼0) so
that the condition R
0
a
s
ðÞ¼γ for the ad level implies that ads are set at the per-consumer
monopoly level, a
m
. However, the tenor of their results applies more generally.
56
They
show that if ad revenue is weak enough, then maximal differentiation attains; while if it is
high enough, the outcome is minimum differentiation with free-to-air media (and both
constellations are equilibria for some intermediate values).
57
56
They assume ad demand is linear. They also consider a three-stage game with locations, then subscription
prices, then ad levels. However, as they show, in the last stage the ad level is set at the monopoly level, a
m
,
so that the upshot is the same.
57
Bourreau (2003) analyzes a similar model appending quality investment, where quality raises consumer
valuations vertically across the board. He contrasts advertising-financed and pay TV outcomes. In both
cases, he finds equilibria that are symmetric in qualities (mimicking). Pay TV gives extremal horizontal
location outcomes, as per
D’Aspremont et al.’s (1979) classic extension to quadratic transport costs of
Hotelling’s (1929) model. For advertising finance, he considers a two-stage location then quality game
with advertising revenues fixed per viewer. The direct location incentive is toward minimal differenti-
ation (counter-programming); this is offset by a strategic effect of more intense quality competition.
The latter effect is weaker the lower are ad revenues, and he finds that minimal differentiation is reached
as ad revenues go to zero.
81
Two-Sided Media Markets
The reasons can be ascribed to the interplay of strategic and direct effects. For weak ad
demand, subscription prices are paramount, and platforms ensure these are high by dif-
ferentiating maximally, which is just an extension of the standard pricing result. How-
ever, for strong ad demand the direct effect takes over because picking up consumers
to deliver to advertisers becomes predominant. When platforms are close enough
together, subscription prices are floored at zero. This takes away completely the strategic
effect and we are back to the model with fixed prices and hence minimum differentiation.
Gabszewicz et al. (2001) relate their finding to the idea of the “Pensee Unique,”
which is a social context in which discrepancies among citizens’ political opinions are
almost wiped out (p. 642) (see Part III of this volume, and in particular the discussion
in Chapter 14).
Gabszewicz et al. (2004) relate the degree of differentiation of free broadcasters to
the elasticity of the nuisance term, higher elasticity leading to less differentiation. Location
choice induces a strategic effect that works through increased levels of advertising when
differentiation increases, which explains why free-media platforms may choose maximal
differentiation. This effect is reduced if consumer demand is very elastic to advertising,
as advertising will vary little with location, and in this case differentiation will be smaller.
Many models compare free-to-air versus pay and thus take the payment technology as
given (an early example is
Hansen and Kyhl (2001), whose thought experiment is to con-
sider a ban on using pay-walls for important sporting events and so put the programming
into the free public domain of commercial broadcasting). For instance,
Peitz and Valletti
(2008)
show that pay-platforms deliver more advertising and higher total welfare than
free platforms when the nuisance from advertising is small. The reason is that large rev-
enues from advertising are passed through to consumers (a see-saw effect). In the context
of the
Vickrey (1964)–Salop (1979) model with free entry (discussed further below),
Choi (2006) shows that, contrasting with excessive entry in pay media, free media
may induce insufficient or excessive product diversity. A difficulty with these compar-
isons is that, as pointed out by
Gabszewicz et al. (2001), whether media platforms are paid
or free depends on the nuisance and constraints on payments. It is when ad nuisance is
small and therefore advertising revenue large, that platforms will prefer to be free rather
than charging a positive subscription price.
Several papers discuss endogenous content quality in media markets.
Armstrong and
Weeds (2007)
analyze program quality in a symmetric Hotelling duopoly under pay TV
and pure advertising–funding, respectively.
58
They find that quality is lower in
ad-financed duopoly than in a duopoly where both platforms use mixed financing. This
is because of the higher marginal profitability when two revenue extraction instruments
are available.
Armstrong and Weeds (2007) get several other interesting results. Under
58
The analysis is extended by Weeds (2013) to a mixed duopoly comprising a free-to-air broadcaster and
another one that uses mixed finance. See also
Weeds (2012).
82
Handbook of Media Economics
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