Financial Intermediation: A Transaction Two-Sided
Market Model Approach
Carlo Gozzelino1
Abstract––Since the early 2000s, the phenomenon of the twosided markets has been of growing interest in academic literature as
such kind of markets differs by having cross-side network effects and
same-side network effects characterizing the transactions, which make
the analysis different when compared to traditional seller-buyer
concept. Due to such externalities, pricing strategies can be based on
subsidizing the participation of one side (i.e. considered key for the
platform to attract the other side) while recovering the loss on the other
side. In recent years, several players of the Italian financial
intermediation industry moved from an integrated landscape (i.e.
selling their own products) to an open one (i.e. intermediating third
party products). According to academic literature such behavior can be
interpreted as a merchant move towards a platform, operating in a twosided market environment. While several application of two-sided
market framework are available in academic literature, purpose of this
paper is to use a two-sided market concept to suggest a new framework
applied to financial intermediation. To this extent, a model is
developed to show how competitors behave when vertically integrated
and how the peculiarities of a two-sided market act as an incentive to
disintegrate. Additionally, we show that when all players act as a
platform, the dynamics of a two-sided markets can allow at least a
Nash equilibrium to exist, in which platform of different sizes enjoy
positive profit. Finally, empirical evidences from Italian market are
given to sustain – and to challenge – this interpretation.
Keywords––Financial intermediation, network externalities, twosided markets, vertical differentiation
I.
in 2007. For a more detailed analysis, including pricing, there is e.g. a
2004 investigation in [1].
All these kinds of investment products, such as mutual funds, are
subject to fees charged to the client. Such charges are normally defined
by the asset management service provider and are divided between
transactions fees (which can be applied for purchase, redemption and
switch of the intermediated amount) and periodic fees (applied for the
management and the performances of the financial product), all
charged to the clients as a percentage of the total asset invested.
With regards to the distribution model, such wide amount of
products can be offered on the market via direct channels or via
different types of brokers, such as independent advisers, banks, etc.
Entailing [2], this means having a one-tire or even multiple-tiers
distribution.
Figure 1 - Distribution in an intermediatied industry
The split over the different types of brokers may significantly vary
across countries. According to [3] and [4], in US and UK the
predominant intermediary is the independent financial advisor, which
holds 70%-80% of the market, while insurance companies and banks
retain less than 10% of the market.
INTRODUCTION
T
HE distribution of financial products has undergone a
significant evolution over the last decades. The traditional
distribution concept, in which a manufacturer’s product or service is
offered to clients via a proprietary network of branches or affiliates is
now challenged at least in two directions. First, the evolution of the
technology makes now possible reaching a larger scale of potential
clients via online integrated channels when compared to the physical
territorial presence of a network of branches. Second, the development
of financial sector over the 1990s and 2000s increased the number of
products and providers available on the market leading to a higher
common knowledge of the financial system itself and in having more
educated or sophisticated clients when compared to the past.
If we take as an example the market of the mutual funds, according
to statista.com in 1997 there were on the US market 6,778 products
available to the clients. As of 2014 they were 9,260, with a total net
asset 4 times higher. Worldwide, the number of mutual funds available
grew from approximately 66.4 thousands in 2007 to approximately
79.7 thousands in 2014. Exchange Trade Funds (ETF) worldwide
assets rose more than ten times over ten years, from 205 billion in 2003
to 2,254 billion in 2013. Hedgefundfacts.org reports an exponential
increase of hedge funds, from 610 in 1990 to more than 10 thousands
Carlo Gozzelino is PhD candidate with the Department of Management,
Economics and Industrial Engineering, Politecnico di Milano, 20156 Italy
(e-mail: [email protected])
Figure 2 - Fund intermediation in US
Figure 3 - Fund intermediation in UK
Quite differently, according to [5] in Europe the distribution
network of the mutual funds is traditionally represented by banks (in
average 58.4%), insurance and pension products sellers (in average
13.7%) and financial advisors (in average 11.1%). Direct and similar
channels summed up to an average of 16.8%.
Figure 4 – Distribution networks across Europe
It must be noted that when the financial product is intermediated
another important fee to be considered is the charge of the distribution
network used. In the predominant US / UK model, where the
distribution is made by authorized financial advisers, this cost is
charged upfront directly to the client as a consultancy fee. When a
financial institution is intermediating and advising the transactions,
like in the predominant continental Europe model, such charges can be
present in the format of a rebate, which means that the asset
management provider is charged by the distribution network with a
fee, percentage of the amount object of the transaction. Using the
technical wording of a two-sided market, this means that while the
different types of distribution might have the same price level (i.e. the
sum of total charges is equal in both scenarios), there is a different
price balance (i.e. in one case the charge is applied upfront to the client
and in the other it lowers the profit on the asset management side).
A closer look to these phenomena comes also from regulatory point
of view. In facts, in 2004 the Market in Financial Instruments Directive
(MiFID, 2004/39/EC) was officially ratified by the European
Parliament explicitly aiming at regulating the financial intermediation
industry and protecting the investors by introducing concepts such as
client categorization, pre- and post-trade transparency and best
execution. Among the others, directive 2004/39/EC dictates that
regardless of the distribution model all fees must be transparent to
clients via specific prospectuses collecting all relevant details about the
investment product. As a result of the 2008 financial crisis, which
highlighted previous inefficiencies of the regulation mainly in terms of
lack of transparency and complexity of financial markets leading to
numerous unregulated trading activities, an amendment of MiFID
directive was approved in 2014 (MiFID 2, 2014/39/EC).
Formally applying starting January 2017, according to eurlex.europa.eu the key points of the new directive are:
1) Ensuring financial products are traded on regulated venues: close
loopholes in the structure of financial markets with a new
regulated trading platform called Organised Trading Facility
(OTF)
2) Increased
transparency:
strengthen
the
transparency
requirements to apply before and after financial instruments are
traded, calibrated differently depending on the type of financial
instrument
3) Limiting speculation on commodities: introduce a EU system
setting limits on the positions held in commodity derivatives
4) Adapting rules to new technologies: establish controls for trading
activities which are performed electronically at a very high speed
(milliseconds or microseconds), such as high-frequency trading
5) Reinforcing investor protection: ensure investment firms act in
accordance with the best interests of their clients, by safeguarding
their assets, offering products designed to meet their needs and
prohibiting staff remuneration and performance assessments
organized in a way that goes against their interests
The last point (specifically the Article 24 of the directive) explicitly
forbids the practice of rebates applied, prohibiting any kind of fees,
commissions or any monetary or non-monetary benefits paid by or
provided by any third party or a person acting on behalf of a third party
in relation to the provision of the service to clients. This concept –
applied to discretionary portfolio management and independent
advisers – strengthens the differentiation between MiFID and MiFID
2, according to [6], placing not only requirements increasing
compliance costs, but also challenges to the business model itself.
While as mentioned the directive will become effective starting 2017,
examples of local regulation can help forecasting possible approaches.
In June 2006, FSA in UK created the so-called RDR (Retail
Distribution Review) program which came into force on 31st
December 2012. As it focuses on independent advising, it removes the
commissions from the system to make sure advisers are not in any case
influenced by product providers. After more than a year, [6] report a
progressive withdrawn of advisory services from mass market due to
the missing profit coming from the rebate system.
This industry background shows several points in common with
what in the academic literature is referred to as a two-sided market. In
facts, in a traditional market structure all end users interact with a
service provider by performing independent and similar functions,
comparable with the traditional role of banking or financial
institutions. Such kind of networks with homogeneous users is called
one-sided to distinguish it from the so called two-sided network, which
differs by having two (or more) different types (sides) of end-users
performing different functions and two kinds of externalities
characterizing the transactions:
1) Cross-side network effects, i.e. members of each group exhibit a
preference regarding the number of users in the other group,
which is normally positive (e.g. purchasing game consoles in
order to have access to hundreds of games supplied by
independent publishers) but can be negative (e.g. consumer
reactions to advertising)
2) Same-side network effects, i.e. each group’s members have
preferences regarding the number of users in their own group,
which may be either positive (e.g. the benefit from swapping
video games with more peers) or negative (e.g. the desire to
exclude direct rivals from an online business to business
marketplace)
As shown in [7], such market structure shows particular pricing
strategies, which are normally based on subsidizing the participation
of one side (i.e. considered key for the platform to attract the other
side) while recovering the loss on the other side. This is what is
normally referred to the comparison between price level (i.e. sum of
prices charged to both sides) and price balance or price structure (i.e.
division of total charges on each side). [8] summarize the main
examples acknowledged in literature of two-sided markets, along with
their related subsidized and subsidizing segments.
Another key feature of these kind of markets is the degree of
exclusivity provided by the platform, which means whether the users
on any side are allow to refer to one and only one platform (i.e. singlehoming), rather than they can transact on multiple competing platforms
(i.e. multi-homing).
While several analyses are available with regards to several twosided markets (typical examples are the credit cards market or the
videogame industry), purpose of this paper is to apply such approach
to the financial intermediation industry. In such industry, the
application of the two-sided logic results in considering the platform
as the pure intermediary matching the offer, i.e. the suppliers of funds
and investment products, with the demand, i.e. the clients looking for
a financial product to buy, in exchange for a fee on one or both sides.
In the specific case of the financial intermediation, the discussed rebate
strategies together with the progressive disintegration of the offer,
enlarged to include third party products as opposite to internally
managed ones, leaves space for a new interpretation of the banking or
financial intermediation industry based on two-sided market
principles. In what follows, an overview of the most relevant literature
on the matter is presented and a model of the intermediation in a twosided framework is developed, to show that under specific market
conditions, there is an incentive to disintegrate and offer third party
products to leverage on typical two-sided market features and increase
profitability.
II.
RELEVANT LITERATURE
From literature point of view, we can identify mainly two
interpretations of a company’s move towards an open architecture, the
“pure” vertical disintegration (stressing the “merchant” concept and
dividing upstream and downstream markets as part of a factory
approach) and the two-sided markets (stressing the platform approach
and dividing the two sets of agents as part of a network approach). We
now start from a brief review of relevant available literature about
vertical disintegration before moving to the two-sided markets, which
are reviewed according to three main points of view: the economic
theory, the available models and the applied frameworks together with
their empirical evidences and policy implications.
A. Vertical Disintegration
The basics of the rationales behind the vertical disintegration can be
found in [9]. He suggests a theory where initially markets are small
and firms integrate their production of inputs. As markets grow, the
upstream division of some firms disintegrates to take advantage of
specialization and economies of scale, to become supplier for the
downstream industry.
When compared to the financial industry, as it did not (at least for
all incumbents) completely vertically disintegrate while opened
upstream market to other supplier, it can also be relevant referring to
[10] and the transaction cost theory developed from then onwards by
[11]. According to the latter, given the number of current competitors
in our upstream market, provisioning of mutual funds can be referred
to as a recurrent nonspecific investment, which leads to the classical
contracting market governance. What is missing in such theory and is
one of the criticality in this field, is that the clients of the downstream
market are not fully taken into account. All studies based on
transaction cost theory, like [12], mainly focus on the internal
economic flows within the company – [13] defines the transaction as
the basic unit of analysis making it central in the study of organizations
– rather than considering the impact on the client perception of the
service.
As pointed out by [14], [9] theory is missing the reason why a
specialized division of an integrated firm cannot exploit economies of
scale and supply the downstream industry in the same way as an
independent firm, meaning why vertical disintegration is needed. He
then shows via a model that vertical disintegration commits a
downstream firm not to gain a strategic advantage from the lower cost
of its upstream division. This means that, at the equilibrium, vertical
disintegration occurs if and only if it results in an industry profit that
is higher than the industry profit under integration.
In recent years, [15], while analyzing the strong M&A tendency in
the financial services industry of the 1990s, concludes that integration
appears to bring larger revenue efficiency gains than concrete cost
efficiencies, showing somehow a disincentive to integrate. This is also
confirmed by [16], who refer to the China’s manufacturing firms,
inferring that the degree of vertical integration causes a negative
impact on firm sales, market share and productivity, and a positive
impact on product prices only.
[17] analyze the disintegration and the related establishment of a
number of contracts between the separated companies as an incentive
to innovation and collaboration. They extend the concepts introduced
by [18] – in which the disintegration throughout the production chain
is seen as a way to divide into “modules” with cutting-hedge knowhow and specialization – and [19] – in which it is proven that vertical
disintegration is greater in areas where industries are localized
(specifically, in the US manufacturing industry). The same concept is
highlighted in [20] for the mortgage banking industry and by [21] who
compares the vertical disintegration to a major source of
entrepreneurial opportunities.
More specifically related with the finance industry, [22] argue that
the financial crisis faced during 2007-2009 period has one relevant
cause in the “industrial” conception of control, in light of which
financial firms vertically integrated in order to capture profits in all
phases of the mortgage industry, including the production of financial
products. They mainly show that such industrial approach drove the
deterioration in the quality of securities that firms issued and
significantly contributed to the eventual failure of the firms that
pursued the strategy.
[23] introduce the focus on the products in scope of the
disintegration. They study the context of an industry in which multiple
vertically-integrated firms compete with each other in one or more
downstream markets and have to decide whether or not to supply an
entrant with an essential input to enter the market. They introduce as
prerequisites to supply the entrant that the incumbents' inputs are
homogeneous (thus not differentiated and they also suggest some
public policy measure to ensure collusion is avoided.
While almost all literature focuses on the benefit of externalization
of intermediate goods to obtain economies of scale, specialized
divisions and lower transaction costs, one relevant aspect which is not
completely addressed in literature is the client perception of the
outsourcing compared with vertical disintegration. As an example, the
Information Technology (IT) department in the companies is expected
to meet high standards of operation and processing integrity while
offering round-the clock availability, security, and good performance;
it is now well-known and common practice that organizations are
outsourcing their IT services in order to meet the challenges exploited
in the last decades (due to the dramatic increase of technology in
companies). But while the outsourcing practice has been deeply
investigated in academic literature since the 1980s – the roots of the
information as a key value for competitive advantage, as embedded in
the value chain concept, are to be found in [24] – less focus had been
given on the specific company department transfer that it is not
transparent to the client. In facts, while the provider of commodities or
pure operational back office activities is not impacting the clients’ view
of the company, the configuration of the company as a platform, which
collects end users on the demand side to match them with the offer side
introduces externalities that are impacting the clients’ choice of
whether or not demand the specific platform for services. For this
reason, choosing whether to transfer the responsibility over such kind
of intermediate goods, meaning whether to vertically disintegrate or
open upstream market to third party providers, might require some
deeper examinations.
B. Two-Sided Markets
The available academic literature on two-sided markets can be
divided into three main pillars (this does not imply that each paper can
refer to one and only one single pillar, however they can focus on this
key directions):
1) (Non-modelled) theory underlying the platform concept, focusing
on network effects, competition and strategies to successfully
sustain a platform business model
2) Theoretical models, from the more generic framework to the
analysis of specific economics and results of strategic decisions
3) Applied models together with empirical evidences or social
implications from an industry or a set of industries, which
leverage on the more generic frameworks to tailor a sectorspecific description of the behavior of a two-sided market
From a purely theoretical point of view, the basic of a two-sided
market entails a platform dealing with two different sets of agents, all
having same-side and cross-side network relationships between them,
which challenges traditional pricing strategies and competition. [25]
describes the first identified two-sided markets as arising in the
literature of the early 2000s gathering examples in a survey over real
estate, media, software and card system industries. He depicts the key
business concerns of such markets as:
1) Getting both sides on board, as due to the network effect the
primary concern is to have sufficient agents on both sides
2) Pricing strategy and balancing interests, in terms of deciding how
to make sure prices are reflecting the interests of the two sets of
agents
3) Types of platforms, which can be coincident (i.e. multi-sided
offering substitutable products on all sides), intersecting (i.e.
multi-sided offering substitutable products on a subset of sides)
or monopoly (i.e. with no competition on any side)
4) Scaling and liquidity, meaning building right-sized liquidity
before investing into platform scaling up
A similar framework is defined by [26] who add the threat of
envelopment as a new challenge, when potentially low entry barriers
and a common user base make attractive for one platform to swallow
the network of another with little investment, requiring a constant
attention of all incumbents in maintaining the shares on both sides.
Also [27] gives an overview of business concerns of two-sided markets
while bridging the strategies (pricing, openness and other strategies)
with public policy implications, such as antitrust and regulation. In all
these researches, two-sided markets are depicted as an emerging
trending type of businesses in which the entry is attractive (due to
potentially low entry barrier, feasibility to scale quickly due to the
expected large number of agents on both sides and possibility to easily
differentiate from competitor with proven pricing strategies) but at the
same time is challenged by new business and policy concepts (such as
the winner takes it all, antitrust and policy regulations that can alter
subsidization of one side at the expenses of the other).
In more recent years, several examples are available that provide a
good review of the key aspects of the two-sided markets. [28] provide
a sort of guide to correctly identify such markets not only in terms of
the industries and practices already examined, rather than to build a
solid structure to identify new ones. They define a number of
qualitative approaches (i.e. deductive, interview and stated or revealed
preferences based) to verify whether the key preconditions – mainly in
terms of network effects – are met.
From a modeling point of view, a key distinction in the available
literature is placed on the charges applied by the platform. First, a
platform can charge upfront its clients based on the fact that it allow
them to transact with a matching agent on the other side while not
seeing nor taking part in the transaction itself (non-transaction twosided market). Second, a platform can take the matching process as a
given and charge clients on a per-transaction basis, considering fully
visible the transactions and their related amounts between the two sets
of agents (transaction two-sided market). Third, the fee can be a towpart tariff, i.e. a mix.
One of the earliest applied models in academic literature of a nontransaction two-sided market can be found in [29]. In their work, they
approach one of the main questions arisen in the information economy
at that time, i.e. how can firms raise profits by giving away products
for free? They introduce a formal model of cross market externalities
based on network effects, price discrimination and product
differentiation aiming at explaining the emerging eagerness of firms to
enter into price competition à la Bertrand. They derive and model that
a firm can rationally invest in a product intended to be sold for free as
this increases demand on the second market, complementary and with
premium goods. This can also mean that the firm can use strategic
products to penetrate a market that becomes competitive post entry (so
that the threat of entry is credible even in cases where it never recovers
its sunk cost directly) to gather market share (and not power). They
also derive that subsidization can happen on any side depending on the
relative network externality benefit.
Among the matching, transaction two-sided markets, applications,
[7] discuss the case of competing matchmakers, such as dating
agencies and real estate agents, showing that depending on the
exclusivity of the services provided multiple equilibria can exist. With
exclusive intermediation services, the only equilibria are dominantfirm equilibria where one intermediary captures all users, charges the
maximal transaction fee, subsidizes registration, and makes zero profit.
With nonexclusive intermediation services, mixed equilibria can
emerge when users of the same group make different choices – thus
multi-homing.
[8], starting from [7] results and taking the matching as a given,
extend the concept with a model based on the observation that most of
the markets with network externalities are two-sided since an
incumbent must get both sides of the market on board. The interesting
conclusion of their work can be summarized to the fact that the volume
of transactions on and the related profit of a platform depend not only
on the total price charged to both parties but also to its decomposition,
meaning that cross subsidization becomes the identifying feature of a
market with network externalities to become two-sided.
Leveraging on these two works, probably the main comprehensive
economic model is the one of [30]. He details a schema identifying the
three main factors determining the structure of prices offered to the two
groups in several market structures, i.e. the relative size of cross-group
externalities, the type of charge fees (fixed or per transaction), and the
platform exclusivity (allowing single or multi-homing). He then
provides three generic models for monopoly, two-sided single-homing
and competitive bottleneck (i.e. one side single-homing and the other
multi-homing), deriving some direct applications for advertising and
supermarkets. A more in-depth analysis and application of competitive
bottlenecks is available in [31].
All these studies focus on the two-sided market architecture
stressing the importance of the externalities in place between all actors
and derive main conclusions especially in terms of price structure. In
facts, since its beginnings, two-sided markets literature gives much
attention to the distinction between price level and price balance (or
structure). Price level is used to indicate some sense of the overall price
charged to the two sides, as it is referred to by [25], [32] and [33]. [34]
define it as the sum of the per interaction prices charged to the two
sides of the market. Price balance or structure usually refers to the way
in which this total price is divided between consumers on the two sides
of the market. An attempt to better define the key aspects of a twosided market and its related distinction between transaction and nontransaction can be found in [35]. He basically defines the key aspects
differentiating the two-sided markets from a pure merchant approach
as the presence of indirect effects between buyers and sellers, higher
level of information asymmetry between sellers and intermediary,
higher sellers’ investment incentives and higher intermediary product
complementariness.
Building on this early literature, more recent works address
specificities of two-sided market strategies such as the effects of tying
([36] and [37]), the effect of single-homing vs multi-homing decisions
([38]), moral hazard implications ([39]) and platform competition with
differentiation and pricing strategies ([40], [41] and [42]). The latter is
addressed by [43] by introducing the attachment curve, i.e. a function
that specifies the probability with which a user of a given type will join
a platform, to suggest its use to study the investment strategies (e.g.
whether a platform should invest extra effort to attract more users on
one side of the platform or the other, the amount of money that could
be invested along with its expected returns, etc.).
In parallel to these generic frameworks, a number of papers focus
on applying such models to specific industries gathering first empirical
evidences. The traditional areas investigated from a modeling and
empirical point of view are:

Videogame industry: [44]

Credit and debit cards: [45]

Television advertising: [46], [47]

Newspaper and magazine advertising: [48], [49]

Yellow pages: [50]

Open-access journals: [51]

Broadband internet access (net neutrality): [52]

Commercial exhibitions: [53]

Instant messenger: [54]

Stationary fuel cells distribution: [55]
From policy point of view, [8], among the firsts, provide several
examples of public policy implications and applications to different
two-sided market. Also [25] collects a wide series of examples of twosided markets showing why such kind of competition needs to be
strongly differentiated from the antitrust point of view. He corrects the
traditional market definition, market power and barriers to entry
concepts showing how violations, as normally intended, can actually
have an underlying reason and efficiency in multi-platform markets.
[32] closely analyzes the (heterosexual) nightclubs market, which
aims at attracting men and women who wish to interact, to spot eight
fallacies of traditional one-side market – collecting most of the points
common in literature and mentioned before – including the
conventional regulation failure. [56] extends the economic model
arguing with the consolidated policy assumption that open platforms
are inherently more efficient than monopoly proprietary platforms. He
addresses specifically the software market, in which the popularity of
the open source software is significantly arising leading an increasing
number of governments around the world to consider (or enact)
policies promoting open source software systems at the expenses of
proprietary systems, as comprehensively depicted by [57].
In a way extending the results already provided by [7], [56] shows
via an economic model that a proprietary platform internalizes (at least
partially) the positive indirect network externalities between users and
third party product suppliers and the direct negative externalities
between producers, whereas an open platform does not. The main
conclusion is thus that the welfare analysis in two-sided markets
environments is very different from the one in the more classic one
sided context and it implies that an a priori preference of open
platforms over proprietary ones (as well as the other way around) is
not economically justified. As a concrete application, bringing support
to the viewpoint just mentioned, [50] analyzes the Yellow Pages
market and his results show the confirmation that a unique preference
between monopoly and competition is not sustainable. His results
actually confirm that internalizing network effects significantly
increases surplus and that encouraging competition improves welfare,
meaning that, despite the network effect, a more competitive market
structure is preferable to a more concentrated one.
[25] and [32] main conclusions with regards to policies are extended
in [58]. He includes a rate – the pass through – at which the firm passes
through the cross subsidies from one side of the market to the other
and the threshold of 1 to identify whether [8] model policy implications
are holding or to be reversed.
[27] suggests merger simulations and regression analyses to be used
by authorities to evaluate cases of two-sided markets competition. He
highlights that one of the main difficulties faced by authorities is
exactly that the exclusive dealing (on one side) potentially adds
benefits in a two-sided market, which might be important
counterpoints to the standard antitrust criticism that they may create
entry barriers. As the “classic” example, i.e. whether the credit cards
related interchange fee – set collectively by all banks – is to be
considered as a collusion or not, he reports the different behaviors and
approaches (allowing it or considering it as a violation to competition)
towards the matter in the US regulation and the European Commission
one, as more deeply analyzed by [59] and [60].
A comprehensive work is reported for the NMa (the Netherlands
Competition Authority) in [61]. With the specific focus of providing
support to control Mergers and Acquisitions decisions, they provide an
overview of the economic and legal literature on two-sided markets,
evaluating the traditional one-sided methods in the assessment of
concentrations when applied to two-sided markets, in particular with
regards to market definition, measurement of market power and
merger evaluation. Their main suggestions are going in the direction
of:
1. Assessment of the two-sidedness of the market
2. Definition of the market, adjusting traditional methods to entail
both sides (considering that a transaction market consists of a
single market, while a non-transaction is having two)
3. Assess horizontal merge effects (e.g. market power) considering
the platform surplus and two customers’ surpluses, having an
underlying decision needed whether to protect overall consumers’
welfare or only the welfare of one of the two groups of customers
4. Decide the outcome taking all aspects into account: from an
economic point of view one would wish to clear a merger which
leads to higher concentration, higher prices and higher consumer
welfare; from a legal point of view this might not be easy as such
a merger might indeed seem to lead to less competition
They also show an applied case to the Dutch newspaper market of
such fallacies.
Extending this concept, it then becomes of interest understanding
how price regulation can help solving authorities concerns on potential
collusions. On one hand, if there is no antitrust violation but the
equilibrium outcome diverges from the social optimum then price
regulation may be a reasonable solution (and actually several countries
followed this approach with regards to the interchange fees for credit
cards). On the other side, [62] analyze the ATM network regulation
history, arguing that the deregulation of the surcharges for ATMs use
had a major role in causing the expansion of their network and that the
following increase of prices led to more consumer usage.
It is clear, according to the works previously mentioned, that a lot
can still be done in this direction. As an example, [63], while
investigating how multinational two-sided platform firms set their
prices on intra-firm transactions between affiliates located in different
countries, emphasize that future research might deepen their
application to the extended oligopoly market (since more complex).
This would allow following their work in motivating and justifying the
deviation from marginal cost of production helping the authorities
making policy decisions.
In what follows, we leverage on the existing modelling literature –
especially [8] for their credit card industry suggestions and [53] for
their transactional two-sided market commercial exhibition application
– to focus on the strategic incentives into vertically disintegrate a
financial intermediation services provider to move towards a platform
concept and how this significantly change its business model in a way
that must be considered by policy authorities when setting regulation.
In facts, we show that equilibria can exist where one side is subsidized
at the expenses of the other, which is facing higher fees to recover
losses and to ensure profits.
While several (mentioned) examples are available taking into
account the strategic importance of entering a two-sided market from
the outside due to the pricing attractiveness (see for example [64]),
there is not an available analysis of how the disintegration of a
traditionally integrated industry can be a sustainable decision to move
from a merchant to a platform behavior.
III.
THE MODEL
After defining the sets of agents together with their utilities and
profit functions, we develop a first model entailing two distribution
networks of financial commodities competing for attracting clients
with products internally managed, thus being vertically integrated.
Starting from this scenario, we show via a perturbation of the model
that both companies have an incentive to deviate towards a platform
behavior in order to gain market shares, increase profits and attract
more clients in the short term, as a first-mover advantage. The question
lastly addressed with a wider generalization of the model is whether an
equilibrium can exists in case both competitors become disintegrated
platforms, competing not only to attract clients but also asset
managers.
A. Introduction
The model comprises three classes of agents. There are two distinct
types of client groups that interact with each other and two
intermediaries that provide services to enable these two client groups
to “meet” each other and perform a transaction, in particular for buying
or selling funds. In such example, the two client groups can be
described as asset managers providing a financial product and clients
who buy such products via a platform, which provides securities
accounts, transaction services and advisory.
The first set of agents on the market is represented by the population
of clients i=1…I looking for investing their available wealth on
products intermediated by the platforms. There are two common
approaches to describe the clients’ utilities, via horizontal or vertical
differentiation. The first approach can be followed modeling the
agents’ utilities à la Hotelling, inferring that the choice of the platform
is driven by a parameter representing the geographical distance. Based
on the fact that in the majority of cases the technology allows to soften
the geographical distances while more importance is given to the
variety of products offered, whose range is considered a key factor,
and advisory services (see e.g. [65] with a relationship marketing
viewpoint), a pure horizontal differentiation might not be the optimal
way to describe clients’ behavior. [66] suggest a vertical differentiation
where the market is not covered and the clients’ behavior model leads
them to be intrinsically attracted more by a certain product, subject to
other parameters’ constraints (in their example of pianist looking for a
piano, such restriction is the available income). Considering this
approach more fitting to the case, we model such attraction by denoting
clients by their type 𝑎𝑖 ∈ [0,1] representing their preference for the
variety provided, which is assumed to be uniformly distributed. At the
limits, 𝑎𝑖 = 0 describes an agent completely indifferent to the number
of products provided (thus relying completely on the choices of the
platform), while 𝑎𝑖 = 1 denotes an agent extremely focused on having
the wider possible choice of products on the platform. The total
population I can be, without loss of generality, normalized to the
unitary value. They decide on which platform k to buy based on their
utility 𝑢𝑖𝑘 = 𝑎𝑖 𝑚𝑘𝑒 − 𝑝𝑘 , where 𝑚𝑘𝑒 denotes the unanimous expectation
of number of agents on the other side of the selected platform and 𝑝𝑘
the price to pay to the intermediary to transact. Using the typical twosided market terminology, clients are only allowed to single-home, i.e.
they can choose one and only one platform to which refer.
The second set of agents on the market is represented by the
population of providers j=1…J looking for investors in their product.
Symmetrically to the characterization of the first set of agents,
providers are denoted by their type 𝑏𝑖 ∈ [0,1] representing their
preference for the cardinality of agents on the other side, which is
assumed to be uniformly distributed. At the limits, 𝑏𝑖 = 0 describes a
product for which it is not relevant the number of agents reached on
the other side (thus relying on their own known investors or having no
incentive in being intermediated, it is the case e.g. for a product with
limited availability or limited investment needed or for a product
addressed for specific large investors), while 𝑏𝑖 = 1 denotes the
maximum willingness to capture the highest possible number of clients
on the platform. The total population J can be, without loss of
generality, normalized to the unitary value. They decide on which
platform k to place their products based on their profit 𝜋𝑗𝑘 = 𝑏𝑗 𝑛𝑘𝑒 −
𝑠𝑘 , where 𝑛𝑘𝑒 denotes the unanimous expectation of number of agents
on the other side of the selected platform and 𝑠𝑘 the price to pay to
transact, often set or referred to as a rebate of the transaction between
the client and the product provider. Also providers are only allowed to
single-home, i.e. they can choose one and only one platform to which
refer.
Two distribution networks k=1,2 are then competing to attract 𝑛𝑘
investors while providing 𝑚𝑘 products at prices 𝑝𝑘 , facing 𝐹𝑘 fixed
distribution costs. They set prices (𝑝𝑘 , 𝑠𝑘 ) on both sides in order to
trigger a right-sized “chicken and egg” loop fitting the expectations of
both sets of agents.
In order to model the competition between the platforms, we have
to define whether we are considering a transactional or a nontransactional two-sided market, as defined e.g. in [28]. According to
such distinction, an environment characterized by a transaction
directly taking place between the two sets of agents is referred to as a
transactional two-sided market, while if each group interacts only with
the platform the situation is depicted as a non-transactional two-sided
market. Considering such differentiation, we model our financial
intermediation industry as a transactional two-sided market, as:

There is a measurable transaction between the two sets of agents
on side 1 and side 2;

Such transaction is observable;

The transaction is the basis for the pricing applied on both sides
as a percentage of it.
While facing a two-sided market in which transactions do not
happen directly on the platform, we now have to define what the
demands are on both sides, basis for the pricing. On the platforms we
have two so-called quasi-demand functions each, meaning 𝐷11 , 𝐷12 on
the first one and 𝐷21 , 𝐷22 on the other one. They represent the quantity
of clients (superscript 1) or asset managers (superscript 2) willing to
interact with a specific platform (subscript 1 or 2). We entail then the
assumption made by [8] for the credit cards market, which is a
transactional two-sided market quite close to our investigated one.
They differentiate from search models focusing on the matching
process between buyers and sellers, like [7], by assuming that for large
sets of agents on both sides all matches actually result in a transaction.
Entailing their approach, the aggregated demands on the platforms in
our case are the multiplication of their quasi-demand functions,
meaning 𝐷11 𝐷21 for the first platform and 𝐷12 𝐷22 for the other one. Their
overall profit can thus be defined as 𝜋𝑘 = (𝑝𝑘 + 𝑠𝑘 )𝐷1𝑘 𝐷2𝑘 − 𝐹𝑘 .
In order to evaluate the quasi-demand functions, we derive the
utility for the client i (on side 1) and profit for the provider j (on side
2) when choosing platform 1 or 2 with the following functions:
𝜋𝑗1 = 𝑏𝑗 𝑛1𝑒 − 𝑠1
𝑢1 = 𝑎𝑖 𝑚1𝑒 − 𝑝1
{ 𝑖2
{
𝑢𝑖 = 𝑎𝑖 𝑚2𝑒 − 𝑝2
𝜋𝑗2 = 𝑏𝑗 𝑛2𝑒 − 𝑠2
In this case the different perception of the platforms on one sets of
agents depends purely on the cardinality of the other side. In order to
evaluate the quasi-demand functions, let’s assume 𝑚2𝑒 > 𝑚1𝑒 > 0 and
𝑛2𝑒 > 𝑛1𝑒 > 0 (such conditions will be verified whether holding
throughout all models). Starting from the case of the indifferent client
i (for which 𝑎𝑖 𝑚1𝑒 − 𝑝1 = 𝑎𝑖 𝑚2𝑒 − 𝑝2 ) and assuming positive utilities
(𝑎𝑖 𝑚1𝑒 − 𝑝1 > 0, 𝑎𝑖 𝑚2𝑒 − 𝑝2 > 0), we can formulate the quasi-demand
functions as follows, where 𝐷𝑘𝑠 represents the “quasi-demand function”
on platform s and side k:
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
𝐷11 = 𝑒 𝑒
𝐷12 = 𝑒 𝑒
𝑒
𝑚1 (𝑚2 − 𝑚1 )
𝑛1 (𝑛2 − 𝑛1𝑒 )
𝑝
−
𝑝
𝑠2 − 𝑠1
2
1
𝐷21 = 1 − 𝑒
𝐷22 = 1 − 𝑒
𝑒
𝑒
𝑚
−
𝑚
𝑛
{
{
2
1
2 − 𝑛1
B. Vertical integration
The first model involves two financial intermediaries vertically
integrated, thus referred to as distribution networks of financial
products and not platforms, as in this case they are not facing two
markets but only the clients’ one. They compete to maximize their
profits by attracting investors and providing a certain number of
products internally managed. They have, for historical (or other)
reasons here considered as exogenously given, 𝑚1 and 𝑚2 products
available. The total amount of available products on the market is
normalized to the unitary value, meaning that it leaves 1 − 𝑚1 − 𝑚2
products available but not offered via a distribution network. This is
the case e.g. of small asset manager not having a distribution chain and
relying on smaller local markets, whose profit is considered negligible
and at the limit equal to zero (when competing à la Bertrand).
Noting that there are no expectations to be considered, as from
clients’ point of view the amount of products offered is a priori known,
we can derive the demands on the vertically integrated networks:
𝑝2 𝑚1 − 𝑝1 𝑚2
𝐷1 = 𝑛1 =
𝑚1 (𝑚2 − 𝑚1 )
{
𝑝2 − 𝑝1
𝐷2 = 𝑛2 = 1 −
𝑚2 − 𝑚1
Having one demand function only, the profit on network k is 𝜋𝑘 =
𝑝𝑘 𝐷𝑘 𝑚𝑘 − 𝐹𝑘 and its maximization via first order conditions on 𝑝𝑘
leads to the following proposition.
Proposition 1: Two distribution networks, vertically integrated and
providing exogenously given 𝑚1 and 𝑚2 number of internally
managed products, have the following best strategies for setting prices
to clients
𝑚1 (𝑚2 − 𝑚1 )
𝑝1∗ =
4𝑚2 − 𝑚1
2𝑚
2 (𝑚2 − 𝑚1 )
𝑝2∗ =
4𝑚
2 − 𝑚1
{
Resulting in the following market sizes and profits
𝑚2
𝑚1 2 𝑚2 (𝑚2 − 𝑚1 )
𝑛1∗ =
𝜋1∗ =
− 𝐹1
4𝑚2 − 𝑚1
(4𝑚2 − 𝑚1 )2
3
2𝑚2
4𝑚2 (𝑚2 − 𝑚1 )
𝑛∗ =
𝜋2∗ =
− 𝐹2
{ 2 4𝑚2 − 𝑚1
(4𝑚2 − 𝑚1 )2
{
According to Proposition 1, prices and profits are defined by 𝑚1
and 𝑚2 , which as mentioned are not under complete direct control of
the distribution network as they are depending on the overall market,
i.e. historical reasons, other local asset managers providing different
products, etc. One objection could be that large networks could
leverage on M&A strategies with the local asset managers in order to
be able to cover a higher market size 𝑚2 < 𝑚
̂ 2 < 1 − 𝑚1 . We
consider throughout the model that companies target is to keep 𝐹𝑘
stable and ensure positive profits, thus aggressive M&A strategies can
hardly allow to concretely set a target quantity of 𝑚𝑘 , as the investment
needed could be higher than the amount companies can afford, 𝐹𝑘 costs
might eat up profit, short term return on investment could be too low
(or negative) or break-even point might be too long term.
Starting with the described scenario, one possible option is to
disintegrate asset management activities while opening the second
market to third party providers. This leads to the question – can
distribution networks (one or both) have any incentive in
disintegrating?
C. Incentive to disintegrate
Considering the vertically integrated scenario, we now evaluate
whether there is an incentive – as a first-mover advantage – to open
asset management side to third parties by setting them a price 𝑠𝑘 in
exchange of the distribution services, thus switching behavior from
distribution network (where the company sells its own products) to
platform (where the company allows its client to purchase from third
parties).
Given that throughout all our models we consider the case where
𝑚2𝑒 > 𝑚1𝑒 > 0, we have to differentiate between two cases. The first
case analyzes the incentive to disintegrate on Network 2 (or
symmetrically on Network 1) when 𝑚2 ≈ 𝑚1 , while the second
investigates the same incentive on Network 1 when 𝑚2 ≫ 𝑚1 .
1.
Figure 5 - Networks competing in vertical integration scenario
Network 2 incentive to disintegrate
Let’s consider the case in which Network 1 and Network 2 are
providing similar offerings (𝑚1 ≈ 𝑚2 ) and Network 2 decides to
offload all asset management activities opening its second side to third
parties (in case of Network 1 deciding the same, the model is clearly
symmetrical – as the starting point involves low differentiation – thus
the names of the intermediaries can be swapped to obtain the same
result).
Lemma 2 specifies the condition on 𝑚1 and 𝑚2 which differentiate
the best pricing strategy in case of subsidization of Side 1.
Lemma 2: Subsidization and optimal charges apply if 𝑚1 ≈ 𝑚2 thus
𝑛∗
𝑚1 , 𝑚2 ≤ 0.5. 𝑠2∗ = 2⁄2 is an optimal strategy when the more
𝑛∗ (1−𝑚1 −𝑚2 )
restrictive condition 𝑚1 + 2𝑚2 ≤ 1 applies, if not 𝑠2∗ = 2
.
1−𝑚1
Higher profits are ensured by the holding conditions 4𝑚22 − 4𝑚1 𝑚2 +
𝑚1 − 1 < 0 in the first case and by 2𝑚22 − 2𝑚1 𝑚2 + 𝑚1 + 𝑚2 − 1 <
0 in the second.
Proof: If 𝑚1 ≈ 𝑚2 , having by construction that 𝑚1 + 𝑚2 < 1 sets
the maximum value for both to 0.5. Setting 𝑚
̂ 2 = 𝐷22 = 𝑚2 to evaluate
𝑛2∗ (1−𝑚1 −𝑚2 )
maximum level of 𝑠2 =
Figure 6 - Competition with Platform 2 vertically disintegrated
In order to simulate the decision process to disintegrate, we now
introduce a two-stage game. The first stage is set at the vertically
integrated optimal pricing for any given 𝑚1 and 𝑚2 resulting in
defined 𝑛1∗ and 𝑛2∗ , where Network 2 decides to disintegrate by setting
its prices 𝑠2 on Side 2 that defines 𝑚
̂ 2 . At the second stage, Network 1
and Platform 2 compete on Side 1 setting 𝑝̂1∗ and 𝑝̂2∗ to maximize their
profits.
Starting from Game 2, quasi demand functions (unchanged from
vertically integrated scenario) and optimal prices (derived from f.o.c.
on profits) are:
𝑝̂2 𝑚1 − 𝑝̂1 𝑚
̂2
𝑚1 (𝑚
̂ 2 − 𝑚1 − 𝑠2 )
𝐷11 =
𝑝̂1∗ =
𝑚1 (𝑚
̂ 2 − 𝑚1 )
4𝑚
̂ 2 − 𝑚1
(𝑚
𝑝̂
−
𝑝̂
2𝑚
̂
̂
2
1
2
2 − 𝑚1 − 𝑠2 )
𝐷1 = 1 −
𝑝̂2∗ =
{ 2
𝑚
̂ 2 − 𝑚1
4𝑚
̂ 2 − 𝑚1
{
Moving to Game 1, we have to consider differentiated demands on
providers’ side for Platform 2, meaning that as a consequence of the
disintegration all asset managers among remaining 1 − 𝑚1 having a
𝑠
sufficiently large 𝑏𝑗 > 2⁄𝑛∗ enjoy positive profits by placing their
2
products on Platform 2:
𝐷12 = 𝑚1
𝑠2
{ 2
𝐷2 = (1 − ∗ ) (1 − 𝑚1 )
𝑛2
Having this demands formulation we can consider the following
Lemma to evaluate how in Game 1 Platform 2 could set its 𝑠2 charges
based on 𝑛2∗ .
Lemma 1: If Network 2 disintegrates while Network 1 remains
integrated, the first can subsidize Side 1 of its two-sided market (thus
setting 𝑝̂2∗ = 0 and forcing 𝑝̂1∗ = 0) by setting 𝑠2 ≥
𝑛2∗ −2𝑚1 𝑚2
1+𝑛2∗ −𝑚1
Proof: Looking at the price strategies coming from Game 2,
considering that 𝑚2 > 𝑚1 > 0 thus 4𝑚2 − 𝑚1 > 0 ∀𝑚1 , 𝑚2 , the
condition for having negative (i.e. zero) prices is 𝑚
̂ 2 − 𝑚1 − 𝑠2 ≤ 0.
Substituting 𝑚
̂ 2 = 𝐷22 in the formula leads to the result of the Lemma
1. Due to the common term in both 𝑝̂1∗ and 𝑝̂2∗ formulation, the result
applies to both intermediaries.
Considering the outcome of Lemma 1, it now becomes of interest
evaluating whether there is an optimal 𝑠2∗ charge in case of
subsidization of Side 1. This results comes out from f.o.c. on profit
functions where 𝑝̂1∗ = 𝑝̂2∗ = 0 in Proposition 2.
Proposition 2: Starting from similar product offering quantities
𝑚1 ≈ 𝑚2 , the network that decides to disintegrate can subsidize Side
1 offering products free of charge and forcing the competitor out of the
𝑛∗ (1−𝑚1 −𝑚2 )
𝑛∗
market by setting the optimal charge 𝑠2∗ = min ( 2⁄2 , 2
).
1−𝑚1
In both cases it ensures its profits are at a higher level than in the
vertically integrated scenario.
𝑛2∗⁄
2 by
𝑛2∗
2
≤
𝑛2∗ (1−𝑚1 −𝑚2 )
1−𝑚1
1−𝑚1
, we can compare it with 𝑠2∗ =
that leads to 𝑚1 + 2𝑚2 ≤ 1. Retrieving 𝜋2∗
𝑚
2 (1−𝑚
2
we can compare it with 𝜋̂2∗ = 𝑠2∗ 𝑛2∗ 𝑚
̂ 2 − 𝐹2 = (4𝑚
obtain
first
case
condition
from
𝑚2 2 (1−𝑚1 )
(4𝑚2 −𝑚1 )2
1)
2
2 −𝑚1 )
>
− 𝐹2 to
4𝑚2 3 (𝑚2 −𝑚1 )
.
(4𝑚2 −𝑚1 )2
Reformulating 4𝑚22 − 4𝑚1 𝑚2 + 𝑚1 − 1 < 0 as 4𝑚22 − 4𝑚1 𝑚2 +
𝑚1 < 1, this condition holds if 4𝑚22 − 4𝑚1 𝑚2 = 4𝑚2 (𝑚2 − 𝑚1 ) <
2𝑚2 , thus if 2(𝑚2 − 𝑚1 ) < 1, which is ensured by 𝑚1 + 2𝑚2 ≤ 1.
Using 𝑠2∗ =
𝑛2∗ (1−𝑚1 −𝑚2 )
1−𝑚1
, same comparison leads to second case
condition 2𝑚22 − 2𝑚1 𝑚2 + 𝑚1 + 𝑚2 − 1 < 0, which holds as 𝑚1 ≈
𝑚2 .
It must be noted that this results only applies to a short term strategy,
as one of the characteristic of the described two-stage game is that 𝑛2∗
comes from the vertically integrated scenario and does not entail the
most typical chicken-and-egg loop feature of a two-sided market. This
assumption is however justified in our scenario as we consider a 𝐷22 =
𝑚
̂ 2 > 𝑚2 on the second platform, thus the primary effect of such
increase would be an adjustment (i.e. increase) of 𝐷21 , which would
adjust 𝑠2 , then 𝑚
̂ 2 again and so on, in any case benefitting the profit
here calculated as a sort of worst case scenario. Our goal is not to
determine whether this loop leads to an equilibrium that can exist in
this scenario, what discussed only aims at showing that there is a
concrete advantage in being the first-mover to disintegrate.
We can also observe that there is another possible outcome of the
game, which does not entail the subsidization of one side of the
resulting two-sided market. In fact, the disintegration of Network 2 via
setting 𝑠2 <
𝑛2∗ −2𝑚1 𝑚2
1+𝑛2∗ −𝑚1
leads to having positive prices and profits on
both competitors. At the limit, in the interval 0 ≤ 𝑠2 <
𝑠2∗
𝐷22
𝑛2∗ −2𝑚1 𝑚2
1+𝑛2∗ −𝑚1
, the
optimal strategy
= 0 leads to
= 1 − 𝑚1 thus the very same
profit level as in the vertically integrated scenario where, for any given
𝑚1 , Network 2 sets its 𝑚2 = 1 − 𝑚1 in order to exploit the effect of
the vertical differentiation and maximize its profit. While theoretically
allowed in our formulation, in reality this possibility is a challenge as
deciding to intermediate all the remaining market of financial products
can lead to a significant increase of distribution costs or to a high
disintegration cost (to reach all asset managers on the market)
potentially cannibalizing the profit available in the short term or having
a long break-even point in the long term.
2.
Network 1 incentive to disintegrate
Let’s now consider the case in which in the vertically integrated
scenario there is a substantial differentiation between the networks
(𝑚2 ≫ 𝑚1 ). In such case Network 2 has an already large market share
and the benefit coming from opening its Side 2 to third parties is not
considered a sufficient incentive to disintegrate. We now investigate
whether under such assumptions there is an incentive on Network 1 to
disintegrate towards Platform 1.
Figure 7 - Competition with Platform 1 vertically disintegrated
Similarly to the previous scenario, we introduce a two-stage game
where at the first stage Network 1 decides to disintegrate by setting its
prices 𝑠1 on Side 2 that defines 𝑚
̃ 1 and at the second Platform 1 and
Network 2 compete on Side 1 setting 𝑝̃1∗ and 𝑝̃2∗ to maximize their
profits.
Similarly to what discussed in previous scenario, quasi demand
functions and optimal prices in Game 2 are:
𝑚
̃ 1 (𝑚2 − 𝑚
̃ 1 ) − 2𝑠1 𝑚2
𝑝̃2 𝑚
̃ 1 − 𝑝̃1 𝑚2
𝑝̃1∗ =
𝐷11 =
(𝑚
)
4𝑚2 − 𝑚
̃1
𝑚
̃1 2 − 𝑚
̃1
𝑝̃2 − 𝑝̃1
4𝑚2 (𝑚2 − 𝑚
̃ 1 ) − 2𝑠1 𝑚2
1
∗
𝐷 =1−
𝑝̃2 =
{ 2
𝑚2 − 𝑚
̃1
2(4𝑚2 − 𝑚
̃1)
{
Moving to Game 1, quasi demand functions are:
𝑠1
𝐷12 = (1 − ) (1 − 𝑚2 )
𝑛1
{
𝐷22 = 𝑚2
Following the same approach as in previous scenario, Proposition 2
shows the best strategy for setting 𝑠1∗ on Platform 1.
Proposition 3: Starting from a substantial differentiation in product
offering quantities, the smaller network that decides to disintegrate can
subsidize Side 1 offering products free of charge by setting the optimal
𝑛∗
charge 𝑠1∗ = 1⁄2, which maximizes its profits to a higher level than in
the vertically integrated scenario.
It must be noted that differently from previous case, when Platform
1 subsidizes Side 1, Network 2 is not forced out of the market as it
anyway remains 𝑚2 > 𝑚
̃ 1∗ , which still ensures positive prices and
profits even though at a lower level when compared to the vertically
integrated scenario (as the differentiation between the competitors
lowers down, being that increasing from 𝑚1 to 𝑚
̃ 1 makes 𝑚2 − 𝑚
̃1 <
𝑚2 − 𝑚1 ).
Lemma 2 derives the condition on 𝑚1 and 𝑚2 which make 𝑠1∗ an
optimal strategy to disintegrate.
𝑛∗
Lemma 3: Subsidization of Side 1 and optimal charge 𝑠1∗ = 1⁄2
apply if and only if starting point is 𝑚2 > 0.5 and 𝑚1 ≈ 0. The
condition 4𝑚13 − 4𝑚12 𝑚2 + 𝑚2 − 𝑚22 > 0 ensures Platform 1 higher
profits when compared to the vertically integrated scenario.
Proof: First condition comes from the fact that in order not to have
the same incentive as the bigger network to disintegrate it must be
unfeasible having 𝑚
̃ 1 > 𝑚2 . This means that 𝑚2 must be sufficiently
large so that 𝑚
̃ 1 − 𝑚2 < 0 ∀𝑚
̃ 1 . Being at the limit 𝑚
̃ 1 = 1 − 𝑚2 and
considering that we only allow an increase of 𝑚1 as incentive to
disintegrate (so 𝑚1 must have as much as possible space to increase,
thus being at the limit equal to zero) first part of Lemma 2 is proven.
Retrieving from the equilibrium in integrated scenario 𝜋1∗ =
𝑚1 2 𝑚2 (𝑚2 −𝑚1 )
(4𝑚2 −𝑚1 )2
− 𝐹1 and 𝑛1∗ =
𝑚2
4𝑚2 −𝑚1
, we can compute 𝜋̂1∗ =
𝑚22 (1−𝑚2 )
4(4𝑚2 −𝑚1 )2
− 𝐹1 and compare when
𝑚22 (1−𝑚2 )
4(4𝑚2 −𝑚1 )2
>
𝑚1 2 𝑚2 (𝑚2 −𝑚1 )
.
(4𝑚2 −𝑚1 )2
Straightforward computations lead to Lemma 2 condition which is
holding as 𝑚2 > 0.5 and 𝑚1 ≈ 0.
As mentioned in previous case, it must be noted that this results only
applies to a short term strategy, as it does not entail the chicken-andegg loop feature. However, same considerations made before still hold
as the profit here calculated is a sort of worst case scenario.
We have now shown that both network can have an incentive to
disintegrate, basically depending on the initial conditions of 𝑚1 and
𝑚2 . This result can be explained with the fact that the main reason
underlying the decision to move towards a platform behavior leads the
company to sell no longer products rather its own distribution network
to third parties. Having such asset managers low or substantially no
profit in the integrated environment, plus facing no other alternatives
when the competitor remains integrated, they allow the disintegrated
one to extract most of their available profit in exchange of the channel
to sell.
Now the question is – if one of the two competitors decides to
become a platform, would the competitor be better off engaging in the
same direction or should it stay out of the market (in case Network 2
disintegrates) of keep lower profits (in case Network 1 disintegrates)
as no equilibria exist when both companies are operating in a two-sided
market environment?
D. Vertical disintegration
We now consider the scenario in which both networks disintegrate
and open Side 2 to third party asset providers.
Figure 8 - Platforms competing in vertical disintegration scenario
Quasi-demand functions are based on expectations as now both
networks disintegrated:
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
𝐷11 = 𝑒 𝑒
𝐷12 = 𝑒 𝑒
𝑒
𝑚1 (𝑚2 − 𝑚1 )
𝑛1 (𝑛2 − 𝑛1𝑒 )
𝑝2 − 𝑝1
𝑠2 − 𝑠1
𝐷1 = 1 − 𝑒
𝐷2 = 1 − 𝑒
𝑚2 − 𝑚1𝑒
𝑛2 − 𝑛1𝑒
{ 2
{ 2
It is now possible to follow [53] and define a Nash equilibrium with
two quadruples (𝑝𝑖∗ , 𝑠𝑖∗ ) and (𝑛𝑖∗ , 𝑚𝑖∗ ) with 𝑖 = 1, 2, such that:
1. Given expectations (𝑛1∗ , 𝑛2∗ , 𝑚1∗ , 𝑚2∗ ), (𝑝𝑖∗ , 𝑠𝑖∗ ) is a
best reply against (𝑝𝑗∗ , 𝑠𝑗∗ ), 𝑖 ≠ 𝑗, and viceversa
2. 𝐷𝑖𝑛 (𝑝1∗ , 𝑝2∗ ) = 𝑛𝑖∗ ; 𝐷𝑖𝑚 (𝑠1∗ , 𝑠2∗ ) = 𝑚𝑖∗ , 𝑖 = 1,2
The first condition can be calculated via f.o.c. on 𝑝𝑘 and 𝑠𝑘 , leading
to the following reaction functions:
2𝑝2 𝑚1𝑒 𝑠2 𝑛1𝑒
2𝑚2𝑒 − 2𝑚1𝑒 + 2𝑝1 − 𝑛2𝑒 + 𝑛1𝑒 − 𝑠1
∗
𝑝1∗ =
𝑝
=
𝑒 −
𝑒
2
3𝑚2
3𝑛2
3
{
𝑒
𝑒
𝑒
𝑒
2𝑠
𝑛
𝑝
𝑚
2𝑛
−
2𝑛
+
2𝑠
− 𝑚2𝑒 + 𝑚1𝑒 − 𝑝1
2
2
1
1
1
2
1
𝑠1∗ =
𝑠2∗ =
𝑒 −
𝑒
3𝑛2
3𝑚2
3
{
Moving now to the second condition, the system can be solved
substituting the expectations with the actual demands:
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
𝐷12 = 𝑒 𝑒
= 𝑚1
𝑒 (𝑚𝑒
𝑒 ) = 𝑛1
𝑚1 2 − 𝑚1
𝑛1 (𝑛2 − 𝑛1𝑒 )
𝑝
−
𝑝
𝑠
−
𝑠
2
1
2
1
𝐷1 = 1 − 𝑒
= 𝑛2
𝐷2 = 1 − 𝑒
= 𝑚2
𝑚2 − 𝑚1𝑒
𝑛2 − 𝑛1𝑒
{ 2
{ 2
This leads to next Proposition 4 (see Appendix 1 for the proof).
Proposition 4: There exist a Nash equilibrium in which both
platforms enjoy positive profit while applying a symmetric pricing
when facing symmetric sides (keeping in mind the assumption 𝑛2𝑒 >
𝑛1𝑒 and 𝑚2𝑒 > 𝑚1𝑒 ), represented by the following scenario:
3
𝑛1 = 𝑚1 =
≈ 0.23
13
9
𝑛2 = 𝑚2 =
≈ 0.69
13
3
𝑝1 = 𝑠1 =
≈ 0.02
169
27
{𝑝2 = 𝑠2 = 169 ≈ 0.16
Profits are:
54
𝜋𝐴 =
≈ 0.002
28561
{
4374
𝜋𝐵 =
≈ 0.15
28561
The key distinctive peculiarity of the applied model results in the
fact that it shows that under specific, vertically differentiated, singlehoming, non-transactional two-sided market assumptions, two
platforms can compete on the same market not by engaging in
traditional price competitions (e.g. à la Bertrand) but leveraging on
agents’ preferences to trigger specific and sustainable “chicken and
egg” loops. Such a sustainability is precisely given by the two-sided
nature of the market itself.
It can be shown that if we remove the specific characteristics of a
two-sided market, for example perturbing the initial model by forcing
prices on clients’ side to a fixed amount (e.g. by pushing a regulation
that does not allow to price discriminate the right side of the market)
the model leads to the trivial result coming from the vertical
differentiation.
In case of treating 𝑝1 and 𝑝2 as exogenously given, the strategies on
the platforms are simply given by choosing s*, which means:
𝑠2 𝑛1𝑒 − 𝑝1 𝑛2𝑒
𝑠1∗ =
2𝑛2𝑒
𝑒
𝑒
𝑛2 − 𝑛1 + 𝑠1 − 𝑝2
∗
{ 𝑠2 =
2
Considering the easiest case of 𝑝1 = 𝑝2 = 0, this translates in:
𝑠2 𝑛1𝑒 − 𝑝1 𝑛2𝑒 𝑝1=0 𝑠2 𝑛1𝑒
𝑠1∗ =
→
2𝑛2𝑒
2𝑛2𝑒
𝑒
𝑒
𝑒
𝑛2 − 𝑛1 + 𝑠1 − 𝑝2 𝑝2 =0 𝑛2 − 𝑛1𝑒 + 𝑠1
∗
𝑠
=
→
2
{
2
2
And:
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝐷11 = 𝑒 𝑒
= 𝑛1 = 0
𝑚1 (𝑚2 − 𝑚1𝑒 )
𝑝2 − 𝑝1
𝐷1 = 1 − 𝑒
= 𝑛2 = 1
𝑚2 − 𝑚1𝑒
{ 2
So that 𝑠1∗ = 0 and 𝑠2∗ = 1, leading to the trivial results of having
profits 𝜋𝐴 = 0 and 𝜋𝐵 = 1.
As a similar results can be derived forcing prices on the other side
of the platform, this leads to the conclusion that in this case of twosided market, forcing prices on one of the two sides significantly
transforms the behavior and the competition as well as the final
outcome. In facts, it has to be noted that such results applies to
whatever price forced on clients’ side (not only to the case of price
equal to 0). This comes from the fact that if the platforms are not able
𝐷11 =
to price discriminate the agents on such side, the market will behave
as a “winner takes it all”, where forcing (by model construction) n2 >
n1 and single homing decisions leads all clients to prefer platform B
disregarding what platform A is offering.
It must be noted as well that in this model no costs were considered
on the providers’ side of the market. This means that production costs
are supposed to be irrelevant when making the decisions at platform’s
level. While this can be accepted studying the equilibrium discussed in
the first place, forcing prices on one side of the market brings the whole
competition on the other side, where prices are set to the maximum
(i.e. 1), leading no chance to profit on the providers’ side and giving
no chance to survive to the agents having higher costs to produce (as a
consequence of the “winner takes it all” modification of the market).
It must be noted as well that this formulation of the competition
between platforms assumes that clients and providers are making their
choices without any initial distribution and without considering the
effects of a first decision of which platform to refer together with the
switching cost in case the other is considered more profitable. To this
extent it could be a suitable option to leverage on [67] model of
switching costs.
IV.
INITIAL EMPIRICAL EVIDENCES
The sector focused on in what follows is the Italian asset
management industry, divided in its set of players: the clients
(investors or side 1), the product providers (asset management
providers or side 2) and the distribution channel (financial
intermediary or platform). The specific Italian market is considered
with its empirical evidence while it serves as a basis to extend the same
analysis to other countries.
The products involved in the financial intermediation industry are
typically mutual funds, asset management and insurance or pension
funds (for a formal classification, see [68] together with its adjustments
of 2012). The proportion of the offer can be retrieved form the capital
structure of the intermediaries (available in [69]–[72]), showing an
average increasing trend over time for mutual (+74% from 2005 to
2014), insurance and pension funds (+99% from 2005 to 2014) while
decreasing in asset management (-46% from 2005 to 2014).
Figure 9 - Distribution of financial intermediaries’ product offering
over time
One peculiar aspect of the Italian banking market is that when
compared to Anglo-Saxon countries the phenomenon of integration
and sector concentration is relatively new. As described in [73], the
essential features of the Italian banking system were substantially
unchanged since the 1930s until the 1990s, and the system was
traditionally dominated by local oligopolies, being branch openings
regulated and rationed and being bank mergers not encouraged or
prohibited given the massive presence of state-owned banks. Since
1990, the structure of the banking system has changed due first to Law
218 of 1990 (so-called Legge Amato) and then by Law 385 of 1993
(Testo Unico Bancario). The number of branches jumped from 16,600
in 1990 to 33,600 in 2010 (+102%), meaning more new branches were
established in these twenty years than in the previous sixty, when
barriers to moving into local markets were in place. According to [74],
between 1990 and 2005, 329 mergers and 186 acquisitions of banking
control were counted. This wave of consolidations was the main factor
in reducing the number of banks from 1,200 in 1990 to under 800 in
2012, while the liberalization of branch openings led to greater
territorial overlap between banks, to the benefit of competition and a
more widespread physical presence.
Such increase and boost of distribution channels favored the rise of
larger banking groups, traditionally vertically integrated, providing
end-to-end services to their clients’ base. It is in this contest that it can
be observed a trend of disintegration of financial products management
in favor of an open architecture. In facts, all traditional financial
products can be either provided by the financial intermediary itself or
via third parties. The trend of third party product offering vs internal
ones significantly increased over time (+106% from 2005 to 2014),
showing the basis of a move towards a platform behavior in a twosided market, where side 1 remains unchanged (i.e. the clients) and
side 2 comes into the market (i.e. the financial products providers).
Figure 10 - Financial intermediaries’ third party vs own products
distribution
This effect is also incentivized by the higher competition in an
industry sector (financial intermediation) traditionally ruled by banks,
where now new players – non-banks – are entering. Assogestioni in
[75] reported a lowering trend of the total assets under management in
Italy handled by bank groups, falling from 76.8% in 2007 to 63.6% in
2011.
Figure 11 – AuM of bank groups (grey), insurances (light grey),
independent (dark grey)
Regarding the pricing of financial products for the clients, Directive
2004/39/EC dictates that all fees, regardless of the distribution
network, are to be made transparent via specific prospectuses
(prospetto informativo) collecting all relevant details about the
investment product. Such charges are traditionally set by the product
provider in the form of a fixed percentage of the amount transacted
(i.e. the asset invested), divided between transaction (for purchase,
redemption and switch) and periodic fees (for management and
performance). Italian fund periodic fees are typically higher that the
European average, Assogestioni reports between 2003 and 2007 the
aggregated percentage of fees over yearly average asset under
management as reaching 1.9%. On the contrary, transaction fees
followed a decreasing trend and an Assogestioni report of 2004 shows
that such fees fell 80% between 1993 and 2003. In 2006 such fees were
in average 0.35% for purchase and 0.16% for redemption while 25%
of the funds were not charging any of such fees, confirming the long
term trend oriented towards the periodic fees.
From the product provider point of view, the main applied charge is
the so-called rebate, i.e. a percentage of the transacted amount between
the client and the product provider which is returned to the platform.
Such price structure currently represents a peculiarity of this market in
Italy and it is being discussed in terms of regulation whether it can
harass the independence of the financial intermediary, who might be
incentivized to offer and sell higher rebates products instead of more
suitable ones according to clients’ profiles. In Italy, [5] reports an
average of 72% of the fees as a rebate to the distribution network,
topping 76% for SGR belonging to foreign bank groups. This rebate
setting could also harass external competition in favor of selling
internal products of the financial institution affiliated with the advisor.
As an example, [76] reports by end of 2006 a significant difference
between rebates towards distribution networks of the same bank group
as the asset manager (i.e. vertically integrated) when compared with
third party rebates (in average charged 6 times less), showing a clear
incentive rational in the sales network.
Figure 12 – Average rebate (as percentage of fee type) returned to
distribution networks
Summarizing, we have a quite non-concentrated industry which
encompasses a large wave of M&As, reducing by more than 40% of
the number of the incumbents, and incentives the entrance of other
non-banking competitors. After 10 years, we have a more concentrated
industry with less competitors each having large distribution networks
and have to face more clients’ demands in terms of products offered.
This led to a progressive vertical disintegration over time of internal
product management activities in favor of contracting with third
parties financial products’ distribution exploiting the market power of
the distribution network and receiving in exchange a rebate fee. As the
current result, platforms are on one side attracting clients widening the
third party product variety offered, while subsidizing on the other the
asset management service providers who pay the distribution. In facts,
while in the past the vertical integration between the sales network and
the asset management resulted in an offering significantly limited to
own products, the recent move of several intermediaries towards an
open architecture (strategically incentivized through the rebates)
suggests the strengthening of the distribution network per se as main
component of market power. This can be interpreted not only and not
necessarily in terms of vertical disintegration (even if several SGR
became separate legal entities they still remained part of the former
bank group) but as a disintermediation of the group’s asset
management, aimed at widening the product offering without
investment on internal resources. Such behavior can also be explained
as a reduction of the transaction costs associated with the internal
product widening versus the external provisioning.
All these generic trends specific for the analyzed industry direct
towards a two-sided market interpretation, however we are still not in
the condition of stating that we are concretely facing a two-sided
market. In facts as widely pointed out in the literature, for example in
[61], one of the key basic aspects of a two sided market is the presence
(and the strength) of cross-side externalities. If such externalities are
not applying, we are facing a merchant approach similar to the
outsourcing of back office activities. If these are applying, we can
further investigate the two-sided market behavior.
For the analysis of the market, a database created collecting Assoreti
data is considered. Assoreti is the association of companies active in
the financial intermediation consultancy and collects the stock
information provided by its members on a quarterly basis. The
information collected for each time period is the amount of stock at
that time invested in mutual funds, Asset Management, insurance or
pension funds products and the number of clients’ accounts active in
the period (inactive accounts are not included). Each investment
category is also divided according to its type (e.g. security-based,
bond-based…) and its source (i.e. product issued by a company of the
same group as the intermediary vs third party).
In order to prepare the analysis, a number of key aspects of available
data have to be considered. First, as mentioned in previous sections,
the disintegration observed in the financial industry is an ongoing
process, which means that the third party products are offered to clients
keeping also an internal product management. This is different from
what we modelled in the previous section’s game where the
disintegration decision was made assuming an immediate dismissing
of internal activities in favour of third party products. To have a proxy
of such disintegration, we take into account the percentage of third
party products offered over internal ones, where high percentage
values means a larger offer of external products (thus a larger variety
of offering together with a larger disintermediation) when compared to
a lower one (i.e. more restricted to internally managed products only
and less disintermediated). This means that basically instead of the
pure cardinality of Side 2, we consider the aperture degree offered by
the platform, where a high ratio of third party asset under management
over internal means a higher variety offered.
Second, as the basic starting point of the model is the vertically
integrated scenario, the analysis is restricted only to the incumbent
players in the sector. For this reason entrants from outside the financial
industry cannot be considered, as initial investment strategies might be
biased by short term goals and/or pushed by strong marketing
campaigns leveraging on services not purely related with investments.
For this reason we set the minimum average market share of 4% to be
considered.
Third, with regards to Side 1, the number of clients can be inferred
using as a proxy the active accounts in the period.
Fourth, we are going to test described incentives to disintegrate.
This means that having set initial market conditions (at first period) we
evaluate if the intermediaries have an incentive to disintegrate, which
results in an increase of clients over time together with a higher
aperture degree over the different type of products (mutual funds, asset
management and insurance or pension funds).
As a result, we have a dataset considering 9 companies (in brackets
the average market share): Fideuram (25.3%), Mediolanum (13.8%),
Allianz (12.1%), Azimut (7.9%), Generali (6.7%), Xelion (6.8%),
Finecobank (5.8%), Sanpaolo (5.1%) and Finanza&Futuro (4.19%).
For all these companies we consider the available provided data over
the period from 2007 to 2010. Such data are:

Number of active current accounts: as mentioned, considered as
a proxy of the active clients on Side 1

Internal funds Asset under Management: i.e. active investments
on internally-managed funds

Third party funds Asset under Management: i.e. active
investments on third party-managed funds

Internal Asset Management: i.e. investments on internallymanaged AM services

Third party funds Asset under Management: i.e. investments on
third party-managed AM services

Internal insurance and pension funds Asset under Management:
i.e. active investments on internally-managed insurance and
pension funds

Third party insurance and pension funds Asset under
Management: i.e. active investments on third party-managed
insurance and pension funds
From these variables we derive:

Fund aperture: i.e. ratio between Third party funds Asset under
Management and Internal funds Asset under Management

Asset Management aperture: i.e. ratio between Third party funds
Asset under Management and Internal Asset Management

Insurance and pension funds aperture: i.e. ratio between Third
party insurance and pension funds Asset under Management and
Internal insurance and pension funds Asset under Management

Market share: i.e. ratio between all internal and third party
investments on the single company in the single period and the
total
We then added some additional variables to capture market and
periodic effects:

Dummy to extract the year effect (3)

Dummy to extract the year seasonality (3)
We consider the following three fixed effects panel data models:
1) ln 𝑐𝑙𝑖𝑒𝑛𝑡𝑠𝑖𝑡 = 𝛼𝑖 + 𝛽1 𝑓𝑢𝑛𝑑𝑎𝑝𝑖𝑡 + 𝛽2 𝑚𝑘𝑡𝑠ℎ𝑡 + 𝛿1 𝑦2007𝑡 +
𝛿2 𝑦2008𝑡 + 𝛿3 𝑦2009𝑡 + 𝛿4 𝑡𝑟𝑖𝑚1 + 𝛿5 𝑡𝑟𝑖𝑚2 + 𝛿6 𝑡𝑟𝑖𝑚3 + 𝜀𝑖𝑡
2) ln 𝑐𝑙𝑖𝑒𝑛𝑡𝑠𝑖𝑡 = 𝛼𝑖 + 𝛾1 𝑎𝑚𝑎𝑝𝑖𝑡 + 𝛽2 𝑚𝑘𝑡𝑠ℎ𝑡 + 𝛿1 𝑦2007𝑡 +
𝛿2 𝑦2008𝑡 + 𝛿3 𝑦2009𝑡 + 𝛿4 𝑡𝑟𝑖𝑚1 + 𝛿5 𝑡𝑟𝑖𝑚2 + 𝛿6 𝑡𝑟𝑖𝑚3 + 𝜀𝑖𝑡
3) ln 𝑐𝑙𝑖𝑒𝑛𝑡𝑠𝑖𝑡 = 𝛼𝑖 + 𝜗1 𝑖𝑛𝑠𝑝𝑒𝑛𝑠𝑎𝑝𝑖𝑡 + 𝛽2 𝑚𝑘𝑡𝑠ℎ𝑡 + 𝛿1 𝑦2007𝑡 +
𝛿2 𝑦2008𝑡 + 𝛿3 𝑦2009𝑡 + 𝛿4 𝑡𝑟𝑖𝑚1 + 𝛿5 𝑡𝑟𝑖𝑚2 + 𝛿6 𝑡𝑟𝑖𝑚3 + 𝜀𝑖𝑡
Returning the following results:
TABLE I
RESULTS OF THE SIMULATION
Standard
p-value
R2
error
.034228
.0878511
0.698
85.72%
1. 𝛽1
87.79%
.347343
.0947771
0.000
2. 𝛾1
.3041161
.081954
0.000
87.84%
3. 𝜗1
From Table I we can derive that there seems to be a quite strong
positive relation between the aperture degrees and the number of
clients. While this relation seems to be relatively strong for Asset
Management and insurance and pension products, it is weaker for
funds.
Model
Coefficient
V.
CONCLUSIONS
In this paper we provided an interpretation of a recent trend
observed in the financial industry of products intermediation. We
started from the observation that over the last decades there has been a
significant increase of products offered on the market together with a
progressive opening of traditionally vertically integrated players who
started intermediating products provided by third parties. We noted
that also the European regulation is addressing specific intermediation
topics in the attempt of protecting clients and boost competition.
Based on the mentioned starting point, we developed a model
explaining how and why vertically integrated player are attracted by
offering third party products instead of internally managed ones. As a
result, we explained that the vertical disintegration of financial
institutions divesting Asset Management departments can be explained
by a differentiation preference on the clients’ side and a distribution
preference on third party providers’ side which act as an incentive to
disintegrate, moving from a traditional merchant approach to a
platform behaviour. The transition phase between pure merchant
approach and platform behavior in such intermediate scenario allows
subsidization of clients’ side (not charged) at the expenses of a higher
price on third party providers’ side (facing no alternatives to enlarge
their products distribution).
We then developed a duopoly in which both incumbent vertically
disintegrate and compete to show that there is at least a Nash
equilibrium in which both platforms enjoy positive profits. In such a
scenario, the behavior of the clients shows that they accept to spend
more (i.e. to diminish their surplus) in favor to a larger selection of
products offered on the other side, while asset managers accept to
lower their profit being charged by a platform that allows them to reach
a larger number of investors.
With this transaction two-sided market model in mind, we derived
some initial evidences from the financial intermediation industry on
Italian market, as characterized by a recent concentration trend of
banking players that are opening their financial advisory services to
third parties. Finally, leveraging on a set of data provided by Assoreti,
we estimated the relation between the number of clients and the mix of
external vs internal products offered by the intermediation platform,
founding a positive relation between them.
While these initial evidences can surely be deepened and further
investigated, we concluded that there is a basic evidence that financial
intermediation industry is going in the direction of a two-sided market.
As a result, as widely described in academic literature, traditional
policy concerns are to be adjusted to make sure all parties (clients,
platforms and product providers) are included – to avoid the risk of
focusing on a single side of the market.
APPENDIX
A. Proof of Proposition 4.
Starting from (𝑝1∗ , 𝑠1∗ ), as
𝜕 2 𝜋𝐴
𝜕𝑝12
< 0, first order condition for setting
𝑝1 to maximize profit on first platform, given (𝑝2 , 𝑠2 ), leads to:
𝜕𝜋𝐴
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
=( 𝑒 𝑒
)
(
)
𝜕𝑝1
𝑚1 (𝑚2 − 𝑚1𝑒 ) 𝑛1𝑒 (𝑛2𝑒 − 𝑛1𝑒 )
𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
− (𝑝1 + 𝑠1 ) ( 𝑒 𝑒
)( 𝑒 𝑒
)
𝑒
𝑚1 (𝑚2 − 𝑚1 ) 𝑛1 (𝑛2 − 𝑛1𝑒 )
=0
As we are looking for an equilibrium in which both platforms
compete and have non-zero demands, i.e. 𝐷12 =
be simplified in:
𝑠2 𝑛1𝑒 −𝑠1 𝑛2𝑒
𝑛1𝑒 (𝑛2𝑒 −𝑛1𝑒 )
> 0, it can
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑝1 𝑚2𝑒 + 𝑠1 𝑚2𝑒
=0
𝑒 (𝑚𝑒
𝑒 ) − 𝑒 (𝑚𝑒
𝑚1 2 − 𝑚1
𝑚1 2 − 𝑚1𝑒 )
𝑒
𝑒
𝑒 (𝑚𝑒
𝑒)
As 𝑚2 > 𝑚1 > 0, 𝑚1 2 − 𝑚1 > 0 thus:
𝑝2 𝑚1𝑒 − 2𝑝1 𝑚2𝑒 − 𝑠1 𝑚2𝑒 = 0
And:
𝑝2 𝑚1𝑒 − 𝑠1 𝑚2𝑒 𝑝2 𝑚1𝑒 𝑠1
𝑝1 =
=
−
2𝑚2𝑒
2𝑚2𝑒
2
Moving to s1, as
𝜕 2 𝜋𝐴
𝜕𝑠12
< 0, first order condition for setting s1 to
maximize profit leads to:
𝜕𝜋𝐴
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
=( 𝑒 𝑒
)
𝑒 )) ( 𝑒 (𝑛𝑒
(𝑚
𝜕𝑠1
𝑚1 2 − 𝑚1
𝑛1 2 − 𝑛1𝑒 )
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑛2𝑒
− (𝑝1 + 𝑠1 ) ( 𝑒 𝑒
)( 𝑒 𝑒
)
𝑒
𝑚1 (𝑚2 − 𝑚1 ) 𝑛1 (𝑛2 − 𝑛1𝑒 )
=0
Considering as holding the assumption of both platforms competing
and having non-zero demands, similarly 𝐷11 =
As 𝑛2𝑒 > 𝑛1𝑒 >
𝑝2 𝑚1𝑒 −𝑝1 𝑚2𝑒
𝑚1𝑒 (𝑚2𝑒 −𝑚1𝑒 )
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒 𝑝1 𝑛2𝑒 + 𝑠1 𝑛2𝑒
−
=
𝑛1𝑒 (𝑛2𝑒 − 𝑛1𝑒 ) 𝑛1𝑒 (𝑛2𝑒 − 𝑛1𝑒 )
0, 𝑛1𝑒 (𝑛2𝑒 − 𝑛1𝑒 ) > 0 thus:
𝑠2 𝑛1𝑒 − 2𝑠1 𝑛2𝑒 − 𝑝1 𝑛2𝑒 = 0
> 0, so:
0
Substitution of 𝑝1 in the latter gives:
𝑝2 𝑚1𝑒 − 𝑠1 𝑚2𝑒 𝑒
𝑠2 𝑛1𝑒 − 2𝑠1 𝑛2𝑒 −
𝑛2 = 0
2𝑚2𝑒
𝑒 𝑒
𝑝2 𝑚1 𝑛2 𝑠1 𝑛2𝑒
𝑠2 𝑛1𝑒 − 2𝑠1 𝑛2𝑒 −
+
=0
2𝑚2𝑒
2
𝑒 𝑒
𝑒
𝑝2 𝑚1 𝑛2
𝑛2
𝑠2 𝑛1𝑒 −
= 𝑠1 (2𝑛2𝑒 − )
2𝑚2𝑒
2
𝑒 𝑒
𝑒
𝑝
𝑚
𝑛
3𝑛
2 1 2
2
𝑠2 𝑛1𝑒 −
= 𝑠1
2𝑚2𝑒
2
2𝑠2 𝑛1𝑒 𝑝2 𝑚1𝑒
𝑠1 =
−
3𝑛2𝑒
3𝑚2𝑒
Using 𝑠1 in 𝑝1 :
𝑝2 𝑚1𝑒 𝑠1 𝑝2 𝑚1𝑒 𝑠2 𝑛1𝑒 𝑝2 𝑚1𝑒 2𝑝2 𝑚1𝑒 𝑠2 𝑛1𝑒
𝑝1 =
− =
−
+
=
−
2𝑚2𝑒
2
2𝑚2𝑒
3𝑛2𝑒
6𝑚2𝑒
3𝑚2𝑒
3𝑛2𝑒
Summarizing, we have the following reaction function on platform
A depending on its expected market dimensions (𝑛1𝑒 and 𝑚1𝑒 ) and on
the market and pricing expected on platform B (𝑛2𝑒 and 𝑚2𝑒 , 𝑝2 and 𝑠2 ):
2𝑝2 𝑚1𝑒 𝑠2 𝑛1𝑒
𝑝1∗ =
−
3𝑚2𝑒
3𝑛2𝑒
𝑒
2𝑠2 𝑛1 𝑝2 𝑚1𝑒
𝑠1∗ =
−
3𝑛2𝑒
3𝑚2𝑒
{
Moving to platform B and following the same approach, its profit
function can be written as:
𝑝2 − 𝑝1
𝑠2 − 𝑠1
𝜋𝐵 = (𝑝2 + 𝑠2 )𝐷21 𝐷22 = (𝑝2 + 𝑠2 ) (1 − 𝑒
) (1 − 𝑒
)
𝑚2 − 𝑚1𝑒
𝑛2 − 𝑛1𝑒
As
𝜕 2 𝜋𝐵
𝜕𝑝22
< 0, first order condition for setting 𝑝2 to maximize profit
leads to:
𝜕𝜋𝐵
𝑝2 − 𝑝1
𝑠2 − 𝑠1
= (1 − 𝑒
)
𝑒 ) (1 − 𝑒
𝜕𝑝2
𝑚2 − 𝑚1
𝑛2 − 𝑛1𝑒
1
𝑠2 − 𝑠1
− (𝑝2 + 𝑠2 ) ( 𝑒
) (1 − 𝑒
)=0
𝑚2 − 𝑚1𝑒
𝑛2 − 𝑛1𝑒
Where assuming usual positive demands:
𝑝2 − 𝑝1
1
(1 − 𝑒
)=0
𝑒 ) − (𝑝2 + 𝑠2 ) ( 𝑒
𝑚2 − 𝑚1
𝑚2 − 𝑚1𝑒
As 𝑚2𝑒 > 𝑚1𝑒 , 𝑚2𝑒 − 𝑚1𝑒 > 0:
𝑚2𝑒 − 𝑚1𝑒 − 2𝑝2 + 𝑝1 − 𝑠2 = 0
And:
𝑚2𝑒 − 𝑚1𝑒 + 𝑝1 − 𝑠2
𝑝2 =
2
𝜕2 𝜋
Moving to 𝑠2 , as 2𝐵 < 0, first order condition for setting 𝑠2 to
𝜕𝑠2
maximize profit leads to:
𝜕𝜋𝐵
𝑝2 − 𝑝1
𝑠2 − 𝑠1
= (1 − 𝑒
)
𝑒 ) (1 − 𝑒
𝜕𝑠2
𝑚2 − 𝑚1
𝑛2 − 𝑛1𝑒
𝑝2 − 𝑝1
𝑠2
− (𝑝2 + 𝑠2 ) (1 − 𝑒
)(
)=0
𝑚2 − 𝑚1𝑒 𝑛2𝑒 − 𝑛1𝑒
With positive demands:
𝑠2 − 𝑠1
1
(1 − 𝑒
)=0
𝑒 ) − (𝑝2 + 𝑠2 ) ( 𝑒
𝑛2 − 𝑛1
𝑛2 − 𝑛1𝑒
As 𝑛2𝑒 > 𝑛1𝑒 , (𝑛2𝑒 − 𝑛1𝑒 ) > 0 thus:
𝑛2𝑒 − 𝑛1𝑒 − 2𝑠2 + 𝑠1 − 𝑝2 = 0
Substitution of 𝑝2 in the latter gives:
𝑚2𝑒 − 𝑚1𝑒 + 𝑝1 − 𝑠2
𝑛2𝑒 − 𝑛1𝑒 − 2𝑠2 + 𝑠1 −
=0
2
𝑒
𝑒
𝑚
−
𝑚
+
𝑝
𝑠
1
2
2
1
𝑛2𝑒 − 𝑛1𝑒 + 𝑠1 −
= 2𝑠2 −
2
2
𝑚2𝑒 − 𝑚1𝑒 + 𝑝1 3
𝑛2𝑒 − 𝑛1𝑒 + 𝑠1 −
= 𝑠2
2
2
𝑒
𝑒
𝑒
2𝑛2 − 2𝑛1 + 2𝑠1 − 𝑚2 + 𝑚1𝑒 − 𝑝1
𝑠2 =
3
Using 𝑠2 in 𝑝2 :
𝑚2𝑒 − 𝑚1𝑒 + 𝑝1 − 𝑠2
𝑝2 =
2
𝑚2𝑒 − 𝑚1𝑒 + 𝑝1 2𝑛2𝑒 − 2𝑛1𝑒 + 2𝑠1 − 𝑚2𝑒 + 𝑚1𝑒 − 𝑝1
=
−
2
6
𝑒
𝑒
3𝑚2 − 3𝑚1 + 3𝑝1 − 2𝑛2𝑒 + 2𝑛1𝑒 − 2𝑠1 + 𝑚2𝑒 − 𝑚1𝑒 + 𝑝1
=
6
2𝑚2𝑒 − 2𝑚1𝑒 + 2𝑝1 − 𝑛2𝑒 + 𝑛1𝑒 − 𝑠1
=
3
So the following reaction function can be defined on platform B
depending on its expected market dimensions (𝑛2𝑒 and 𝑚2𝑒 ) and on the
market and pricing expected on platform A (𝑛1𝑒 and 𝑚1𝑒 , 𝑝1 and 𝑠1 ):
2𝑚2𝑒 − 2𝑚1𝑒 + 2𝑝1 − 𝑛2𝑒 + 𝑛1𝑒 − 𝑠1
𝑝2∗ =
3
{
2𝑛2𝑒 − 2𝑛1𝑒 + 2𝑠1 − 𝑚2𝑒 + 𝑚1𝑒 − 𝑝1
∗
𝑠2 =
3
So we now have both reactions functions on the platforms:
2𝑝2 𝑚1𝑒 𝑠2 𝑛1𝑒
2𝑚2𝑒 − 2𝑚1𝑒 + 2𝑝1 − 𝑛2𝑒 + 𝑛1𝑒 − 𝑠1
∗
𝑝1∗ =
𝑝
=
𝑒 −
𝑒
2
3𝑚2
3𝑛2
3
𝑒
𝑒 {
𝑒
𝑒
2𝑠
𝑛
𝑝
𝑚
2𝑛
−
2𝑛
+
2𝑠
− 𝑚2𝑒 + 𝑚1𝑒 − 𝑝1
2
2
1
1
1
2
1
𝑠1∗ =
𝑠2∗ =
𝑒 −
𝑒
3𝑛2
3𝑚2
3
{
Where the system can be solved substituting the expectations with
the actual demands:
𝑝2 𝑚1𝑒 − 𝑝1 𝑚2𝑒
𝑠2 𝑛1𝑒 − 𝑠1 𝑛2𝑒
2
𝐷11 = 𝑒 𝑒
=
𝑛
𝐷
=
= 𝑚1
1
1
𝑚1 (𝑚2 − 𝑚1𝑒 )
𝑛1𝑒 (𝑛2𝑒 − 𝑛1𝑒 )
𝑝2 − 𝑝1
𝑠2 − 𝑠1
𝐷1 = 1 − 𝑒
= 𝑛2
𝐷2 = 1 − 𝑒
= 𝑚2
𝑚2 − 𝑚1𝑒
𝑛2 − 𝑛1𝑒
{ 2
{ 2
Let’s now look whether there exist an equilibrium, solving
formulated systems, where both platforms enjoy positive profit while
applying a symmetric pricing when facing symmetric sides (keeping
in mind the assumption 𝑛2𝑒 > 𝑛1𝑒 and 𝑚2𝑒 > 𝑚1𝑒 ), which means when:
𝑛1 = 𝑚1 = 𝑎
𝑛2 = 𝑚2 = 𝑏
{𝑝 =𝑠 =𝑐
1
1
𝑝2 = 𝑠2 = 𝑑
In such case we have the following system to solve:
𝑎𝑑 − 𝑏𝑐
=𝑎
𝑎(𝑏 − 𝑎)
𝑑−𝑐
𝐷21 , 𝐷22 : 1 −
=𝑏
𝑏−𝑎
2𝑎𝑑 𝑎𝑑 𝑎𝑑
𝑝1 , 𝑠1 :
−
=
=𝑐
3𝑏
3𝑏 3𝑏
2𝑏 − 2𝑎 + 2𝑐 − 𝑏 + 𝑎 − 𝑐 𝑏 − 𝑎 + 𝑐
=
=𝑑
{𝑝2 , 𝑠2 :
3
3
Starting from the subsystem derived from 𝑝𝑘 and 𝑠𝑘 :
𝑎𝑑
=𝑐
3𝑏
{
𝑏−𝑎+𝑐
=𝑑
3
We obtain 𝑐(𝑎, 𝑏):
𝑎𝑑
𝑎 𝑏 − 𝑎 + 𝑐 𝑎(𝑏 − 𝑎) 𝑎
𝑐=
=
=
+
𝑐
3𝑏 3𝑏
3
9𝑏
9𝑏
𝑎(𝑏 − 𝑎)
𝑎
= 𝑐 (1 − )
9𝑏
9𝑏
𝑎(𝑏 − 𝑎)
𝑐=
9𝑏 − 𝑎
And 𝑑(𝑎, 𝑏):
𝑏−𝑎+𝑐 𝑏−𝑎 𝑎
3𝑏(𝑏 − 𝑎) 𝑎
𝑑=
=
+
𝑑=
+
𝑑
3
3
9𝑏
9𝑏
9𝑏
3𝑏(𝑏 − 𝑎)
𝑎
= 𝑑 (1 − )
9𝑏
9𝑏
3𝑏(𝑏 − 𝑎)
𝑑=
9𝑏 − 𝑎
Considering now the subsystem derived from the demand functions:
𝑎𝑑 − 𝑏𝑐
=𝑎
𝑎(𝑏 − 𝑎)
𝑑−𝑐
{1 − 𝑏 − 𝑎 = 𝑏
Substituting 𝑑 and 𝑐 in 𝑏 leads to:
𝑑−𝑐
1 (3𝑏 − 𝑎)(𝑏 − 𝑎)
3𝑏 − 𝑎
𝑏 =1−
=1−
=1−
𝑏−𝑎
𝑏−𝑎
9𝑏 − 𝑎
9𝑏 − 𝑎
𝑏(9𝑏 − 𝑎) = 9𝑏 − 𝑎 − 3𝑏 + 𝑎
9𝑏 − 𝑎 = 6
Doing the same for 𝑎 brings:
𝑎𝑑 − 𝑏𝑐
3𝑎𝑏(𝑏 − 𝑎) − 𝑎𝑏(𝑏 − 𝑎)
2𝑏
2𝑏 𝑏
𝑎=
=
=
=
=
𝑎(𝑏 − 𝑎)
𝑎(𝑏 − 𝑎)(9𝑏 − 𝑎)
9𝑏 − 𝑎
6
3
Which leads to:
𝑏 26
9𝑏 − =
𝑏=6
3
3
And finally to:
3
𝑎 = 𝑛1 = 𝑚1 =
≈ 0.23
13
9
𝑏 = 𝑛2 = 𝑚2 =
≈ 0.69
13
3
𝑐 = 𝑝1 = 𝑠1 =
≈ 0.02
169
27
{𝑑 = 𝑝2 = 𝑠2 = 169 ≈ 0.16
Profits are:
54
𝜋𝐴 =
≈ 0.002
28561
{
4374
𝜋𝐵 =
≈ 0.15
28561
𝐷11 , 𝐷12 :
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