Digital platforms to close the information asymmetry GAPS
Market intermediaries coordinate the actions of buyers and sellers. Digital platforms, including platform-as-a-service, assume the role of market intermediaries with some innovative roles. In a world with multiple intermediaries, consumers and suppliers continue to face time search costs due to inte...
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| Veröffentlicht in: | Проблемы управления и информатики |
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| Datum: | 2022 |
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Інститут кібернетики ім. В.М. Глушкова НАН України
2022
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| Zitieren: | Digital platforms to close the information asymmetry GAPS / A. Gaivoronski, V. Gorbachuk, M. Dunaievskyi, S.-B. Suleimanov // Проблеми керування та інформатики. — 2022. — № 6. — С. 67–82. — Бібліогр.: 20 назв. — англ. |
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| author | Gaivoronski, A. Gorbachuk, V. Dunaievskyi, M. Suleimanov, S.-B. |
| author_facet | Gaivoronski, A. Gorbachuk, V. Dunaievskyi, M. Suleimanov, S.-B. |
| citation_txt | Digital platforms to close the information asymmetry GAPS / A. Gaivoronski, V. Gorbachuk, M. Dunaievskyi, S.-B. Suleimanov // Проблеми керування та інформатики. — 2022. — № 6. — С. 67–82. — Бібліогр.: 20 назв. — англ. |
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| container_title | Проблемы управления и информатики |
| description | Market intermediaries coordinate the actions of buyers and sellers. Digital platforms, including platform-as-a-service, assume the role of market intermediaries with some innovative roles. In a world with multiple intermediaries, consumers and suppliers continue to face time search costs due to interacting with several intermediaries. Consumers and suppliers reduce future net gains through the monetization of search costs. Consumers have different levels of willingness to pay, suppliers have varying opportunity costs, and intermediary firms have different transaction costs. These firms set both selling and buying prices (acting as price setters). Consumers search for firms offering lower buying prices, while suppliers look for firms offering higher selling prices. Due to this heterogeneity and search costs, market equilibrium is determined by the distribution of selling prices and the distribution of buying prices.
Ринкові посередники координують дії покупців і продавців. Цифрові платформи, у тому числі платформа як послуга, беруть на себе роль ринкових посередників з деякими новітніми ролями. У світі з декількома посередниками споживачі та постачальники продовжують зазнавати витрат часу пошуку внаслідок реагування на кількох посередників. Споживачі та постачальники знижують майбутні чисті виграші завдяки монетизації витрат часу пошуку. Споживачі мають різний рівень готовності платити, постачальники мають різні альтернативні витрати, а фірми-посередники мають різні трансакційні витрати. Ці фірми встановлюють як ціни продажу, так і ціни купівлі (є ціновстановлювачами). Споживачі шукають фірми, які пропонують нижчу ціну купівлі, а постачальники — фірми, які пропонують вищу ціну продажу. Через таку неоднорідність і витрати пошуку ринкова рівновага є розподілом цін продажу та розподілом цін купівлі.
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| first_indexed | 2026-03-14T20:10:56Z |
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© A. GAIVORONSKI, V. GORBACHUK, M. DUNAIEVSKYI, S.-B. SULEIMANOV, 2022
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 67
ДОСЛІДЖЕННЯ ОПЕРАЦІЙ ТА СИСТЕМНИЙ АНАЛІЗ
UDC 519.8
A. Gaivoronski, V. Gorbachuk, M. Dunaievskyi, S.-B. Suleimanov
DIGITAL PLATFORMS TO CLOSE THE
INFORMATION ASYMMETRY GAPS
Alexei Gaivoronski
Norwegian University of Science and Technology, Trondheim,
https://orcid.org/0000-0002-8470-8780
Alexei.Gaivoronski@ntnu.no
Vasyl Gorbachuk
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv,
https://orcid.org/0000-0001-5619-6979
GorbachukVasyl@netscape.net
Maksym Dunaievskyi
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv,
https://orcid.org/0000-0002-6926-398X
MaxDunaievskyi@gmail.com
Seit-Bekir Suleimanov
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv,
https://orcid.org/0000-0002-7141-6113
SBSuleimanov@gmail.com
Market intermediaries coordinate the actions of buyers and sellers. Digital
platforms, including the case Platform as a Service (PaaS), take the roles of
market intermediaries with some novel ones. In a multi-intermediary world,
consumers and suppliers continue to incur search costs due to reacting to
multiple intermediaries. Consumers and suppliers discount future net gains
due to monetization of search time costs. Consumers have different levels of
willingness to pay, suppliers have different opportunity costs, and interme-
diary firms have different transaction costs. These firms set both bid prices
and ask prices. Consumers look for firms that offer a lower purchase price,
and suppliers look for firms that offer a higher sale price. Due to such heter-
ogeneity and search costs, the market equilibrium is a distribution of sale
prices and a distribution of purchase prices. This equilibrium depends on the
discount rate of consumers and suppliers, for whom a higher discount rate
stands for a decrease in activity (the number of active consumers and sup-
pliers), while a higher discount rate means an increase in the activity of
intermediary firms (the number of active firms): a higher discount rate
increases the costs of time-consuming search for consumers and suppliers.
mailto:alexei.gaivoronski@ntnu.no
68 ISSN 2786-6491
Intermediary firms then raise their purchase prices and lower their sale pric-
es because consumers and suppliers are willing to pay a premium to avoid
further search, thus increasing the returns to intermediation for firms and
stimulating growth in the number of intermediary firms active at the market
equilibrium. Thus, the discount rate determines the search costs. When this
rate falls to zero, the search costs are eliminated and the relationships be-
tween the size of the bid-ask spread and transaction costs are revealed. Then
the Walras equilibrium will be the limiting case of the intermediated market
when transaction costs fall, and the supply and demand model can be con-
sidered an ideal case compatible with the market under consideration at the
presence of search costs and price-setting firms. The cloud technologies are
saving the general search costs. The two basic cases of providers for such
technologies are monopoly and competition.
Keywords: network effects, intermediated trade, self-selection, decentral-
ized pricing, matching, big data.
Monopoly case
Contrary to uncompatible products, compatible products have network exter-
nalities [1, 2]. It is shown that under uniformity of consumer preferences the output
of compatible or uncompatible products by a monopoly is socially optimal one [3, 4].
But under non-uniformity of such preferences market failures are possible [5, 6]. Con-
sumer preferences are said to exhibit network externalities if the utility of each consum-
er increases as the total number of consumers buying the same or compatible brand in-
creases [7, 8]. One approach to modeling consumers’ preferences for the compatibility
of the personal computers (PCs) they buy is to assume that their preferences exhibit
network externalities [9, 10]. This assumption approximates the consumer’s desire for
compatibility in the sense that the consumer’s utility is expressed simply in terms of the
number of consumers of the same or compatible brand, not in terms of the degree of
compatibility between the machine (computer) this consumer buys and the machines
other people use. Before starting the analysis, it is necessary to find out what are the
main problems and questions that should be explained and what answers can be ex-
pected: how increasing the compatibility of brands affects the price and profit levels of
brand-producing firms; how increasing brand compatibility affects consumer utility and
social welfare; how variations in the market structure (increasing the number of firms
producing brands, for example, the transition from a monopoly to a duopoly) affect the
degree of compatibility of brands and/or the pricing of differentiated brands [11, 12].
A monopoly pricing strategy in the presence of network externalities can be seen in a
market with one computer manufacturer selling a single brand to identical users who
value compatibility [3, 13]. In a single-brand computer market, all computers run the
same operating system (OS) and are therefore considered compatible, provided that the
machines can be connected via cables attached to communication ports (directly or via
the Internet) or by transferring such storage tools as floppy disks and portable hard
drives [14]. These cables and devices are generally called adapters. Thus, in the case of
monopoly, compatibility is valued because installing an adapter will allow any two
machines to communicate and work together. Since the installation of an adapter in-
creases the cost of production, computer manufacturers often find it unprofitable to
install such an adapter.
Let there be identical potential computer users who value compatibility. Each
consumer buys no more than one computer at a price of .p If the monopoly sold
[0, ]q computers, then the actual number of computer buyers is ,q and the utility
function of each consumer is given by
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 69
,adapter was installed,
, adapter was not installed,
0, computer was not bought,
p q
U p
(1)
where: — the basic utility that each consumer gets from using a computer, regardless
of its compatibility; — the degree of importance of compatibility. Profit q
measures the total utility gain from a machine with an adapter that can interface with the
rest ( 1)q of the machines sold in that market.
A1. Suppose that a monopoly computer manufacturer can produce only one type of
computer — a non-adapter computer 1 or an adapter computer 2, but not both 1 and 2
types. This assumption reflects assembly line technology, which does not allow produc-
tion scheduling for two types of goods. In practice, manufacturers often offer different
packages with different storage devices (CD-ROM and DVD drives) and communica-
tion ports (RS-232, SCSI, Universal). As ensuring compatibility requires much more
than attaching an adapter, we assume that the cost of redesigning a machine is high
enough to exclude any conversion of an incompatible machine into a compatible one.
Neglecting sunk and fixed costs associated with machine development, let’s focus
on the cost of producing one machine. The cost c of producing a machine equipped
with all the adapters necessary for its compatibility with the rest of the machines is not
less than the cost 0n of producing a machine with no compatibility. Then the total
production costs of the monopoly are equal
, produces machines
( )
, produces machines
c
n
q 2,
TC q
q 1.
(2)
Suppose that the manufacturer makes a decision sequentially in three steps.
At step I (design), the firm decides which machine to produce from machines 1 and 2;
in the production of a compatible machine 2 the cost of production of the machine is
greater by ( )c nq q .
In step II (pricing), the machine design is assumed to be given, and the manufac-
turer chooses the same price p for all machines.
At step III (purchase), each consumer decides whether to buy a machine or not. At
the same time, each user considers the total quantity q of computer users to be given.
After consumers’ purchasing decisions are made, the monopoly takes its revenue from
the buyers and calculates its profit.
These steps describe the game in an extended form where the monopoly has to act
in steps I and II and consumers only in step III. Applying backward induction to find the
subgame perfect equilibria, we compute the Nash equilibria first in step III, then in step
II, and finally in step I.
Consumers are said to have perfect foresight if, at the time of purchase (in step III),
any one of them can accurately predict (form an expectation) how many consumers will
buy each brand. Perfect prediction is often associated with coordination, where all con-
sumers agree to buy a brand or not, based on, say, ancillary reviews in consumer maga-
zines. In addition, perfect forecasting often gives rise to multiple equilibria, because the
situations 0q (there is no consumer who buys the machine) and 0q (there is
a consumer who buys the machine) are possible.
Failure of coordination characterizes the equilibrium, where 0q , if:
there are at least two equilibria with perfect foresight;
70 ISSN 2786-6491
in equilibrium, where 0q , the utility of each buyer exceeds his utility in equi-
librium, where 0q .
A2. In the following, we shall assume that consumers have perfect foresight, and
there is no coordination failure.
In step III, each consumer, making a purchase decision, observes three variables:
whether the monopoly manufacturer has installed adapters (whether the machines
on the market are compatible with other machines);
the price p of the machine;
the total number q of consumers who buy a computer.
For a computer without signs of compatibility, in the absence of coordination fail-
ure, from relation (1) it follows 0U :
, ,
0, .
p
q
p
(3)
If p , then, by virtue of relation (1), the consumer gets zero utility when she
buys a computer, and zero utility when she does not buy a computer. If the consumer
does not care whether to buy a computer or not, then the monopoly can reduce the price
to p , where 0 is a sufficiently small number (for example, the smallest curren-
cy denomination is 1 cent) to induce all consumers to buy the machine and obtain utility
( ) 0U p p .
A3. We assume that a consumer, who is indifferent to the purchase, buys a ma-
chine.
If the manufacturer installs adapters on each machine, making all machines com-
patible, then from relation (1) it follows 0U :
, ,
0, .
p
q
p
(4)
Relation (4) constitutes a single consumer equilibrium under assumptions A2 and
A3. If assumption A2 is not fulfilled, then if coordination fails, the situation 0q in re-
lations (3) and (4) is possible, that is, compatibility does not affect the purchase. In step
II, the monopoly chooses the price that maximizes its profit given the consumer demand
function (3) (for machines 1) or (4) (for machines 2). For machines 1 the monopoly
price p is . Then, taking into account the cost function (2), the total monopoly profit
is equal to
( ) ( )n n np q TC q . (5)
For machines 2, the monopoly price p is . Then, taking into account the
cost function (2), the total monopoly profit is equal to
( ) ( ) ( )c c cp q TC q . (6)
In step I, the monopoly decides how to design its machine, knowing that the instal-
lation of compatibility adapters will increase the cost of production by and allow
the price to increase by . To make a monopoly decision, it is only necessary to
compare the values of profits (5) and (6). Therefore, the monopoly will produce ma-
chines 2, if
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 71
( ) ( )с с n n ,
с n for 0 , (7)
that is, the gain from compatibility is not less than the difference in production costs.
A natural question then arises whether monopoly reduces social welfare by provid-
ing or not providing compatibility adapters. In general, a monopoly reduces welfare be-
cause it charges a high price and sells a volume that is less than optimal. However, this
does not necessarily mean that monopoly distorts social welfare by installing or not in-
stalling adapters when their social cost exceeds the social gain. Social welfare is deter-
mined by the sum U of consumer benefits and monopoly profit :
W U . (8)
If the social planner decides to produce machines 1, then from the relations
n , (1), (5), (8) it follows that welfare does not depend on the price p :
( ) ( ) ( )n n n nW W U p p . (9)
The point is that firm revenues must always equal total consumer spending, and
firms are owned by consumers. Then prices reflect only the transfer from consumers to
firms, and then from firms to consumers through the distribution of profits. Thus, in the
ratio (9) measures the aggregated consumer utility, and n measures the aggre-
gated cost of production of the economy. If the social planner decides to produce ma-
chines 2, then relations c , (1), (6), (8) imply
( ) ( ) ( )c c c cW W U p p . (10)
Equations (9) and (10) mean that compatibility is socially desirable when
0 ( ) ( ) ( )c n c n c nW W ,
с n for 0 ,
which coincides with condition (7).
Proposition 1 [13]. A monopoly selling computers to identical consumers will in-
stall compatibility adapters if and only if it is socially optimal to do so: here monopoly
does not lead to market failure.
Proposition 1 resembles the result that a monopoly manufacturer of electric lamps
will have no incentive to reduce the duration of operation of electric lamps below the
socially optimal level. A monopoly uses the price mechanism to extract additional rents,
but at the same time acts as a social planner to solve the same problem of technology
choice (cost of production). When consumers have different compatibility preferences
and the monopoly cannot discriminate between different types of consumers, then
statement 1 does not hold.
Let’s continue the analysis of the market with a single manufacturer selling a sin-
gle computer brand to heterogeneous users who differ only in their compatibility prefer-
ences. There are 2 potential computer users divided into two equally large groups —
a group с that values compatibility and a group n that does not value compatibility
(does not use compatibility, despite the preinstalled adapter). Each consumer buys no
more than one computer at a price of p . If the monopoly sold [0, 2 ]q computers,
then the actual number of buyers of computers is q , the utility function of the type con-
sumer is given by the ratio
72 ISSN 2786-6491
, adapter was installed,
, adapter was not installed,
0, computer was not bought,
c
p q
U p
(11)
and the utility function of the type n consumer is given by the ratio
, buys a computer,
0, does not buy a computer.
n
p
U
(12)
The choice of decision-making time does not change: in step III, consumers make a
purchase decision; if a computer is produced without signs of compatibility, then the to-
tal number of buyers follows from relations (11) and (12)
2 when ,
0 when ,
p
q
p
(13)
if the monopoly manufacturer installs adapters on each machine, making them compati-
ble, then relations (11) and (12) imply in step II,
2 when ,
when ,
0 when ,
p
q p
p
(14)
the monopoly chooses the price that maximizes its profit, based on the consumer de-
mand functions (13) and (14).
For machines of type 1 due to the relation (13), the monopoly price p is equal
to , 2q , and the profit is determined similarly to equation (5)
( ) 2 2 ( ) 2n n np q TC q . (15)
For machines of type 2 due to the relation (14), the monopoly profit is
( ) when ,
( ) 2 when .
c
c
c
p
p
(16)
In step I, the monopoly decides whether to plan to install compatibility adapters on
its machines and increase production costs by .
When p , it follows from relations (15) and (16) that investing in the installa-
tion of adapters is unprofitable. Then the monopoly’s decision to produce compatible
machines occurs if and only if
0 ( ) ( ) 2 ( 2 )c n c n ,
2c n at 0 ,
( )c n n at 0 . (17)
which is a consequence of condition (7) when n .
If the social planner decides to produce machines of type 1, then relations (11),
(12), (15) imply the social welfare
( ) ( ) 2 ( ) 2 ( )n c n n n nW U U p p p ; (18)
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 73
if the social planner decides to produce machines of type 2 at a lower price to sell them
to all consumers 2q , then realtions (11), (12), (16) imply the social welfare
( 2 ) ( ) 2 ( )c c n c cW U U p p p
2 ( )с . (19)
Comparing the values of welfare (18) and (19), we conclude that compatibility is
socially desirable if and only if
0 2 ( ) 2 ( ) 2 ( )c n c n n cW W ,
that is, under condition (7). Conditions (7) and (17) do not coincide, and therefore there
are market failures:
a) c n n ;
b) c n n .
Situation a) means n (high cost of machines of type 1 and that it is profitable
for the monopoly to produce machines of type 2, although it is not socially optimal; sit-
uation b) means n (low cost of machines of type 1 and that it is profitable for the
monopoly to produce machines of type 1, but it is not socially optimal. Conditions (7)
and (17) coincide when n .
Proposition 2 [13]. If consumers are not identical, then a market failure can occur,
where it is profitable for a monopoly to produce one type of machine, and it is socially
optimal to produce another type of machine.
The main conclusion is that the monopoly cannot discriminate price between the
two groups of consumers c and n , and therefore cannot induce the consumers of the
group n to buy the machine and the consumers of the group c to increase their utility:
since the monopoly cannot identify a certain type of each consumer, it cannot charge a
price to the consumers of type n and price 2 from consumers of type c , ac-
cording to their utility functions (11) and (12).
Competition case
The entry of a new firm into the telecommunications industry increases the utility
of already joined consumers and leaves the utility of newly joined consumers un-
changed. A monopoly maximizes its profits by setting its price to join so that the num-
ber of users exceeds half of all available users. It leaves low-paying consumers out of
the network [15].
The formulation of the problem consists in investigating the possibility of an
endogenous and almost discontinuous path of diffusion (for a new network technology),
based on the effect of the installed base (the available number of the technology us-
ers) [1, 8]. Current research in the field of global cellular telephony suggests that tech-
nology exhibits installed base effects in (new technology) adoption and that cellular dif-
fusion varies between countries and groups of countries due to technological, socioeco-
nomic and regulatory factors that influence the diffusion process.
As a rule, existing models cannot empirically distinguish periods of rapid diffu-
sion, common in most industrialized countries, from a critical mass that does not rely on
price reductions or exogenously changing technologies. There are known attempts to
exclude another potential cause of endogenous diffusion − epidemic effects, in which
the level of penetration increases with a constant intensity of use. An unsolved question
74 ISSN 2786-6491
is the properties of the models that allow finding the critical mass of the technology
expansion and proposing appropriate regulations [16, 17]. The purpose of the work
is to justify strictly regulation in the field of telecommunications.
The main results are derived from an economic model consisting of two equal
groups of consumers who want to join a certain telecommunications service (say, re-
ceiving a telephone connection): consumers of the type H value joining this service
higher, and 0 consumers of the type L value joining this service lower.
Denote 0p the fee for joining this service. If the actual number of consumers
connected (to the service) is q , then the utility function of the consumer of type L
is equal to
, consumer is connected,
0, consumer is not connected,
L
q p
U
(20)
and the consumer’s utility function of the type H is
, consumer is connected,
0, consumer is not connected,
H
q p
U
(21)
where 1 measures the importance of the service for the consumer type H :
H LU U .
When constructing the demand function (in vertical p and horizontal q coordi-
nates) for telecommunication services, we use assumption A2 about the absence of co-
ordination failure: if each consumer of the group ( H or L ) benefits from subscribing
to the service, then all consumers of the group will subscribe to the service. Then the
consumers of the group H join the service on the condition that the entire given group
( consumers) joins, and the consumers of the group L — on the condition that all ex-
isting 2 consumers join.
Note that the utility 2LU q p p exceeds 0 under the condition 2p ,
that is, at a sufficiently low price. Thus, 2q at 0 2p . It remains to consider
cases q and 0q .
For q inequalities
0 LU q p p , 0 HU q p p
take place at p , i.e. at 1 . Considering the case 0 2p , the volume
of demand is q at 2 p , for which we assume
2 . (22)
Thus, 0q at p , and the aggregated demand function is given by
2 when 0 2 ,
when 2 ,
0 when .
p
q p
p
. (23)
After constructing the demand curve, let’s define a concept that telecommunica-
tions firms find very useful when marketing their new service: for a given service sub-
scription fee, the critical mass is the minimum number of users needed to guarantee that
at least this number of users will have the non-negative utility from subscriptions. In or-
der to organize a party or a weekend trip, the organizer must convince potential partici-
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 75
pants that a certain minimum number of people will definitely attend, which in effect
means even more participants due to increasing network effects.
In telecommunications, the critical mass is always a function of market price: an
increase in price will mean an increase in the critical mass, and a decrease in market
price will decrease the critical mass, because at a lower price users will be satisfied by a
smaller network size. Commanding such concepts, the former student of one of the au-
thors developed the Djuice project, which earned Kyivstar more than two billion dollars
in five years [18]. If in equilibrium only one type of consumer joins a given service,
then this is the type H : consumers, who value the service highly, will be the first to
purchase it. The relation (21) means that a consumer of type H will join the service
under the condition p q , from which the value of the critical mass follows:
.cm p
q
In the coordinates p along the ordinate axis and q along the abscissa axis,
these values lie on the segment of the beam from the origin of the coordinates (0, 0)
to the point ( , ) . In marketing, it is important to know the critical mass to deter-
mine the level of advertising for new telecommunications services: if cmq consumers
buy the service, even more consumers will join it, despite the reduction in advertising.
Until the 1980-s, most countries had a monopoly market structure in the field of tele-
communications. For example, in Ukraine such a monopoly firm was called
Ukrtelecom, in Estonia — Estonia Telecom. In Israel, until the 1960-s, a similar
firm also provided postal services.
Suppose that the only firm that ensures the connection of consumers to the market
with the demand given by the ratio (23) must spend the amount
p (24)
for each consumer, as well as some fixed amount for entering the market (network
technology) [1, 19]. Non-negativity of monopoly profit
2 ( ) when 0 2 ,
( ) ( ) when 2 ,
0 when
p p
p p p
p
(25)
takes place under the condition
min{ ( ), 2 (2 )} (26)
and the monopoly price mp p .
The maximum profit from serving consumers of only the type H is greater than
the maximum profit from serving all consumers, provided
2 2 20 ( ) [2 (2 ) ] 4 2 ( 4) ,
4
. (27)
Due to relations (20), (21), (25), the social welfare function
( )m
H LW U U p
is equal to
76 ISSN 2786-6491
(2 ) (2 ) 2 ( ) when 0 2 ,
( ) ( ) when 2 ,
0 when
m m m m
m m m
m
p p p p
W p p p
p
=
(2 2 ) (2 2 ) 2 (2 ) when 2 ,
( ) ( ) when ,
0 when
m
m
m
p
p
p
=
(2 2 ) 2 (2 ) when 2 ,
( ) when ,
0 when .
m
m
m
p
p
p
The value of this function when serving all consumers is greater than when serving
only consumers of type H , provided
0 2 ( 2 ) [ ( ) ] 2 ( ) ( )
(2 2 2 ) ( 2 ) ,
2
2
. (28)
Inequalities (22) and (24) imply
min{2 , } 2mp p , 2
,
and then inequality (28) follows from inequality (27). Thus, a monopoly provider of tel-
ecommunications services does not maximize social welfare by maximizing its profits.
During the 1980-s, governments began to realize that monopolistic market struc-
tures in the telecommunications industry, which were believed to be natural monopo-
lies, were distorting industry markets. The main event that led to the introduction of
competition in this field was the division of the US AT&T company into 7 regional
telephone companies in 1982, as well as the creation of MCI and SPRINT companies
as the main competitors in the long-distance and international markets.
In the 1980-s, regulators discussed three basic issues:
knowing that many users (of type H ) are already connected to the existing
monopoly provider of telecommunications services, social welfare may be im-
proved by allowing the new operator to connect other users (of type L ) to the network;
whether a new operator entering the market will make a profit;
when the entry of new providers is socially desirable, how can the existing mo-
nopoly be prevented from engaging in predatory pricing to attract more customers,
thereby narrowing the potential market for a new firm entering the telecommunications
industry.
In 1997, the market for international telephone calls in Israel was deregulated when
two new firms entered the market at the same time. In order to prevent Bezeq Compa-
ny’s existing monopoly from engaging in unfair price-cutting practices, the Israeli Min-
istry of Telecommunications issued a restriction that prohibited price discounts by
Bezeq Company when Bezeq Company’s market share exceeded 70 %. Therefore, we
assume that the regulator orders the existing monopoly not to reduce its price (fee) for
connection (to the network) when the market entry of a competing provider is not com-
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 77
pleted: the existing monopoly serves only consumers of type H , and the new firm can
serve all consumers of type L , reducing its connection fee below the fees of the exist-
ing monopoly.
When a new telecommunications provider (entrant) enters the industry after
consumers of the type H have already paid the existing monopoly for joining, then the
aggregate demand for its service will not be (23) but expressed by the residual demand
when 2 ,
0 when 2 .
e p
q
p
Then the new provider, maximizing his profit, chooses a price 2ep and gets
a positive profit, due to inequality (26).
( ) (2 ) 0e e eq p .
Thus, when a new provider enters the market, it increases its profit from 0 to e ,
the existing monopoly keeps its profit from previously connected consumers, the con-
sumer of type H increases its gain from 0m
HU p to
2 ( 2) 0e
HU p , and the gain of the type L consumer remains
equal 0 2 2e
LU q p .
Proposition 3 [19]. Entry into the telecommunications industry increases the utili-
ty of already connected consumers and leaves the utility of newly joined consumers un-
changed, increases the profit of the new firm and leaves the profit of the existing firm
unchanged. When, in addition to the market for accessions, the market for the flow of
services provided (telephone calls) after the addition consumers of the type L during
the entry of a new firm is taken into account, the existing firm will suffer a reduction in
profits, but social welfare will increase due to a decrease in price.
Let the economy consist not of two, but of three groups of consumers of the same
number of types i 1, 2, 3, and the utility of a consumer of the type i is determined by
, consumer is connected,
0, consumer is not connected.
i
i q p
U
If the number of consumers of one type is , then joining only q consumers
means that consumers of type 3 are willing to pay no more than 3p for the service
in order to obtain non-negative utility 30 3U i q p p ;
when 2q , consumers of type 2 are ready to pay no more than 4p to re-
ceive non-negative utility 20 2(2 ) 4U i q p p p ;
when 3q , type 1 consumers are willing to pay no more than 3p to re-
ceive non-negative utility 10 3U i q p p .
Then the aggregate demand function is given
3 when 0 3 ,
2 when 3 4 ,
0 when p 4 ,
p
q p
(29)
because for 2 ,q 3 4 ,p there are inequalities
78 ISSN 2786-6491
30 3 3(2 ) 6U q p p p , 20 2 2(2 ) 4 .U q p p p
If the monopoly service provider has no production costs associated with connect-
ing consumers to the network ( 0 ), then due to the relation (29) the monopoly
chooses between a) price 3 at demand 3 and b) price 4 at demand 2 . Obvious-
ly, the option a) gives a higher monopoly profit. Since the monopoly has no costs, the
social welfare is maximized by joining all consumers, which occurs in the option a).
Analysis of the telecommunications industry assumes that a consumer’s utility from a
communication service increases when others join the service [1]. We denote [0,1]x
the willingness of the consumer to pay for the service: the greater the value of x , the
less the consumer is willing to pay. We define the utility of a type x consumer as
(1 ) , consumer is connected,
0, consumer is not connected,
e
x
x q p
U
(30)
where eq is the expected number of consumers joining this network. Since this utility
of the consumer increases with increasing ,eq it reveals network externalities.
For indifferent (to subscription) at price p consumer ˆ ( )x p , the following equali-
ties take place:
ˆ ˆ0 (1 ) ,x eU x q p (31)
ˆ1
e
p
x
q
, ˆ ˆ( ) 1 e
e e
q pp
x p x
q q
.
It stands for that consumers ˆ[0, )x x join the network and all consumers
ˆ( , 1]x x do not. We note that x̂ increases with increase eq : under network externali-
ties, with a larger expected number of users, more consumers join the network.
If is a constant cumulative distribution function of the type of consumers on
[0, 1] , then the total number of consumers is
1
0
d x , and the number of connected
consumers is
ˆ ˆ
0 0
ˆ
x x
q d x d x x . (32)
Although consumer expectations can be influenced by advertising or other cam-
paigns of providers, we will assume that consumers, seeking to receive reliable infor-
mation, correctly predict the number of users: eq q . Then equations (31) and (32)
give the inverse demand function for telecommunication services
ˆ ˆ ˆ ˆ(1 ) (1 ) (1 )ep x q x q x x , (33)
which increases for ˆ [0; 0,5]x and decreases for ˆ [0,5; 1]x . This means that at low
levels of aggregate demand, consumer willingness to pay p increases as demand in-
creases, because the network effect outweighs the price effect; at high levels of demand,
the price effect prevails over the network effect. The value is directly proportional to
the magnitude .p
It follows from equation (33) that the fixed connection fee fp corresponds to two
levels ˆ ( )fx p of indifferent consumer:
2ˆ ˆfp x x , 2ˆ ˆ 0fx x p ,
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 79
2 4
ˆ
2
fp
x
,
( 4 )1
ˆ
2 2
f
l
p
x
,
( 4 )1
ˆ
2 2
f
h
p
x
,
where we assume
4
fp
. At a low level of demand ˆlq x , consumers who value
the service highly join, and at a high level of demand ˆhq x , consumers who value
the service low also join. Therefore, all consumers of the type ˆ[0, )lx x and all con-
sumers of the type ˆ[0, )hx x join, which means the joining of all consumers of the
type ˆ ˆ( , ]l hx x x after reaching the critical mass ˆlx of the network. In the case
0 the profit of the monopoly is
2 2 2ˆ ˆ ˆ(1 ) (1 )pq x q x x , (34)
whence we have the first-order maximization condition
2 2 2 2ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ0 ( ) 2 (1 ) ( 2 2 ) (2 3 )
ˆ
x x x x x x x x
x
. (35)
The expression (34) implies ˆ ˆ( 0) 0 ( 1)x x : the profit of the monopoly is
zero both in the absence of subscribers and for the subscriptions of all potential con-
sumers, because in the latter case the monopoly will have to reduce the fee for joining to
0 (according to the relation (33)). From condition (35), we get two extrema: ˆ 0x and
2
ˆ .
3
x Since it is the second derivative
2
2 2
2
ˆ ˆ ˆ(2 3 3 ) 2 (1 3 )
ˆ
x x x
x
is negative at the point
2
ˆ
3
x , then this point is a local maximum;
2
ˆ
3
x is the point of
the global maximum of ˆ( )x , because the first derivative is positive for
2
ˆ 0,
3
x
.
Then, due to the relation (33), the monopoly price is equal to
2 2 2
ˆ ˆ(1 ) 1
3 3 9
p x x
. (36)
Hence, the monopoly profit due to equality (34) is
22 2 4
ˆ
9 3 27
p q p x
.
Proposition 4 [19]. A monopoly telephone company maximizes its profits by set-
ting its subscription price so that the number of users exceeds half of all existing users
and there are unconnected customers.
Due to the relations (30), (32), (36), when
2
ˆ
3
x , the utility of the connected con-
sumer ˆ[0, )x x is proportional to the value :
2 (1 ) 2 2 (3 3 1) 2 (2 3 )
(1 ) 0
3 9 9 9
x e
x x x
U x q p
.
80 ISSN 2786-6491
Proposition 5 [19]. When the total number of consumers increases, the monop-
oly price and utility of the connected users increase proportionally, and the monopoly
profit increases quadratically.
Installed base effects may derive from other social diffusion effects, including
social learning under uncertainty and social-normative pressures. With a strong decrease
in the intensity of use, the epidemic effect is mostly absent or at least overshadowed
by other factors, primarily consumer heterogeneity. It follows that the driving forc-
es of diffusion are constantly falling prices and/or increasing quality. The main
conclusion is that the entry of a new firm into the telecommunications industry in-
creases the utility of already joined consumers and leaves the utility of newly joined
consumers unchanged. A monopoly maximizes its profit by setting its subscription
price so that the number of users exceeds half of all available users and there are
unconnected consumers. Questions that require further investigation: whether exog-
enous changes are responsible for all diffusion (without a critical mass); whether
there is an element of endogenous diffusion.
О.О. Гайворонський, В.М. Горбачук, М.С. Дунаєвський,
С.-Б. Сулейманов
ЦИФРОВІ ПЛАТФОРМИ ДЛЯ ЗВУЖЕННЯ
РОЗРИВІВ АСИМЕТРІЇ ІНФОРМАЦІЇ
Гайворонський Олексій Олексійович
Норвезький університет науки і технологій, м. Тронхейм,
https://orcid.org/0000-0002-8470-8780
Alexei.Gaivoronski@ntnu.no
Горбачук Василь Михайлович
Інститут кібернетики ім. В.М. Глушкова НАН України, м. Київ,
https://orcid.org/0000-0001-5619-6979
GorbachukVasyl@netscape.net
Дунаєвський Максим Сергійович
Інститут кібернетики ім. В.М. Глушкова НАН України, м. Київ,
https://orcid.org/0000-0002-6926-398X
MaxDunaievskyi@gmail.com
Сулейманов Сеїт-Бекір
Інститут кібернетики ім. В.М. Глушкова НАН України, м. Київ,
https://orcid.org/0000-0002-7141-6113
SBSuleimanov@gmail.com
Ринкові посередники координують дії покупців і продавців. Цифрові
платформи, у тому числі платформа як послуга, беруть на себе роль
ринкових посередників з деякими новітніми ролями. У світі з
декількома посередниками споживачі та постачальники продовжують
зазнавати витрат часу пошуку внаслідок реагування на кількох
посередників. Споживачі та постачальники знижують майбутні чисті
mailto:alexei.gaivoronski@ntnu.no
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2022, № 6 81
виграші завдяки монетизації витрат часу пошуку. Споживачі мають
різний рівень готовності платити, постачальники мають різні
альтернативні витрати, а фірми-посередники мають різні трансакційні
витрати. Ці фірми встановлюють як ціни продажу, так і ціни купівлі (є
ціновстановлювачами). Споживачі шукають фірми, які пропонують
нижчу ціну купівлі, а постачальники — фірми, які пропонують вищу
ціну продажу. Через таку неоднорідність і витрати пошуку ринкова
рівновага є роз-
поділом цін продажу та розподілом цін купівлі. Ця рівновага зале-
жить від ставки дисконту споживачів і постачальників, для яких вища
ставка дисконту означає зменшення активності (кількості активних
споживачів і постачальників), позаяк вища ставка дисконту означає
збільшення активності фірм-посередників (кількості активних фірм):
вища ставка дисконту збільшує витрати трудомісткого пошуку для
споживачів і постачальників. Тоді фірми-посередники підвищують свої
ціни купівлі та знижують свої ціни продажу, оскільки споживачі та по-
стачальники готові платити надбавку, щоб уникати подальшого пошу-
ку, таким чином збільшуючи віддачу від посередництва для фірм і
стимулюючи зростання кількості фірм-посередників, активних за
ринкової рівноваги. Таким чином, ставка дисконту визначає витрати
пошуку. Коли ця ставка спадає до нуля, витрати пошуку зникають, ви-
являючи зв’язки між величиною спреду купівлі-продажу та
транcакційними витратами. Тоді рівновага Вальраса буде граничним
випадком посередницького ринку, коли трансакційні витрати спада-
ють, а модель попиту і пропозиції може вважатися ідеальним випад-
ком, сумісним із вищезазначеним ринком за наявності витрат пошуку
та фірм-ціновстановлювачів. Хмарні технології економлять загальні
витрати пошуку. Двома основними випадками постачальників таких
технологій є монополістичний та конкурентний ринки.
Ключові слова: мережеві ефекти, посередницька торгівля, самовідбір,
децентралізоване ціноутворення, відповідність, великі дані.
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Submitted 21.01.2023
http://doi.org/10.34229/2786-6505-2022-2-6
http://doi.org/10.34229/2786-6505-2022-2-6
|
| id | nasplib_isofts_kiev_ua-123456789-210921 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0572-2691 |
| language | English |
| last_indexed | 2026-03-14T20:10:56Z |
| publishDate | 2022 |
| publisher | Інститут кібернетики ім. В.М. Глушкова НАН України |
| record_format | dspace |
| spelling | Gaivoronski, A. Gorbachuk, V. Dunaievskyi, M. Suleimanov, S.-B. 2025-12-20T22:12:30Z 2022 Digital platforms to close the information asymmetry GAPS / A. Gaivoronski, V. Gorbachuk, M. Dunaievskyi, S.-B. Suleimanov // Проблеми керування та інформатики. — 2022. — № 6. — С. 67–82. — Бібліогр.: 20 назв. — англ. 0572-2691 https://nasplib.isofts.kiev.ua/handle/123456789/210921 519.8 10.34229/2786-6505-2022-6-6 Market intermediaries coordinate the actions of buyers and sellers. Digital platforms, including platform-as-a-service, assume the role of market intermediaries with some innovative roles. In a world with multiple intermediaries, consumers and suppliers continue to face time search costs due to interacting with several intermediaries. Consumers and suppliers reduce future net gains through the monetization of search costs. Consumers have different levels of willingness to pay, suppliers have varying opportunity costs, and intermediary firms have different transaction costs. These firms set both selling and buying prices (acting as price setters). Consumers search for firms offering lower buying prices, while suppliers look for firms offering higher selling prices. Due to this heterogeneity and search costs, market equilibrium is determined by the distribution of selling prices and the distribution of buying prices. Ринкові посередники координують дії покупців і продавців. Цифрові платформи, у тому числі платформа як послуга, беруть на себе роль ринкових посередників з деякими новітніми ролями. У світі з декількома посередниками споживачі та постачальники продовжують зазнавати витрат часу пошуку внаслідок реагування на кількох посередників. Споживачі та постачальники знижують майбутні чисті виграші завдяки монетизації витрат часу пошуку. Споживачі мають різний рівень готовності платити, постачальники мають різні альтернативні витрати, а фірми-посередники мають різні трансакційні витрати. Ці фірми встановлюють як ціни продажу, так і ціни купівлі (є ціновстановлювачами). Споживачі шукають фірми, які пропонують нижчу ціну купівлі, а постачальники — фірми, які пропонують вищу ціну продажу. Через таку неоднорідність і витрати пошуку ринкова рівновага є розподілом цін продажу та розподілом цін купівлі. en Інститут кібернетики ім. В.М. Глушкова НАН України Проблемы управления и информатики Дослідження операцій та системний аналіз Digital platforms to close the information asymmetry GAPS Цифрові платформи для звуження розривів асиметрії інформації Article published earlier |
| spellingShingle | Digital platforms to close the information asymmetry GAPS Gaivoronski, A. Gorbachuk, V. Dunaievskyi, M. Suleimanov, S.-B. Дослідження операцій та системний аналіз |
| title | Digital platforms to close the information asymmetry GAPS |
| title_alt | Цифрові платформи для звуження розривів асиметрії інформації |
| title_full | Digital platforms to close the information asymmetry GAPS |
| title_fullStr | Digital platforms to close the information asymmetry GAPS |
| title_full_unstemmed | Digital platforms to close the information asymmetry GAPS |
| title_short | Digital platforms to close the information asymmetry GAPS |
| title_sort | digital platforms to close the information asymmetry gaps |
| topic | Дослідження операцій та системний аналіз |
| topic_facet | Дослідження операцій та системний аналіз |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210921 |
| work_keys_str_mv | AT gaivoronskia digitalplatformstoclosetheinformationasymmetrygaps AT gorbachukv digitalplatformstoclosetheinformationasymmetrygaps AT dunaievskyim digitalplatformstoclosetheinformationasymmetrygaps AT suleimanovsb digitalplatformstoclosetheinformationasymmetrygaps AT gaivoronskia cifrovíplatformidlâzvužennârozrivívasimetrííínformacíí AT gorbachukv cifrovíplatformidlâzvužennârozrivívasimetrííínformacíí AT dunaievskyim cifrovíplatformidlâzvužennârozrivívasimetrííínformacíí AT suleimanovsb cifrovíplatformidlâzvužennârozrivívasimetrííínformacíí |