Analyzing the Market Growth in API Economy
using Time-evolving Model
Hiroki Yoshikai, Shin’ichi Arakawa, Tetsuya Takine, Masayuki Murata

Abstract—API (Application Programming Interface) economy
is expected to create new value by converting corporate services
such as information processing and data provision into APIs andusing these APIs to connect services. Understanding dynamics
of a market of API economy under strategies of participants is
crucial to fully maximize the values of API economy. To capture
the behavior of a market in which the number of participantschanges over time, we present a time-evolving market model
for a platform in which API providers who provide APIs toservice providers participate in addition to service providers
and consumers. Then, we use the market model to clarify therole API providers play in expanding market participants andforming ecosystems. The results show that the platform with API
providers increased the number of market participants by 67%
and decreased the cost to develop services by 25% comparedto the platform without API providers. Furthermore, during the
expansion phase of the market, it is found that the proﬁts ofparticipants are mostly same when 70% of the revenue fromconsumers is distributed to service providers and API providers.
It is also found that, when the market is mature, the proﬁts ofthe service provider and API provider will decrease signiﬁcantly
due to their competitions and the proﬁt of the platform increases.
Index Terms—API Economy, Ecosystem, Platform, APIprovidersI. I NTRODUCTION
The API economy is attracting attention as a way to create
new value by converting corporate services such as information processing and data provision into APIs and using these
APIs to connect services [1]. In the API economy, service
providers and consumers connect to the platform and supply
and consume services via APIs.
A two-sided market is a model for analyzing the market
economy. The model has two user groups that provide services
each other via a platform and captures the most basic structureof the market. The two user groups activate the market throughan interaction called the indirect network effect. In Refs. [2]–[4], studies have analyzed the behavior of the digital ecosystemusing a two-sided market model. Modeling market behavior
and seeking equilibrium points under a certain platform strategy will be important in understanding the qualitative behaviorof the market. Sen et al. [4] has found that for an increasein the number of platform functions, the number of platformfunctions should be reduced under conditions of a gradualHiroki Yoshikai, Shin’ichi Arakawa and Masayuki Murata are with Graduate School of Information Science and Technology, Osaka University, Osaka,
Japan (e-mail: {h-yoshikai, arakawa, murata}@ist.osaka-u.ac.jp).
Tetsuya Takine is with Graduate School of Engineering, Osaka University,
Osaka, Japan (e-mail: takine@comm.eng.osaka-u.ac.jp).

decrease in service development costs, and under conditions ofa rapid decrease, the number of platform functions should be
increased to maximize platform proﬁts. However, seeking anequilibrium state in the market by maximizing proﬁts does notreveal an appropriate market form. For example, even whenindirect network effects cause an increase in the number ofservice providers and consumers, the effect is in turn increasein the price imposed on them to connect the platform. Thatis, the optimal strategy to increase the proﬁts of platform
providers will result in the shrink of the market [5]. Therefore,
it is important to capture the behavior of the market as thenumber of market participants changes over time and identify
the strategies that platforms should take rather than to capture
equilibrium points under certain conditions.
In this paper, we present a time-evolving market modelthat aims to capture the behavior of a market in which thenumber of participants changes over time. Speciﬁcally, we
present time-evolving market models for AWS-type platform[6] in which consumers and service providers participate, andAzure-type platform [7] in which API providers participate inaddition to them. We then identify the sustainability conditions
to expand the number of market participants in each market
using these market models. Here, the sustainability conditions
are the parameter region that forms the ecosystem by staying in
the market and ensuring that each of the market participants’interests are properly served, not simply the parameter areathat maximizes the proﬁts of the platform. By clarifying
the sustainability conditions, we can obtain some principles
to form coexistence, cooperative platforms; for example, thestrategies that should be adopted by each market participant,including platforms, during the early phase and/or maturity
phase of the market.
The Azure-type platform targets the API economy, which is
expected to leverage a combination of different APIs to drive
innovation and improve value creation and time-to-market
for new products using APIs [8]. However, when API costs
increase excessively without proper competition among API
providers, service providers are expected to leave the platform
and the market may shrink. Therefore, by contrasting the
behavior of an AWS-type platform without API providers, wewill clarify the role of API providers in expanding market
participants and forming an ecosystem.
II. P LATFORM M ODEL
A. AWS-type Platform
AWS-type platform is a platform involving consumers andservice providers. The interaction model of the market partic-

Fig. 1. Relationships among market participants in an AWS-type platform

ipants is shown in Fig. 1. By using the libraries provided by
the platform, service providers develop services while reducing
development costs and starting small. Consumers pay platform
usage fees to the platform and use various services developed
by service providers. The platform pays service providers a
fee based on the frequency of use of individual services fromthe fees collected from consumers. The platform’s proﬁt willbe the difference between fees from consumers and reward
to service providers. In addition, platform proﬁt is added bycollecting platform usage fees from service providers.
Amazon Web Services (AWS) is a classic example of service providers developing and offering services to consumers.
Service providers develop the functionality required for theirservices while controlling service development costs by using
libraries provided by AWS, such as Amazon ECS and AWS
Lambda, for example. Since service providers use only thelibraries provided by the platform, the abundance of libraries
is required to deploy a variety of services on the platform.
However, since libraries are provided only by the platform,
the cost of library development is structured to increase as thenumber of libraries increases.
B. Azure-type Platform
Azure-type platform is a platform involving consumers,
service providers and API providers. The interaction modelof the market participants is shown in Fig. 2. The platformcollects usage fees from consumers, service providers, andAPI providers. The platform gives a portion of its revenue toservice providers and API providers. In this platform model,
there are more functions available due to the presence ofAPI providers. Furthermore, one API provider can lower
development costs by using functions provided by other API
providers in a complementary relationship. Service providers
can further reduce development costs compared to AWS-type
platforms because they can use APIs as well as libraries
provided by the platform. Newly developed functions can also
be provided as APIs, contributing to lower development costs
for other market participants.
In Azure-type platform, the ease of developing diverse
services depends on the number of APIs, and the more API
providers participate in the market, the lower the cost ofdeveloping functions and developing services becomes.
III. T IME - EVOLVING MARKET MODEL FOR AN API
E CONOMYThis section presents a time-evolving market model for
the AWS-type platform and the Azure-type platform. In theFig. 2. Relationships among market participants in an Azure-type platform

following, we describe the market model for the Azure-type
platform since the market model for the AWS-type platform isobtained when the number of API providers is set to be zeroin the market model for the Azure-type platform.
A. Market
The following are participating in market M.
• Platform p• Consumers ui : u1 , u2 , . . .
• Service providers si : s1 , s2 , . . .
• API providers ai : a1 , a2 , . . .
The market M is time evolving, and the state Mt of thenumber of market participants at time t is represented asfollows:
Mt = {Pt , Ut , St , At }Each variable is represented as follows:
Pt = {p},Ut = {u1 , u2 , . . . , ui , . . . , uU (t) },St = {s1 , s2 , . . . , si , . . . , sS(t) },At = {a1 , a2 , . . . , ai , . . . , aA(t) }Pt is the only participant of the platform at time t and istime independent. U (t), S(t), A(t) are the number of persons
who participated in market M by time t, respectively. Here,the number of participants is the total of those who areeconomically active and participating at time t and those whohave left the market without being economically active at timet − 1.
B. Time Evolution of the Market
In the market model in this paper, the number of participantschanges as a result of their interactions, and proﬁts anddevelopment costs change based on these changes. The detailsof the interactions are described in sections III. C through III.

F. We will simulate a time evolving market model using thefollowing procedure.
1) Determine the initial number of market participants
appropriately, and time t is set to t = 0.
M0 = {P0 , U0 , S0 , A0 }2) Follow the established procedure to ﬁnd U (t), S(t),A(t).
3) Calculate Mt+1 by applying the various equations described in Sections III. C through III. F.
4) Return to 2.
We repeat the calculation of Mt+1 and observe the behaviorof Mt+1 until enough time has elapsed.

ζ and ω are parameters that deﬁnes the behavior of the increasein early adopters and majority respectively, and δ(t) is a binaryparameter that indicates whether market M and other markets
are in a competitive environment. Let ζ, ω, δ(t), oearly (t) begiven in advance.
In this paper, we set parameters that there is no withdrawalof consumers and that the number of consumers increases
monotonically with each incremental step, reaching a ceilingat a certain step.
E. API Providers
The set of API providers participating in market M by timet, At , is deﬁned below.
At = {a1 , a2 , . . . , ai , . . . , aA(t) }C. Platform
The proﬁt Up (t) of platform p at time t is
Up (t) = ps · Ŝ(t) + pa · Â(t) + P (t) · (1 − αs − αa )Ŝ(t) and Â(t) are the number of service providers and API
providers participating in market M at time t, respectively,
and are deﬁned in Section III. E and thereafter. ps , pa are theplatform usage fees of the service providers and API providers,
respectively. In addition, αs , αa are parameters that deﬁne thecost paid to the service providers and API providers, respectively. Furthermore, platform p pays the service providers and
API providers a fee based on the number of times the service
is used or the API is used, and the source of the fee, P (t), is
P (t) = pc · U (t) − Ip (t)The pc is the platform fee for consumers. We assume that
consumers enter into subscription-type contracts and interpret
P (t) as being ﬁnanced by part of pc . The Ip (t) is the costof capital investment in platform p at time t, augmenting thelibrary at a cost of Ip (t) = η · (pc · U (t)). η is a parameterthat deﬁnes the investment ratio.
Although the number of libraries F (t) held by the platform
increases with investment, we interpret this as an increase ininvestment cost with the increase in the number of libraries.
Therefore, the number of libraries is deﬁned as follows:
F (t + 1) = F (t) + e−γ·F (t)/Ip (t)where γ is a parameter for increasing investment cost.
D. Consumers
The consumers consist of two elements: early adopters andmajority.
U (t + 1) = U early (t) + U majo (t)Each element is given below based on the maximum numberof early adopters, K(t), and the number of early adoptersparticipating in other markets that are not market M, oearly (t),and its change.

In this section, we deﬁne the behavior of the API provider
ai . The proﬁt Uai (t) of ai is
Uai (t) = αa P (t) ∑F(ai , St , At , Rt )−pa −Ka (F +J(Ti ))ak F(ak , St , At , Rt )αa is a parameter that deﬁnes the cost to be paid to the
API providers. The function F(ai , St , At , Rt ) represents thenumber of times the API provided by ai is used and isdetermined by the market participants at time t and theirfrequency of use (popularity) Rt . αa P (t) is part of the revenue
earned by the platform at time t. The ratio of the number ofuses of the API provided by ai , F(ai , St , At , Rt ), to the total
number of uses of the API existing in the market at time tdetermines ai ’s revenue (income). F(ai , St , At , Rt ) is given
below:
1
F(ai , St , At , Rt ) =exp(−0.003I(Ti ))Â(t)where Ti is a list of complementary and competitive relationships between ai and other API providers, and function
I counts the number of competitive relationships by taking
a list containing competitive relationships as an argument.
Therefore, the greater the number of APIs in a competitive
relationship I(Ti ), the smaller the value of exp(−0.003I(Ti )),and the fewer times that API is used.
API provider ai decides whether to join or leave market M
based on the positivity or negativity of the proﬁt. In this paper,
the leave condition is that the proﬁt is negative. Assumingthat participation and withdrawal are represented by binary
variables with ∆i|u≥0 , the number of participants in market
M at time t, Â(t), is∑Â(t) =
∆k|u≥0k

The complementary and competitive relationship Ti between an API provider ai and another API provider is represented as follows:d
U early (t)d earlyU) − δ(t) oearly (t)(t) = ζU early (t)(1.0 −
dt
K(t)
dt

Ti = [1, −1, . . . , (ai =)0, . . . , 1, 0]dd majoU(t) = ωU early (t) − δ(t) oearly (t)dtdt

In this example, ai and a1 are complementary, a2 is competitive, and ai (itself) is irrelevant (0).

(1)

F. Service Providers

1.6x106
1.4x106
number of consumers

When there is a complementary relationship, it can beinterpreted as lower development costs for the API providers.
Therefore, assuming that the sum of the number of libraries
F provided by the platform and the number of API providers
in a complementary relationship J(Ti ) act on the development cost of ai , the API development cost is represented as
Ka (F + J(Ti )). Function J counts the number of complementary relationships by taking a list containing complementary relationships as arguments. Ka (F ) is the development
cost (monotonically decreasing with F ) when the number oflibraries provided by the platform is F . It expresses that the
number of API providers J(Ti ), which is complementary, acts
to reduce the development cost.

1.2x106
1x106
80000060000040000020000000 100 200 300 400 500 600 700 800 900 1000
weeks

Fig. 3. Number of consumers

A. Model Settings

Service providers compose and provide services to consumers using APIs provided by API providers.
The set of service providers participating in market M bytime t, St , is deﬁned below.
St = {s1 , s2 , . . . , si , . . . , sS(t) }The competitive relationship Vi between one service
provider si and another service provider is represented asfollows:
Vi = [0, −1, . . . , 0, . . . , −1, 0](2)
In this example, si and s1 are irrelevant, s2 is a competitive
relationship, and si is irrelevant. Unlike the case of API
providers, we do not consider complementary relationships
among service providers.
The number of times the service is used is as follows:1exp(−0.012I(Vi ))G(si , St , At , Rt ) =Ŝ(t)Similar to the equation for the number of times the API is used,
the greater the number of service providers in a competitive
relationship I(Vi ), the smaller the value of exp(−0.012I(Vi )),and the fewer times the service is used.
The proﬁt Usi (t) of si is expressed as follows:G(si , St , At , Rt )Usi (t) = αs P (t) ∑sk G(sk , St , At , Rt )− ps − {Ks (F + |Φi (At )|)}
where Φi (At ) represents the set of APIs provided by the API
providers that are used by the service provider si .
IV. A NALYSIS OF M ARKET DYNAMICS USING A
T IME - EVOLVING M ARKET M ODELThis section analyzes the impact of the presence of API
providers on the number of market participants and each participant’s proﬁt by comparing an AWS-type platform without
API providers and an Azure-type platform with API providers.
In addition, we will also analyze the impact on the market ofchanging the parameters that deﬁne platform usage fees andpayment costs.

In this section, we describe the model for increasing market
participants and development cost models in the simulation.
1) Increase of consumers: We deﬁned a model of consumers in Section III. D, and in this paper, we adopt a model
based on the transition of consumers for existing services. For
example, this could be the number of Spotify subscription
subscribers [9], [10] or the number of premium membersof Niconico service [11] which is one of popular streaming
platform in Japan. In this paper, we use the model in which
the number of consumers will reach about 1.5 million in about
10 years (500 weeks) and reach a peak, based on the numberof Niconico premium members (Fig. 3). To ﬁt this model, we
use a value of U (t) scaled by one-eighth. Speciﬁcally, we set
ζ, ω, and δ(t) to 0.1, oearly (t) to 10000, and K(t) to 300000.
ω is set to decrease by 0.0003 from 250 weeks. In addition,
we set U early (0) to 10000 and U majo (0) to 0. This allows theanalysis to observe the behavior of market participants during
periods when the number of consumers continues to increase
and during periods when the number of consumers remains
constant, respectively.
2) Increase of service providers: An increasing model ofservice providers is shown below.
S(t + 1) = S(t) + sbirth + Ŝ(t) ∗ 0.015
where sbirth is a variable that is 1 at each step of the simulation
with probability 0.1 and 0 otherwise. We also consider that
0.015 service providers are attracted to the market for every
one service provider participating in the market.
With the case for the Azure-type platform, each service
provider randomly selects APIs to use.
3) Increase of API providers: An increasing model of API
providers is shown below.
A(t + 1) = A(t) + abirth + Â(t) ∗ 0.01
where abirth is a variable that is 1 at each step of thesimulation with probability 0.5 and 0 otherwise. We also
consider that 0.01 API providers are attracted to the market
for every one API provider participating in the market.

4) Development Cost: The greater the number of libraries
and complementary APIs (x), the lower the development costin the development cost model for API providers. Therefore,
the development cost model for API providers is shown as
Ka (x) = 25 exp(−0.003x). In addition, we consider that
service providers will incur more costs than API providers
because they will need to manage customers and operate andmaintain the service. Therefore, the development cost model
for service providers is shown as Ks (x) = 25 exp(−0.003x)+
20.
5) Complementary/Competitive Relationships: Ti in (1) is
randomly determined with a probabilities of 0.4 for a complementary relationship, 0.1 for a competing relationship, and
0.5 for no relationship. Also, Vi in (2) is randomly determinedwith a probability of 0.5 for a competing relationship and 0.5
for no relationship.
B. Parameter Settings
The initial value of the number of platform libraries is 3,
the initial value of the number of API providers is 4, and theinitial value of the number of service providers is 1.
C. Business Strategy of Platform
Platforms can set usage fees for consumers as well as forservice providers and API providers, and a variety of businessstrategies are possible. In this section, we deﬁne the parametersin the market model that can be set by the platform and deﬁnethem as the platform strategy.
First, we will describe the basic settings that will serveas the basic strategy for the platform. The basic settings areshown in Table I. Parameters related to fees such as platform
usage fees are set to be in thousands of yen [/week].
In the basic settings, the platform pays 35% of the feescollected from consumers to the service providers and the API
providers, respectively. Thus, 30% of the fees collected fromconsumers would be proﬁt for the platform. We set this parameter with reference to the margins in the Google Play Storeand the Apple Store [12]. Based on these parameter settings,
we will introduce the following three platform strategies which
the platforms can choose.
In high usage fee setting, we set higher fees for service
providers and API providers to use the platform. This will leadto increase the platform revenue and to decrease the proﬁts ofservice providers and API providers, which results in fewer
market participants. We will observe how much the market
shrinks when the platform sets the price selﬁshly.
In high margin setting, we set a low percentage of therevenue earned by the platform from consumers to pay service
providers and API providers. Platform revenue will increase,but overall revenues of service providers and API providers
will decrease, which will result in less market participants due
to increased competition among market participants at an earlystage. Then observe how much the market shrinks when theplatform monopolizes proﬁt.
In low margin setting, we set a higher percentage of therevenue earned by the platform from consumers to pay service

TABLE IP LATFORM S TRATEGIES
αs
αa
pa
ps

basic
0.35
0.35
1.25
12.5

high usage fee
0.35
0.35
12.5
125

high margin
0.10
0.10
1.25
12.5

low margin
0.50
0.50
1.25
12.5

providers and API providers. Platform revenue will decrease,but overall revenues for service providers and API providers
will increase, which is expected to result in more market
participants. Then, observe how much proﬁt can be securedby the service provider and API provider.
The above parameter settings are shown in Table I. The
common settings for the four platform strategies, including
the basic settings, we set pc to 0.125, η to 0.1, γ to 10000.
In the platform strategy described above, in the case of
an AWS-type platform with no API providers, the platform
receives the fees that are paid to the API providers on the
Azure-type platform. For example, in the basic setting, theplatform pays 35% of the fees collected from consumers to
the service providers. Thus, 65% of the fees collected fromconsumers will beneﬁt the platform.
D. Numerical Results
In this section, we present the results of our analysis of
Azure-type platforms in four different platform strategies andthe results of our comparison of Azure-type platforms and
AWS-type platforms. In this paper, one step in the simulationis considered as one week, and the behavior is observed up to
1000 weeks.
1) Market growth: In this section, we evaluate the market
model from the perspective of market growth, using thenumber of market participants as an indicator. The number ofmarket participants is deﬁned here as the number of service
providers and API providers participating in the market as of1000 weeks.
First, we compare Azure-type platforms. Fig. 4 and 5 show
the number of service providers and API providers for the four
platform strategies, respectively.
In the high usage fee platform strategy, the decrease in
the number of service providers is lower than that of API
providers. This could be due to the small number of service
providers relative to the number of API providers and the lackof competition with a 90% reduction in the number of service
providers. The fact that the high margin platform strategy has
resulted in a similar rate of decrease in the number of service
providers and API providers suggests that the number ofmarket participants will continue to increase until appropriatecompetition is in place.
Next, compare with an AWS-type platform. In the basic
setting platform strategy, the Azure-type platform has about
67% more service providers. In addition, about 15%, 70%,
and 65% more are in the high usage fee, high margin, andlow margin settings, respectively. Therefore, for all platform

Azure-type

the proﬁt of each participant as an indicator. The coexistentplatform referred to here is a platform where not only theplatform beneﬁts, but also the service providers and API
providers participating in the market beneﬁt while contributing
to the development of the market. The evaluation will also be
conducted at two time points: at 500 weeks, after the numberof consumers has continued to increase, and at 1000weeks,
after the number of consumers has peaked.

AWS-type

2000
1800

1600
1400

1200
1000

800
600

400
200

0
basic

high usage feehigh margin

low margin

Fig. 4. Comparison of number of service providers

70000

First, we evaluate Azure-type platforms and AWS-type
platforms at 500 weeks. The proﬁts of each participant at 500
weeks are shown in Fig. 6. In the Azure-type platform, proﬁt
is divided into three equal parts in the basic setting platform
strategy, indicating that a coexistence has been achieved.
The high usage fee setting and high margin setting platform
strategies show that platform proﬁts are the majority of the
proﬁts. However, low margin setting platform strategies havenot ensured platform proﬁts.

60000

Service provider proﬁts on Azure-type platforms relative to
AWS-type platforms increased for all four platform strategies.
Speciﬁcally, they increased by 3% in the basic setting, 3% in
the high usage fee setting, 10% in the high margin setting, and
2% in the low margin setting. Again, this is likely due to thelower development costs of Azure-type platforms compared to
AWS-type platforms, resulting in increased proﬁts for service
providers on Azure-type platforms compared to AWS-type
platforms.

50000
40000
30000
20000
10000

0
basic

high usage feehigh margin

low margin

Fig. 5. Comparison of number of API providers

strategies, we found that Azure-type platforms have more
service providers participating in the market.
In the basic setting platform strategy, the total development
cost of the Azure-type platform was about 26700, which
was lower than the total development cost of the AWS-type
platform, about 35500, even though the Azure-type platform
has more service providers participating in the market. The
results show that service providers can lower development
costs by using APIs on Azure-type platforms. Therefore, it
was found that this has allowed more service providers toparticipate in the market because the Azure-type platform
reduces the ratio of development costs to service provider
revenues and allows them to make more proﬁt compared to the
AWS-type platform. The same is true for the high usage fee,high margin, and low margin platform strategies. However, therate of increase in the number of service providers in the highusage fee setting platform strategy is small compared to therate of increase in the basic setting, high margin setting, andlow margin setting platform strategies. This suggests that whenplatform fees are set high, the effect of reduced development
costs due to the presence of API providers will be small, and it
may be difﬁcult to beneﬁt from the presence of API providers.
2) Platform for coexistence: In this section, we will evaluate the parameter areas that form a coexistent platform, using

Next, we evaluate Azure-type platforms and AWS-type
platforms at 1000 weeks. The proﬁts of each participant at
1000 weeks are shown in Fig. 7. For Azure-type platforms,
platform proﬁt account for the majority in all platform strategies. In addition, service providers and API providers proﬁt
more from a low margin platform strategy than from a basic
setting that had achieved tripartite coexistence at the 500
weeks point. Therefore, after 500 weeks, when the numberof consumers peaks, it is better to allocate more money toservice providers and API providers to maintain the market.
In addition, service providers proﬁt on Azure-type platforms
relative to AWS-type platforms increased on all four platform
strategies. Furthermore, except for the high usage fee platform
strategy, the results show a higher rate of increase than at 500
weeks. Speciﬁcally, they increased by 23% in the basic setting,
1% in the high usage fee setting, 22% in the high margin
setting, and 19% in the low margin setting. Therefore, for aplatform strategy with low usage fee, an Azure-type platform
is more likely to maintain the market during market maturity
than an AWS-type platform.
Based on the above evaluations, coexistence and cooperation of three participants can be achieved by the basic strategy
during the period of market growth. However, as the market
matures, the competitions among service providers and API
providers suffers their proﬁts even by the low margin strategy.
We believe a fair competition regulated by the platform’s
strategy is required to achieve the sustainabe market growthand it is left for our future work.

Platform

Service providers

API providers

Azure-type

low margin

high margin

high usage fee

basic

low margin

high margin

high usage fee

basic

180000160000140000120000100000
80000
60000
40000
20000
0

AWS-type

Fig. 6. Breakdown of market participants’ proﬁts (500 weeks)

Platform

Service providers

two participants and increases platform proﬁt after a period of
constant revenue from consumers. At this time, it was foundthat the Azure-type platform was about 20% more proﬁtable
for service providers than the AWS-type platform for a low
platform usage fee setting, making it easier to maintain themarket during the market’s maturity period. The analysis in
this paper revealed the effectiveness of Azure-type platforms
while changing the platform strategy.
However, in the real market, service providers, APIproviders, and consumers also have selection strategies. Particularly regarding consumers, since they may increase or
decrease depending on the number of services and othermarket attractions, we will introduce a time-evolving market
model that includes the selection strategies of each participant
to clarify the behavior of the market.
ACKNOWLEDGEMENT
This work is supported in part by the KDDI Foundation.

API providers

180000160000140000120000100000
80000
60000
40000
20000
0

Azure-type

low margin

high margin

high usage fee

basic

low margin

high margin

high usage fee

basic

R EFERENCES

AWS-type

Fig. 7. Breakdown of market participants’ proﬁts (1000 weeks)

V. C ONCLUSION
In this paper, we presented a time-evolving market model
to capture the behavior of a market in which the number ofparticipants changes over time. We then analyzed the impact
on the market of changing the parameters that deﬁne theplatform usage fees and the costs paid by the platform to
the service providers and API providers. Furthermore, we
analyzed the impact of the presence of API providers on thenumber of market participants and their respective proﬁts bycomparing platforms without API providers with those with
API providers. The results showed that the platform with API
providers increased the number of market participants by 67%
and decreased the cost of developing services by 25% compared to the platform without API providers in the parameterarea closest to the coexistence. We also found that coexistence
is feasible during periods of increasing consumers, when theplatform allocates 70% of its revenue from consumers toservice providers and API providers. On the other hand, it
was also found that competition among service providers andcompetition among API providers decreases the proﬁt of these[1] IBM, “IBM unveils matchmaking technology to navigate API
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