# Cloud computing as a platform for monetizing data services: A two-sided game
business model

Ahmed Saleh Bataineh, Jamal Bentahar, Rabeb Mizouni, Omar Abdel Wahab, Gaith
Rjoub, May El Barachi

###### Abstract

With the unprecedented reliance on cloud computing as the backbone for storing
today’s big data, we argue in this paper that the role of the cloud should be
reshaped from being a passive virtual market to become an active platform for
monetizing the big data through Artificial Intelligence (AI) services. The
objective is to enable the cloud to be an active platform that can help big
data service providers reach a wider set of customers and cloud users (i.e.,
data consumers) to be exposed to a larger and richer variety of data to run
their data analytic tasks. To achieve this vision, we propose a novel game
theoretical model, which consists of a mix of cooperative and competitive
strategies. The players of the game are the big data service providers, cloud
computing platform, and cloud users. The strategies of the players are modeled
using the two-sided market theory that takes into consideration the network
effects among involved parties, while integrating the externalities between
the cloud resources and consumer demands into the design of the game.
Simulations conducted using Amazon and google clustered data show that the
proposed model improves the total surplus of all the involved parties in terms
of cloud resources provision and monetary profits compared to the current
merchant model.

###### Index Terms:

Cloud computing business model; game theory; big data, two-sided-market.

##  I Introduction

Cloud computing is witnessing a striking increase in the number of enterprises
and manufacturers that are relying on this paradigm to store and process their
data. For example, the study reported in [1] revealed that one million
customers deploy their own enterprises on Amazon, spending $30$ billion USD on
persistent storage on Amazon EC$2$ instances and generating $600$ ZB of data
per year [2]. This explosive amount of data generated and stored on cloud
resources forms the backbone for Artificial Intelligence (AI) services and
opens the door for a new cloud business paradigm, enabling the latter to be an
active platform for monetizing data that benefit AI services. However, the
cloud is not the actual owner for these big chunks of data, and has no right
to trade and use these data without considering its actual owners.

Motivated by the vision of the cloud as platform for monetizing data services,
we propose in this paper a novel cloud business model which allows data
consumers (e.g., market research enterprises) to run their data analytics on
the huge and diverse data that are stored on the cloud. This not only gives
data consumers the opportunity to extract valuable patterns from massive data
coming from multiple data providers, but also releases them from having to
search and discover appropriate providers for each particular type of data
they need to analyze. Data providers, in addition to favoring the access to
cloud-based infrastructure over purchasing their own computing and storage
platforms, find in the enormous and varied number of data consumers that deal
with the cloud an extra motivation to store their data on this platform to
improve their exposure and increase their market shares. This indirectly
makes, as shown in Figure 1, the cloud computing platform a mediator between
data providers and data consumers and a principal player in the whole big data
analytics process. This opens the door for new and innovative business models
to take advantage of this scenario to increase the profits of all the involved
parties, apart from the traditional business models which treat the cloud as
being a passive virtual market for offering services via the Internet.

Figure 1: Overview of the new cloud business model

Specifically, the literature on business-oriented data trading can be
classified into two main categories, i.e., pure merchant approaches and
collaborative approaches. The proposals under the pure merchant approach such
as [3, 4] and [2] adopt classic economic approaches, mainly the demand-supply
model and one-sided game theory/auction-based pricing to model the
interactions among data providers, data consumers and third-party platforms
(i.e., information service providers). In this approach, the third-party
platform aims to maximize its revenue through buying data from their owners,
reprocessing them, extracting useful information and selling this information
to consumers. This approach suffers from several limitations when applied in
cloud computing scenarios. The first limitation is related to the diversity in
the data consumers’ interests, which entails higher processing costs (in terms
of information extraction for different customers’ interests) for the third-
party platform. Moreover, under the pure merchant model, data providers aim to
maximize their revenue of using their data commodities while the third-party
platform aims to minimize the cost of raw data bought from these providers. In
parallel, from the data consumers’ side, the third-party platform aims to
maximize its revenue from selling the processed information while consumers
aim to minimize the cost of information commodities, considering the maximum
available quality and quantity of information. The resulting equilibrium from
such aggressive competitions among the different involved parties leads to
less and coarse distribution of the total surplus. In addition, data differ
from other economic goods for its potential of being (re)-sold to many
consumers at the same time. In the pure merchant model, since economic goods
cannot be resold, the equilibrium of the market lies at the intersection of
the demand and supply curves. This means that the quantities of goods needed
by consumers is equal to the quantities of goods provided by the sellers. This
however does not hold in our case since the same data can be shared with more
than one consumer at a time, which leads to an aggressive competition among
data providers to sell their data even at lower prices. The drawbacks of the
merchant model are deply discussed in [5] which alternatively proposes a two
sided market model for monetizing personal data. In more detail, Bataineh et
al.[5] propose an open market model in which individuals (actual data owners)
and data consumers trade data over a third party platform that helps them
discover each other. The authors show that the two-sided market outperforms
the merchant model in maximizing the total surplus. However, the main
limitation of this approach is that it is based on a static analysis of
consumer’ demand and data prices, which makes it unsuitable for dynamic cloud
markets.

Under the umbrella of collaborative approaches, some proposals, for instance
[6] and [7], tried to model the interactions among three entities in the
domain of business-oriented IoT. In [6], the authors propose a model in which
client peers are interested in sharing video content with the help of the
cloud. In [7], the authors propose game theoretical models among IoT sensors,
IoT service providers and data consumers. In these games, two entities (i.e.,
IoT sensors and IoT service providers) cooperate together in one game and then
compete as one entity against data consumers. Such an approach suffers from
three drawbacks: (1) it does not consider the cross-group externalities (e.g.,
the mutual impact of the clientele size of one party on that of the other
party) among the involved parties, which makes it unable to capture the whole
and more concrete and realistic picture of the three-sided economical model;
(2) the cooperation and competition strategies adopted by the different
players are highly impacted by the cross-group externalities which might not
always lead to the best outcome for these players; and (3) it does not clarify
how cooperating entities would share their earned revenues.

Adopting traditional game theory concepts (e.g., Shapley value and Nash
equilibrium) to distribute the revenue that results from the cooperation among
the different parties suffers from several limitations when applied in dynamic
data trading scenarios over the cloud. Specifically, 1) although such concepts
might be highly efficient in scenarios wherein all the involved parties are
rational, their effectiveness starts to decrease in the presence of parties
that are heterogenious and prefer to deviate from the equilibrium points. For
example, recent studies have revealed that only $37\%$ of the players tend to
accept the Nash equilibrium in cooperative games (interested readers can
consult behavioral games and ultimatum games [8] for further details); and 2)
even though the Shapley value approach fairly splits the revenues among the
cooperative entities based on their contributions, it becomes inapplicable in
cases wherein the contributions of entities cannot be measured (which applies
to the cloud scenario considered in this work). Specifically, the cloud
provider adds an ethereal/intangible, yet significant, contribution to the
coalition via introducing the wide social networks of data consumers to those
of data providers. On other hand, data providers own the data which forms the
core of this new business. This creates a continuous dilemma between data
providers and cloud providers about who makes the most significant
contribution to the coalition and hence who deserves the biggest share of the
revenues. Equal distribution, so-called _fifty-fifty_ , is one approach to
split the revenues between the cloud provider and data provider. However, as
mentioned before, the rationality and greediness of the involved parties
(i.e., the cloud provider and data provider) prohibit the success of such a
strategy. This leads us to the conclusion that we are dealing with a
behavioral and ultimatum game in which two players (proposer and responder)
argue to split a certain amount of revenue. The proposer is endowed with a sum
of revenue and is responsible for splitting this sum with the responder. The
responder may accept or reject the sum. In the case the responder accepts the
sum, the revenue is split as per the proposal; otherwise, both players receive
nothing.

Contributions. To solve the aforementioned problems, the two-sided market
model [9], which is praised for its success in modeling situations that
involve brokers and cross-group externalities, is investigated to study the
cloud-based data trading problem. The main idea of our solution is that the
cloud computing platform tries to attract data consumers by offering them
higher amounts of computing resources to deploy their data analytic tasks.
This in turn contributes in attracting a larger number of data providers to
reach the cloud’s network of data consumers. Consequently, the data providers
have incentives to offer higher portions of their revenues to the cloud
computing platform. Two-sided market provides effective solution concepts for
situations that are characterized by a third-party platform connecting two
other parties. However, the main limitation of the two-sided market theory is
that it is effective in modeling scenarios in which the demand is static, but
becomes less effective in elastic environments that characterize cloud
computing where the demand is subject to dynamic and continuous changes. To
address this problem, we integrate a novel game theoretical model, as shown in
Figure 2, on top of the two-sided market model. The players of our game are
(multiple) independent competing service providers (followers) and the cloud
computing platform (leader). The players opt for hybrid cooperative and non-
cooperative strategies, where strategies are modeled as closed loops of
dependencies. Data consumers and the cloud platform exhibit cross group
externalities between each other, where a higher demand from consumers leads
to a revenue increase for the cloud platform and a higher supply of computing
resources from the cloud creates more demand from consumers.

In the first stage of the game, the leader (cloud platform) announces the
desired portion of returned revenues out of the data providers’ gain, and then
in the second stage, data providers decide about their pricing strategy for
data consumers. The resulting equilibrium forces the cloud platform to offer
higher and reasonable supply of computing resources to guarantee maximal
levels of revenues, while not showing greedy behavior in terms of its share of
data providers’ revenue. Moreover, following our solution, the data providers
are forced to offer the cloud platform a higher portion of their revenues to
ensure appropriate Quality of Service (QoS) delivered to data consumers. In
the case of a greedy behavior from the cloud, our game uses a subsidizing
mechanism. This mechanism pushes data providers to increase the shared portion
offered for the cloud to sustain high and reasonable levels of computing
infrastructure so as to guarantee high levels of consumers’ demand. Similarly,
in cases where data providers behave greedily by offering small portions of
revenues to the cloud, the subsidizing mechanism pushes the cloud to pump out
more infrastructure units to increase the consumers’ demand so as to guarantee
the highest possible level of revenue portion.

To validate our solution, we conduct empirical experiments using real-world
data from Google and Amazon. Experimental results show that by following our
solution, all the involved parties (i.e., cloud platform, data providers and
data consumers) achieve higher revenues than those achieved by the traditional
cloud computing business model.

Figure 2: Overview of the proposed two-sided game

##  II Related Work

In this section, we provide a literature review on cloud computing business
models. The existing proposals can be classified into two main categories:
classical market and game theoretic-based pricing models. The proposals under
the classical market category such as [10, 11, 12] tackle the pricing of the
cloud services using simple pricing models including those of cost-based
pricing, differential pricing, Ramsey pricing, and demand curve function. They
model the pricing of cloud computing resources as an optimization problem
among multiple cloud providers and cloud users. However, the main drawback of
these approaches lies in their static pricing strategy which does not suit the
highly variable and dynamic environment of cloud computing.

On the other hand, the game theoretical models consider the instantaneous
interactions that might occur among the involved entities and their effects on
each party’s welfare. The objective is to dynamically capture the optimal
price and distribution of the cloud computing resources. Many proposals such
as [13, 14, 15, 16, 17] applied different approaches including games and
machine learning [18] to the cloud resource allocation and pricing problem. In
[13], the authors propose an economic model based on a Stackelberg game to
trade video contents and movies over a cloud platform. The proposed model
formulates the interactions between a service provider (e.g., Netflix) and end
users. The service provider acts as the game leader and aims to minimize the
cloud bandwidth consumption while guaranteeing at the same time users’
satisfaction. The work in [19] models the interactions among multiple Software
as a Service (SaaS) providers and Infrastructure as a Service (IaaS) provider
as a two-stage Stackelberg game. In the first stage of the game, SaaS
providers determine the number of required VM instances while accounting for
both the QoS delivered to their users and the associated costs. In the second
stage, the IaaS providers seek to maximize their revenues in the light of the
bids done by the SaaS providers [20, 21]. The author in [6] proposes an
economic model in which cloud users seek to share video content with other
users over the cloud. The model is solved using both cooperative and non-
cooperative games between the cloud and its users. Similar studies are
investigated in [7, 16] for different cloud applications. The authors in [22]
propose a game theoretical model to deliver a bundle of complementary IoT
services. The proposed solution studies the merchant-consumer scenario in
which the IoT services are directly traded between the service providers and
service consumers without the intervention from any third party. However, this
solution cannot be adopted in our case, where the cloud computing is not the
actual data owner and hence it cannot monetize the data directly for the
consumers. Nevertheless, the cloud computing (the third party in our paper) is
considered as a global market where the data services and data consumers meet
each other, thus increasing their market shares. The authors in [23] and [24]
introduce a market model for managing, trading, and pricing big data services.
Both proposals use the two-sided market theory in order to provide incentives
for both cloud providers and users to increase their data shares. The work
presented in [5] extends the work proposed in [23] and comprehensively studies
the two-sided market model as a successful model for monetizing personal data.
However, these proposals consider a static environment in which the demands on
cloud resources are computed in a static manner, which makes them unable to
accommodate the cloud’s elasticity property.

To the best of our knowledge, the proposed work is the first that addresses
big data services monetization, while considering the cross-group
externalities among the involved entities. Unlike the classical cloud
computing business model (where the main challenge is how to optimize the
cloud utilization while incorporating only operational cost and QoS metrics),
our approach : 1) supports and helps junior big data service providers
especially those that have limited monetary budgets; 2) uses the two-sided
market theory to model the interactions among the involved parties, while all
above-discussed proposals use the classical merchant model; (3) includes a
subsidizing technique to push the resulting equilibrium toward a Pareto
optimal point. On the other hand, the above-discussed proposals adopt the
fairness criterion that rewards the involved parties based on their
contributions. We also differ from the other proposals that adopt the two-
sided market theory by providing a dynamic pricing method, instead of a static
game theoretic-based pricing strategy.

##  III Proposed Big Data Services Monetization Model over the Cloud: A Two-
sided Game Model

We explain in this section the details of our proposed Big data services
monetization.

###  III-A Solution Architecture and Game Formulation

Figure 3: Two-sided model

The proposed cloud market platform, depicted in Figure 3, consists of three
entities: consumers of services $CS$ ($CS_{i}$ denotes Consumers of Service
$i$), big data service providers $SP$ (a Service Provider providing service
$i$ is denoted $SP_{i}$) and a typical Cloud Platform ($CP$). The cloud
platform, such as Google and Amazon, is a market leader with huge computing
and storage capabilities, capitals, and social consumer networks. In our
model, a certain big data service provider $SP_{i}$ that provides a service
$i$ deploys its service on the cloud and receives a monetary value of $P_{i}$
for each consumer access to its service $i$. The cloud platform $CP$ is in
charge of sustaining the consumer access through providing the needed
computing and storage infrastructure including hardware, software and security
services. The relationship between consumer $CS_{i}$’s demand, denoted by
$D_{c_{i}}$, and the computing and storage resources $D_{s_{i}}$ supplied to
$CS_{i}$ is modeled using the two-sided market model as cross group
externalities $\alpha$ and $\beta$. Here, $\alpha$ represents the benefits
that a consumer obtains when some new computing and storage resources are
added to $D_{s_{i}}$ and $\beta$ represents the amount of benefits that the
cloud platform earns when more new consumers are added to $D_{c_{i}}$. The
parameters $\alpha$ and $\beta$ are dependant on the service $i$. However,
instead of using the notations $\alpha_{i}$ and $\beta_{i}$, the index $i$ is
omitted to simplify the equations where the service $i$ is understood from the
context. The same simplification is used for the other parameters that appear
as powers (exponents) in our equations.

The interaction between $SP$ and $CP$ is modeled as a two-stage game where
$CP$ acts as the game leader and $SP$ are the followers. In the first stage of
the game, each service provider providing service $i$ $SP_{i}$ observes the
amount of money returns $\chi_{i}$ requested by $CP$, in order to adjust the
price to be charged to $CS_{i}$. In quest of the price specified by $SP_{i}$,
$CP$ determines the optimal amount of computing and storage resources
$D_{s_{i}}$ that should be supplied to $CS_{i}$. The model forms a closed loop
of dependencies that involves techniques from Stackelberg and Ultimatum game
theory as well as a subsidizing technique.

In the Stackelberg game, the interactions take place in two stages where the
leader ($CP$) makes the first move and then does each follower ($SP_{i}$)
after having observed the leader’s move. In the ultimatum game, the first
player ($CP$) proposes a strategy to divide the amount of returned revenue
with the second player ($SP_{i}$). In case $SP_{i}$ rejects the offer, neither
player gains anything. Otherwise, the first player gets the amount it
requested and the second player gets the rest. In the subsidizing technique,
$SP_{i}$ may chose to subsidize $CP$ by an extra amount of payment that
exceeds the contribution of this $CP$. The objective is to keep an optimal
level of $D_{s_{i}}$ that maximizes the return revenues $P_{i}*D_{c_{i}}$.
Alternatively, $CP$ may subsidize $SP_{i}$ by low portion of the resulting
revenues to keep an optimal level of $P_{i}$. The different parameters and
symbols used in our proposed solution are depicted in Table I.

Model Parameters | Descriptions.
---|---
$SP_{i}$ | Service provider providing service $i$.
$CP$ | A typical cloud platform.
$CS_{i}$ | Consumers of service $i$.
$D_{c_{i}}$ |  $CS_{i}$’s demand.
$D_{s_{i}}$ | IT-infrastructure supply to $CS_{i}$.
$P_{i}$ | Service $i$’s price.
$\phi$ |  $D_{s_{i}}$’s elasticity with respect to $\chi_{i}$.
$\chi_{i}$ | Portion of revenue required by $CP$ from $SP_{i}$.
$\gamma$ |  $D_{c_{i}}$’s elasticity with respect to $P_{i}$.
$\beta$ | The Network effects (externality) on $D_{s_{i}}$ by $D_{c_{i}}$
$\psi$ |  $D_{s_{i}}$’s elasticity with respect to $P_{i}$.
$\alpha$ | The Network effects (externality) on $D_{c_{i}}$ by $D_{s_{i}}$.
$f_{c}$ | Associated costs per service consumer.
$k_{1}$, $k_{2}$ | Constant multipliers.
$\pi_{i}$ |  $SP_{i}$’s payoff.
$f_{s}$ | Associated costs per IT-infrastructure unit.
$\pi$ | Cloud platform’s payoff.
$a_{1}$ |  $=\gamma-\alpha\psi$.
$a_{2}$ |  $=1-\alpha\beta$.
$a_{3}$ |  $=\psi-\gamma\beta$.
$a_{4}$ | $=\alpha\phi$
Table I: Model parameters

###  III-B Players’ Demand and Utility Functions

A precise estimation of the needed computing and storage resources requires a
price estimation mechanism for the number of consumers and the variation of
their demand with respect to the provided QoS. To do so, we define the
consumer’s demand and supply using the Cobb-Douglas function that effectively
captures the elasticity of the computing and storage resources supply
($D_{s_{i}}$) and its variations for each specific user’s demand. This
elasticity is a characteristic property of cloud computing environments. The
demand functions we use are continuous, concave or convex, and capture the
elasticity with respect to each input parameter. Two elasticity parameters are
used $\gamma$ and $\psi$ (see Table I). These two parameters depend on the
service $i$, which is omitted from the notations for simplicity as mentioned
earlier. In our model, the consumer’s demand ($D_{c_{i}}$) is a function of
$P_{i}$ and $D_{s_{i}}$ as shown in Equation (1).

$D_{c_{i}}=k_{1}P_{i}^{-\gamma}D_{s_{i}}^{\alpha}$ (1)

$D_{s_{i}}$ is given in Equation (2). Clearly, higher consumers’ demands would
have an influence on the quantity of supplied resources. The cloud platform
$CP$ uses more computing and storage resources to keep up with the increasing
number of consumer accesses, to maintain a high quality level. The parameter
$\chi_{i}^{\phi}$ represents the cloud platform’s preferences (i.e., desired
profit) and implicitly captures the rationality of both $CP$ and $SP_{i}$. In
fact, it reflects the level of perfect/imperfect information that $CP$ and
$SP_{i}$ have about one another. High elasticity $\phi$ is caused either by a
greedy monopolist cloud platform or by a weak service with few capitals
accepting small portions of returns on profits. The parameter $\phi$ depends
on the service $i$, but as mentioned earlier, the index $i$ is omitted when
the service $i$ is understood from the context. The charged price $P_{i}$ also
positively contributes to $D_{s_{i}}$. We can arguably claim that charging
consumers with higher prices $P_{i}$ forces $CP$ to provide more computing and
storage resources so as to satisfy the consumers’ needs. Modeling $D_{s_{i}}$
as a function of $\chi_{i}$ and $P_{i}$ with different elasticity values
connects $CP$ and $SP_{i}$ strategies with each other, which captures the
sensitivity of $CP$ to $SP_{i}$’s strategy (i.e., structure of the charged
price and shared portion), and highlights the importance of the subsidizing
technique. This aspect is illustrated and discussed further in the simulation
section (Section IV-D).

$D_{s_{i}}=k_{2}\chi_{i}^{\phi}P_{i}^{\psi}D_{c_{i}}^{\beta}$ (2)

By substituting Equation (2) into Equation (1) and vice versa, we can express
$D_{c_{i}}$ and $D_{s_{i}}$ as functions of $P_{i}$ and $\chi_{i}$ as follows:

$D_{c_{i}}=(k_{1}k_{2}^{\alpha}P_{i}^{-a_{1}}\chi_{i}^{a_{4}})^{1/a_{2}}$ (3)

$D_{s_{i}}=(k_{2}k_{1}^{\beta}P_{i}^{a_{3}}\chi_{i}^{\phi})^{1/a_{2}}$ (4)

Each big data service provider $SP_{i}$ is subject to a fixed cost $f_{c}$ per
each consumer access. $SP_{i}$ aims to maximize its payoff as given in
Equation (5). We express the service provider’s payoff $\pi_{i}$ as a function
of $P_{i}$ and $\chi_{i}$ by substituting Equation (3) into Equation (5) and
taking the $\log$ for both sides as shown in Equation (6).

$\pi_{i}=((P_{i})(1-\chi_{i})-f_{c})D_{c_{i}}$ (5)

$\begin{multlined}\log\pi_{i}=\log(P_{i}(1-\chi_{i})-f_{c})+(1/a_{2})(\log
k_{1}k_{2}^{\alpha}\\\ -a_{1}\log
P_{i}+a_{4}\log\chi_{i})\end{multlined}\log\pi_{i}=\log(P_{i}(1-\chi_{i})-f_{c})+(1/a_{2})(\log
k_{1}k_{2}^{\alpha}\\\ -a_{1}\log P_{i}+a_{4}\log\chi_{i})$ (6)

The cloud platform $CP$ is subject to a fixed cost $f_{s}$ per each unit of
computing and storage resources. The $CP$ aims to maximize its payoff as given
in Equation (7). We express the cloud platform’s payoff $\pi$ as a function of
$P_{i}$ and $\chi_{i}$ by substituting Equations (3) and (4) into Equation (7)
as shown in Equation (8).

$\pi=P_{i}\chi_{i}D_{c_{i}}-f_{s}D_{s_{i}}$ (7)

$\pi=(k_{1}k_{2}^{\alpha})^{\frac{1}{a_{2}}}P_{i}^{1-\frac{a_{1}}{a_{2}}}\chi_{i}^{\frac{a_{4}}{a_{2}}+1}-f_{s}((k_{2}k_{1}^{\beta})^{\frac{1}{a_{2}}}P_{i}^{\frac{a_{3}}{a_{2}}}\chi_{i}^{\frac{\phi}{a_{2}}})$
(8)

###  III-C Game Equilibrium

The equilibrium of the above-described game is solved using a backward
induction methodology. Thus, the followers’ (service providers) sub-game is
solved first to obtain their response $P_{i}$ to the service consumers. The
leader’s (cloud platform) sub-game is then computed considering all the
possible reactions of its followers to maximize its payoff [25]. Every service
provider $SP_{i}$ determines its optimal decision $P_{i}^{*}$, while
considering the $CP$’s optimal decision $\chi_{i}^{*}$ as an input parameter.
The players’ best responses are discussed in the following.

######  Theorem 1.

The best responses in the two-sided game are as follows:

  1. 1.

The best response of the service provider $SP_{i}$ is given by:

$P_{i}^{*}=\frac{a_{1}f_{c}}{(a_{1}-a_{2})(1-\chi_{i})}$ (9)

if: $\frac{a_{1}}{a_{1}-a_{2}}>0$ and $\frac{a_{1}}{a_{2}}>1$

  2. 2.

The best response of the cloud platform with respect to a service $i$ is given
by:

$\begin{multlined}\chi_{i}^{\frac{a_{4}-\phi}{a_{2}}+1}(1-\chi_{i})^{\frac{a_{1}+a_{3}}{a_{2}}-1}=f_{s}\times(\frac{\phi}{a_{4}+a_{2}})\\\
\times(\frac{k_{2}k^{\beta}_{1}}{k_{1}k^{\alpha}_{2}})^{\frac{1}{a_{2}}}\times(\frac{a_{1}f_{c}}{a_{1}-a_{2}})^{\frac{a_{1}+a_{3}}{a_{2}}-1}\end{multlined}\chi_{i}^{\frac{a_{4}-\phi}{a_{2}}+1}(1-\chi_{i})^{\frac{a_{1}+a_{3}}{a_{2}}-1}=f_{s}\times(\frac{\phi}{a_{4}+a_{2}})\\\
\times(\frac{k_{2}k^{\beta}_{1}}{k_{1}k^{\alpha}_{2}})^{\frac{1}{a_{2}}}\times(\frac{a_{1}f_{c}}{a_{1}-a_{2}})^{\frac{a_{1}+a_{3}}{a_{2}}-1}$
(10)

if: $a_{4}+a_{2}-\phi<0$

###### Proof.

Consider the service payoff given by Equation (6), the optimal price
$P_{i}^{*}$ is defined by $\partial\pi_{i}/\partial P_{i}=0$ as follows:

$\frac{1}{\pi_{i}}\times\frac{\partial{\pi_{i}}}{\partial{P_{i}}}=\frac{1-\chi_{i}}{P_{i}(1-\chi_{i})-f_{c}}-\frac{a_{1}}{(a_{2})P_{i}}=0$
(11)

$\Rightarrow$

$P_{i}^{*}=\frac{a_{1}f_{c}}{(a_{1}-a_{2})(1-\chi_{i})}$ (12)

Since $P_{i}^{*}$ is always positive, then

$\frac{a_{1}}{a_{1}-a_{2}}>0$ (13)

To verify the type of $P_{i}^{*}$’s optimality, i.e maximum or minimum, we
compute a second derivative test by deriving Equation (5):

$\frac{\partial\pi_{i}}{\partial
P_{i}}=(1-\chi_{i})D_{c_{i}}+(P_{i}(1-\chi_{i})-f_{c})\frac{\partial
D_{c_{i}}}{\partial P_{i}}$ (14)

By deriving Equation 3, then

$\frac{\partial D_{c_{i}}}{\partial P_{i}}=\frac{-a_{1}}{a_{2}P_{i}}D_{c_{i}}$
(15)

By substituting Equation 15 into Equation 14, then

$\frac{\partial\pi_{i}}{\partial
P_{i}}=(1-\chi_{i})D_{c_{i}}-\frac{a_{1}}{a_{2}P_{i}}(P_{i}(1-\chi_{i})-f_{c})D_{c_{i}}$
(16)

By rewriting Equation (16) using Equation (5), then

$\frac{\partial\pi_{i}}{\partial
P_{i}}=(1-\chi_{i})D_{c_{i}}-\frac{a_{1}}{a_{2}P_{i}}\pi_{i}$ (17)

$\frac{\partial^{2}\pi_{i}}{\partial
P^{2}_{i}}=\frac{-(1-\chi_{i})a_{1}}{a_{2}P_{i}}D_{c_{i}}-\frac{a_{1}}{a_{2}P_{i}}\frac{\partial\pi_{i}}{\partial
P_{i}}+\frac{a_{1}}{a_{2}P^{2}_{i}}\pi_{i}$ (18)

By simplifying Equation (18) and substituting Equation (12), we obtain:

$\frac{\partial^{2}\pi_{i}}{\partial
P^{2}_{i}}=\frac{D_{c_{i}}}{P_{i}}(1-\frac{a_{1}}{a_{2}})(1-\chi_{i})$ (19)

Since $D_{c_{i}}$ and $P_{i}$ are always positives, then

$\frac{\partial^{2}\pi_{i}}{\partial
P^{2}_{i}}<0\Rightarrow(1-\frac{a_{1}}{a_{2}})<0\Rightarrow\frac{a_{1}}{a_{2}}>1$
(20)

Similarly, to obtain the optimal $\chi^{*}_{i}$, we derive Equation (8) with
respect to $\chi_{i}$ as given by Equation (21):

$\frac{\partial\pi}{\partial\chi_{i}}=(k_{1}k_{2}^{\alpha})^{\frac{1}{a_{2}}}(\frac{a_{4}}{a_{2}}+1)P_{i}^{1-\frac{a_{1}}{a_{2}}}\chi^{\frac{a_{4}}{a_{2}}}_{i}-(\frac{\phi
f_{s}(k_{2}k_{1}^{\beta})^{\frac{1}{a_{2}}}}{a_{2}})P_{i}^{\frac{a_{3}}{a_{2}}}\chi^{\frac{\phi}{a_{2}}-1}_{i}=0$
(21)

$\chi_{i}^{\frac{a_{4}-\phi}{a_{2}}+1}=f_{s}(\frac{\phi}{a_{4}+a_{2}})(\frac{k_{2}k^{\beta}_{1}}{k_{1}k^{\alpha}_{2}})^{\frac{1}{a_{2}}}P^{\frac{a_{1}+a_{3}}{a_{2}}-1}_{i}$
(22)

By substituting Equation (12) in Equation (22), we get:

$\chi_{i}^{\frac{a_{4}-\phi}{a_{2}}+1}(1-\chi_{i})^{\frac{a_{1}+a_{3}}{a_{2}}-1}=f_{s}(\frac{\phi}{a_{4}+a_{2}})(\frac{k_{2}k^{\beta}_{1}}{k_{1}k^{\alpha}_{2}})^{\frac{1}{a_{2}}}(\frac{a_{1}f_{c}}{a_{1}-a_{2}})^{\frac{a_{1}+a_{3}}{a_{2}}-1}$
(23)

To verify the type of $\chi_{i}^{*}$’s optimality, we compute a second
derivative test by deriving Equation (21) as given by Equation (24):

$\begin{multlined}\frac{\partial^{2}\pi}{\partial\chi_{i}^{2}}=(k_{1}k_{2}^{\alpha})^{\frac{1}{a_{2}}}(\frac{a_{4}(a_{4}+a_{2})}{a^{2}_{2}})P^{\frac{a_{2}-a_{1}}{a_{2}}}_{i}\chi^{\frac{a_{4}}{a_{2}}-1}_{i}\\\
-(\frac{f_{s}\phi(\phi-
a_{2})(k_{2}k_{1}^{\beta})^{\frac{1}{a_{2}}}}{a^{2}_{2}})P_{i}^{\frac{a_{3}}{a_{2}}}\chi^{\frac{\phi}{a_{2}}-2}_{i}<0\end{multlined}\frac{\partial^{2}\pi}{\partial\chi_{i}^{2}}=(k_{1}k_{2}^{\alpha})^{\frac{1}{a_{2}}}(\frac{a_{4}(a_{4}+a_{2})}{a^{2}_{2}})P^{\frac{a_{2}-a_{1}}{a_{2}}}_{i}\chi^{\frac{a_{4}}{a_{2}}-1}_{i}\\\
-(\frac{f_{s}\phi(\phi-
a_{2})(k_{2}k_{1}^{\beta})^{\frac{1}{a_{2}}}}{a^{2}_{2}})P_{i}^{\frac{a_{3}}{a_{2}}}\chi^{\frac{\phi}{a_{2}}-2}_{i}<0$
(24)

By substituting Equation (22) in Equation (24), we obtain:

$a_{4}+a_{2}-\phi<0$ (25)

∎

##  IV Simulations and Empirical Analysis

Figure 4: Simulation overview

In this section, we evaluate the performance of the proposed two-sided game
solution in comparison with the fifty-fifty and the pay-as-to-go approaches in
terms of total surpluses of involved parties (i.e., payoffs of the cloud
platform, service data providers and service data consumers). Specifically, we
aim to: 1) verify the effectiveness of the proposed game vis-à-vis the current
cloud computing business model (i.e., the pay-as-to-go model); 2) study the
equilibrium of the two-sided game in presence of the fifty-fifty choice (i.e.,
egalitarian choice in ultimatum games) which is the typical solution for such
games; and 3) investigate the impact of the model parameters on the
performance of our solution. Figure 4 shows an overview of our simulation
setting in terms of inputs, scenarios, and results. The simulation inputs and
scenarios are described in Sections IV-A and IV-B respectively, while the
simulation results are discussed in detail in Sections IV-C, IV-D and IV-E.

###  IV-A Simulation Setup

In this section, we conduct a simulation analysis grounded on statistical
observations from BMR [1] and real data from [26]. According to [1], in
$2019$, Amazon Web services (AWS) received $30$ billion USD in revenue with
net income around $10$ billion USD from $1$ million active customers running
monthly $70$ million hours of their enterprises on custom instances of Elastic
Compute Cloud (EC2). So, 1) an enterprise customer spends on average up to
$30,000$ USD per year in monthly renting $70$ hours of cloud resources; and 2)
the marginal operating costs for the cloud platform is $66\%$ of revenues
(amazon received $10,000$ USD as net payoff from each consumer). By entering
these numbers in the Amazon calculator [27], we can conclude that the customer
rents on average $70$ hours monthly of $32$ instances of Amazon EC2 where each
instance includes $16$ VMs, $30$ GB of Memory, and $1000$ GB of hard disk
storage at rate $36$ USD$/$hour. The price rate ($36$ USD$/$hour) is denoted
by $P_{s}$, which will be used later to calculate the cloud and data providers
payoffs in the pay-as-to-go model as explained in Section IV-B. The cloud
provider (amazon) entails $66\%$ of instances price ($36$ USD$/$hour) as
operating costs, which is $23.7$ USD$/$hour. The operating costs are denoted
in our model by $f_{s}$. In fact, $40\%$ of revenues as a profit and $60\%$ as
an operation cost are common in business. Thus, we assume the marginal cost of
data consumers ($f_{c}$) entailed by data providers has the same distribution
as ($f_{s}$). The enterprise customer and its consumption of EC$2$ instances
are represented by $SP_{i}$ (service data provider) and $D_{s_{i}}$
respectively. The mean of the supply function $D_{s_{i}}$ consists of $32$
EC$2$ instances. However, enterprise customers have varying business types and
hence vary in terms of the amount of needed cloud resources. To model this
variation in our simulations, the customers’ demand on EC$2$ instances is
normally distributed around the mean with a standard deviation of $10$. This
means that the co-domain of the supply function $D_{s_{i}}$ ranges from $1$ to
$53$ EC$2$ instances. The real dataset [26] registers the log file of
computational big data jobs executed by tremendous enterprise customers over
similar instances of EC2. This dataset helps us extract reliable ranges of
consumers’ demands $D_{c_{i}}$ as well as the externalities $\alpha$ and
$\beta$ as described in what follows. The computational power of each
instance, extracted from the same dataset [26], is normally distributed with a
mean of $0.38$ job per second and a standard deviation of $0.1$. The average
computational power is represented in the proposed model by the externality
factor $\alpha$, which means that $\alpha$ ranges from $0.1$ to $0.7$.
According to the assumption presented in [9], the cross group externalities
factor should be bounded by $0$ and $1$, i.e., $0<\alpha\beta<1$. Hence, the
externality factor $\beta$ would range from $0$ to $1/\alpha$. A consumer’s
demand $D_{c_{i}}$ on each enterprise ranges from $0.1\times 1$ to $0.7\times
53$, which is $0.1$ to $37$ requests per second. The service price, $P_{i}$,
is estimated through observing the prices of $150$ business intelligence
computing services including big data and IoT services located in the the AWS
marketplace [28]. According to the observed prices, $P_{i}$ is normally
distributed with a mean of $1.7$ USD$/$hour and a standard deviation of $0.5$
USD. This means that the service prices range from $0.2$ USD$/$hour to $3.2$
USD$/$hour. The parameter $\phi$ represents the greediness of the cloud
platform with respect to the service providers. The subsidizing factor
$0<\phi<1$ represents the rational behavior (subsidizing behavior) of the
cloud, while $1<\phi$ represents the greedy behavior of the cloud platform.
The price elasticities are set up between $0.1-0.35$ (i.e., $\gamma$), which
are similar to the sensitivity of mobile/telecommunication services price
shown in the literature [29]. We assume that $k_{2}=1$ in our simulation. By
substituting the expected values of $\alpha$, $D_{s_{i}}$, $D_{c_{i}}$,
$\gamma$, and $P_{i}$ into Equation (1) and considering the assumption
$(k_{2}=1)$, we find that the multiplier $k_{1}$ ranges from $0.1$ to $0.99$.
It is worth mentioning that consumers demand $(D_{c_{i}})$ and cloud resources
(i.e., computing and storage resources) $D_{s_{i}}$ supplied to $CS_{i}$ are
only estimated under simulation setup to extract a suitable range for the
multiplier $k_{1}$, but they are not given as simulation inputs. The
simulation calculates the expected consumer demand and the optimal supply of
cloud resources as explained in Section IV-B. The values of all associated
parameters are summarized in Table II.

System Parameters | Values
---|---
$P_{i}$ |  $0.2$ \- $3.2$ USD per hour
$\phi$ |  $0$ \- $5$
$\alpha$ |  $0.1$ \- $0.7$
$\beta$ |  $0$ \- $1/\alpha$
$\gamma$ |  $0$ \- $0.35$
$P_{s}$ | 36 USD per hour
$k_{1}$ | $0.1-0.9$
Table II: Simulation parameters values

###  IV-B Simulation Scenarios

We consider a group of $300$ data service providers in the cloud under three
scenarios: 1) proposed two-sided game; 2) fifty-fifty scenario which follows
our model except that the cloud platform and data provider agree to share the
revenue equality; and 3) pay-as-to-go scenario, which is the current business
model adopted by the main cloud providers such as Amazon and Google.

####  IV-B1 Two-sided scenario

The two-sided model, explained in details in Section III-A, is described in
Algorithm 1. Given a data service price $P_{i}$, the cloud platform determines
the optimal portion of revenue $\chi_{i}$ and the required amount of cloud
resources that maximize its payoff.

Algorithm 1 Two-sided scenario

Input: $\alpha$, $\beta$, $\phi$,$\gamma$, $k_{1}$, $f_{s}$, $f_{c}$
Output: CloudPayoff, ProvidersPayoff, ConsumersDemand

1:for each $Data\,service\,provider\,SP_{i}$ do

2: $SP_{i}$ declares its price $P_{i}$

3: $\chi_{i}$ is calculated through maximizing Equation (5)

4: The cloud calculates $D_{s_{i}}$ through maximizing Equation (7)

5: Equation (1) is used to determine ConsumersDemand

6: Equation (5) is used to determine ProvidersPayoff

7: Equation (7) is used to determine CloudPayoff

8:end for

####  IV-B2 Fifty-fifty scenario

The egalitarian (fifty-fifty) scenario follows the two-sided market model in
terms of consumer demand and supply function, thus considering the
externalities among the involved parties (i.e., Equations (1) and (2)). Thus,
the utilities of the cloud platform and data providers are formalized using
the same payoff equations used in the two-sided model (i.e., Equations (7) and
(5) ). However, under this scenario, the cloud platform requests $50\%$ of the
revenue and hence the subsidizing factor $\phi$ is reset by $1$. The fifty-
fifty scenario is described in Algorithm 2. Specifically, given a shared
portion $\chi_{i}=0.5$ and a subsidizing factor $\phi=1$, the data provider
determines its optimal service price $P_{i}$ through maximizing its payoff
given in Equation (5). Thereafter, the cloud platform calculates the optimal
computing infrastructure $D_{s_{i}}$ by maximizing its payoff given in
Equation (7).

Algorithm 2 Fifty-fifty scenario

Input: $\alpha$, $\beta$,$\gamma$, $k_{1}$, $f_{s}$, $f_{c}$
Output: CloudPayoff, ProvidersPayoff, ConsumersDemand

1:for each $Data\,service\,provider\,SP_{i}$ do

2: $\chi_{i}\leftarrow 0.5$

3: $\phi\leftarrow 1$

4: $SP_{i}$ declares $P_{i}$ through maximizing Equation (5)

5: The cloud calculates $D_{s_{i}}$ through maximizing Equation (7)

6: Equation (1) is used to determine ConsumersDemand

7: Equation (5) is used to determine ProvidersPayoff

8: Equation (7) is used to determine CloudPayoff

9:end for

####  IV-B3 Pay-as-to-go model

Figure 5 depicts the pay-as-to-go model. As shown in the figure, the data
provider rents the cloud computing infrastructure $(D_{s_{i}})$ for a price of
$P_{s}$ USD$/$hour. Thereafter, the data provider delivers its own data
services to the data consumers for a price of $P_{i}$ USD$/$hour. The data
provider and cloud payoffs under the pay-as-to-go model are given in Equations
(26) and (27) respectively. The consumer’s demand function under the pay-as-
to-go model has the same characteristics as under the two-sided market model.
This means that the consumer’s demand is formalized as given in Equation (1).
However, the provided cloud computing infrastructure $(D_{s_{i}})$ is not
given as a function under the pay-as-to-go model since the cloud platform and
data consumers do not directly interact nor do they exhibit mutual cross group
externalities between each other. The pay-as-to-go model is described in
Algorithm 3. Given a price rate of $P_{s}$ USD$/$hour, the data provider
determines the optimal amount of rented cloud computing infrastructure through
maximizing Equation (26). The optimal amount of rented cloud computing
infrastructure $D^{*}_{s_{i}}$ is given in Equation (28) through substituting
Equation (1) with Equation (26) and computing its derivatives with respect to
$D_{s_{i}}$.

Figure 5: Pay-as-to-go model

$\pi_{i}=(P_{i}-f_{c})D_{c_{i}}-P_{s}D_{s_{i}}$ (26)

$\pi=(P_{s}-f_{s})D_{s_{i}}$ (27)

$D^{*}_{s_{i}}=(\frac{P_{s}}{\alpha
k_{1}(P_{i}-fc)P^{-\gamma}_{i}})^{\frac{1}{\alpha-1}}$ (28)

Algorithm 3 Pay-as-to-go scenario

Input: $\alpha$, $\beta$,$\gamma$, $P_{s}$, $k_{1}$, $f_{s}$, $f_{c}$
Output: CloudPayoff, ProvidersPayoff, ConsumersDemand

1:for each $Data\,service\,provider\,SP_{i}$ do

2: The cloud declares $P_{s}$

3: $SP_{i}$ declares $P_{i}$

4: $SP_{i}$ calculates $D_{s_{i}}$ using Equation (28)

5: Equation (1) is used to determine ConsumersDemand

6: Equation (26) is used to determine ProvidersPayoff

7: Equation (27) is used to determine CloudPayoff

8:end for

###  IV-C Sensitivity analysis of externalities

We first investigate in Figures 6, 7, and 8 the impact of the externality
parameters $(\alpha\beta)$ on the payoffs of the cloud platform, data
providers, and data consumers respectively. We run the simulation with
different ranges of the subsidizing factor $(\phi)$, i.e., $0.5$, $1.0$,
$1.5$, $2.0$, and $5.0$. Those values of externality and subsidizing factor
are given as inputs to the simulation program to adjust the strategies of the
involved players. Specifically, the cloud platform adjusts the amount of
provided infrastructure $(D_{s_{i}})$ and the demanded portion $(\chi_{i})$,
while the data provider $(SP_{i})$ calculates the impact of variation in
$(D_{s_{i}})$ and $(\chi_{i})$ on the expected demand of data consumers
$(D_{c_{i}})$ and accordingly adjusts its price $(P_{i})$.

In Figure 6 , we study the impact of varying the externality parameters
$(\alpha\beta)$ and subsidizing factor $(\phi)$ on the cloud’s payoff. As
shown in the figure, the cloud platform obtains in general higher payoff when
it follows the two-sided model, rather than the pay-as-to-go model. For
example, under the two-sided model, the cloud platform receives $1200$, $500$
and $400$ USD as payoff when $(\alpha\beta)=0.2$ and $\phi=5.0$, $2.0$ and
$1.5$ respectively. On the other hand, under the pay-as-to-go model and under
the same externality and subsidizing parameters, the cloud platform receives
less payoff of $(200)$ USD. Similarly, data providers receive higher payoff
and data consumers’ demand is increased under the two-sided model compared to
the pay-as-you-go model as shown respectively in Figures 7 and 8 .

Figure 6: Cloud payoff over externalities $\alpha\beta$

In addition, we study the impact of the fifty-fity (egalitarian) choice on the
two-sided market model, where the cloud platform and data providers share
fifty percent of revenues considering the sitting of our two-sided model. As
shown in Figure 6, the fifty-fifty choice shows more efficient outcomes than
the two-sided model in terms of cloud payoff under week externalities
$(\alpha\beta\in[0.1-0.3])$ and certain values of subsidizing factor $\phi$.
However, the cloud platform can receive higher payoff if it chooses higher
subsidizing factor $\phi$ such as $\phi=5$. Nevertheless, the egalitarian
choice shows less efficient outcomes when the externalities become stronger
(i.e $\alpha\beta\in[0.3-0.7]$) where the cloud platform receives less payoff
under certain subsidizing factor such as $(\phi=1.5)$ or $(\phi=2)$. On the
other hand, the fifty-fifty choice and the two-sided model show similar
outcomes in terms of data providers’ payoff and consumers demand as shown in
Figures 7 and 8 respectively. However, as mentioned in Section I, the involved
parties do not follow the egalitarian choice despite its good outcomes in some
cases, mainly because of their greediness and because of high subsidies in
real cloud markets.

Figure 7: Data providers payoff over externalities $\alpha\beta$

As can be observed from these figures, the two-sided market model shows less
efficient outcomes as the externalities become stronger. Specifically, the
cloud platform, data providers and consumers’ surpluses gradually decrease as
the values of the externality parameters increase. For example, in Figure 7,
the data providers receive a payoff of $800$ USD at an externality parameters
value of $(\alpha\beta=0.2)$ and subsidizing factor of $\phi=5.0$, which is
higher than that received with externality parameter value of
$(\alpha\beta=0.3)$ and subsidizing factor of $\phi=5.0$. This decrease
continues until the two-sided market model reaches almost the same efficiency
of the pay-to-go model under the strong externality values of $[0.55$ \-
$0.7]$. Similar behavior is observed in terms of cloud payoff and data
consumers’ demand as depicted in Figures 6 and 8 respectively. In fact, the
cloud’s payoff and data consumers’ demand are higher under weak externality
values, i.e., $[0-0.5]$ rather than in strong externality values $[0.5-0.7]$ .
The reason behind such a behavior is that the cloud platform needs to provide
more computing and storage resources under strong externalities to attract
smaller number of data consumers, which adds more costs and then leads to less
payoff.

Figure 8: Data consumers demand over externalities $\alpha\beta$

Figure 9 shows the number of computing infrastructure units provided by the
cloud platform over varying externality values. As shown in the figure, at a
subsidizing factor of $\phi=2.0$ and externality values of $(\alpha\beta=0.2)$
and $(\alpha\beta=0.53)$, the cloud platform provides $4800$ units of
computing infrastructure. However, in Figure 8, at a subsidizing factor of
$(\phi=2.0$) and externality values of $(\alpha\beta=0.2)$, the cloud platform
attracts $(3.3\times 10^{6})$ data consumers, while it attracts a smaller
number of data consumers, i.e., $(0.5\times 10^{6})$ with externality values
of $(\alpha\beta=0.53)$. In other words, the cloud platform attracts
$(3.3\times 10^{6})$ of data consumers by providing $4800$ units of computing
infrastructure at externality values of $(\alpha\beta=0.2)$, while it attracts
$(0.5\times 10^{6})$ data consumers by providing the same number of computing
infrastructure units with externality values of $(\alpha\beta=0.53)$.
Consequently, in such a case, the cloud platform asks for a higher portion
$\chi_{i}$ of revenues to maximize its payoff, which negatively affects the
payoff of the data providers. In Figure 10, we study the impact of the
externality parameters on the portion of revenues asked by the cloud platform.
As shown in the figure, the cloud platform asks for higher portions as the
values of externality parameters are increased. For example, at a subsidizing
factor of $\phi=1.5$ and externality values of $(\alpha\beta=0.3)$, data
providers share $40\%$ of their revenues, while they share $68\%$ of their
revenues with externalitiy values of $(\alpha\beta=0.6)$ and a constant
subsidizing factor of $\phi=1.5$.

###  IV-D Sensitivity analysis of subsidizing factor and greedy behavior of
involved parties

The exponential function $\chi_{i}^{\phi}$ captures the rational/greedy
behavior of the cloud platform and data providers. The subsidizing factor
$\phi$ implicitly describes the reactions of the cloud platform to the sharing
portions offered by data providers. Theoretically, the cloud platform
subsidizes the data providers by imposing a subsidizing factor $\phi$ that is
less than $1$. This leads to having $\chi_{i}^{\phi}>\chi_{i}$ since the base
$\chi_{i}$ is defined to be between $0$ and $1$, meaning that larger amounts
of computing infrastructure units $D_{s_{i}}$ should be provided. On the other
hand, data providers offer higher portions $\chi_{i}$ when the cloud platform
acts greedily by imposing a subsidizing factor $\phi$ that is greater than
$1$. This leads to having $\chi_{i}^{\phi}<\chi_{i}$, meaning that smaller
amounts of computing infrastructure units $D_{s_{i}}$ need to be provided.
When the subsidizing factor is equal to $1$, the data providers offer a market
share to the cloud platform based on the size of its contribution. This leads
to having $\chi_{i}^{\phi}=\chi_{i}$, meaning that the provided computing
infrastructure is linearly probational with respect to the market share
$\chi_{i}$. In this case, neither the cloud platform nor data providers act
greedily, and they do not subsidize each other at the same time.

Figure 9: Cloud Infrastructure over externalities $\alpha\beta$

In Figures 6, 7 and 8, we consider the impact of the subsidizing factor $\phi$
in the sensitivity analysis of the externalitiy parameters. As can be observed
from those figures, the cloud platform and data consumers receive higher
payoff than the data providers as the subsidizing factor increases. For
example, in Figure 6, the cloud’s payoff is higher under a subsidizing factor
of $\phi=2.0$ than it is under a subsidizing factor of $\phi=1.0$. Similarly,
we can observe in Figure 8 that data consumers’ demand is higher under a
subsidizing factor of $\phi=2.0$ than it is under a a subsidizing factor of
$\phi=0.5$. Unlike the cases of cloud and data consumers, data providers’
payoff is less under $\phi=5.0$ than it is when $\phi=1.5$, as depicted in
Figure 7.

Figure 10: Shared revenue among the cloud and data providers $(\chi_{i})$ over
externalities $\alpha\beta$ Figure 11: Cloud payoff over the subsidizing
factor $\phi$

To better clarify the impact of the subsidizing factor on the payoffs of
involved parties in our model, we run the simulation over a continuous,
reasonable and wider range of subsidizing factor values. Specifically, we
describe the payoff of the cloud, data providers and data consumers as a
function of the subsidizing factor $\phi$ in Figures 11, 12 and 13
respectively. The results shown in these figures confirm the insights
extracted from Figures 6, 7 and 8. Furthermore, we notice in Figures 12 and 13
that the payoff of the data providers and consumers increases when the value
of $\phi$ is between $0$ to $1$. Then slightly decreases$\ /$stabilizes as
$\phi$ becomes greater than $1$. On the other hand, the cloud’s payoff, as
shown in Figure 11, largely increases when $\phi$ becomes greater than $1$.

Figure 12: Data providers payoff over the subsidizing factor $\phi$

This behavior can be practically interpreted with the results shown in Figure
10. In this figure, we notice that data providers react to the greedy behavior
of the cloud platform via increasing the shared revenue, which negatively
affects the payoff of data providers as shown in Figures 7 and 12, but
positively affects the cloud’s payoff as shown in Figures 6 and 11.

Figure 13: Consumer demand over the subsidizing factor $\phi$

However, the behavior of the data providers (reacting to the greedy behavior
of the cloud platform via increasing the shared portions) sustains a higher
level of consumers’ demand as shown in Figures 11 and 8. Similarly, as shown
in Figure 10, the cloud platform acts to the low offered portion by imposing a
subsidizing factor $\phi$ that is less than $1$. This negatively impacts the
cloud’s payoff but positively affects the cloud platforms’ payoff. In summary,
we conclude that our game includes a recovery mechanism that helps sustain
efficient payoff outcomes for all the parties, in case any of the involved
parties decides to act greedily toward the others.

Figure 14: Cloud payoff over demand elasticity $\gamma$

###  IV-E Sensitivity analysis of consumer demands elasticity $(\gamma)$ and
the multiplier ($k_{1}$)

We now move to analyzing the impact of consumers’ demand elasticity on the
surpluses of all involved parties (Figures 14 \- 16). A high negative
elasticity value positively impacts the surplus of all parties under the two-
sided game model through yielding higher payoffs for the cloud platform and
data providers. The reason is that the exponential function $P_{i}^{-\gamma}$
increases when $\gamma$ increases from $0$ to $0.34$ as long as the base
$P_{i}$ is less than $1$. This makes data providers able to charge their
consumers higher prices without significantly leading to a decrease in the
demands.

Figure 15: Data providers payoff over demand elasticity $\gamma$ Figure 16:
Consumers demand over demand elasticity $\gamma$ Figure 17: Cloud payoff over
multiplier $k_{1}$ Figure 18: Data providers payoff over multiplier $k_{1}$
Figure 19: Consumers demand over multiplier $k_{1}$

We also study the impact of the multiplier $k_{1}$ on the surplus of all
involved parties. As shown in Figures 17 \- 19, the surpluses of the cloud
platform, service data providers and consumers increase as the value of the
multiplier $k_{1}$ increases. The reason is that increasing the multiplier
$k_{1}$ leads to increasing consumers’ demands, which positively affects the
total revenues.

##  V Conclusion

In this paper, we proposed a game theoretical model based on the two-sided
market theory to monetize big data services over the cloud. In particular, we
studied the impact of cross group externalities between the amount of provided
cloud resources and number of service consumers. The objective is to come up
with a new vision in which the cloud can play a primordial role in introducing
big data service providers and data consumers to each other, which results in
higher benefits for all the involved players. To achieve this goal, we
designed a game theoretical model in which the cloud platform and big data
service providers engage in a closed loop of dependencies that makes them
interested in satisfying each other interest, instead of following an
aggressive competition strategy. Empirical results showed that our model
outperforms the state-of-the-art cloud business models, i.e., the fifty-fifty
and pay-as-you-go models in terms of total surpluses earned by the different
parties.

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Ahmed Saleh Bataineh received the bachelor’s degree in computer engineering
from Jordan University of science and technology, Jordan, in 2010, and the
master’s degree in electrical and computer engineering from Concordia
University, Canada, in 2014. He is currently pursuing the Ph.D. degree with
the Concordia Institute for Information Systems Engineering (CIISE) under the
supervision of Prof. Jamal Bentahar. His past research activities include
multi-agent systems, verification and model checking. His current research
interests include economics, optimization problems and game theory applied to
IoT services and big data.

Jamal Bentahar received the Ph.D. degree in computer science and software
engineering from Laval University, Canada, in 2005. He is a Professor with
Concordia Institute for Information Systems Engineering, Concordia University,
Canada. From 2005 to 2006, he was a Postdoctoral Fellow with Laval University,
and then NSERC Postdoctoral Fellow at Simon Fraser University, Canada. He is
an NSERC Co-Chair for Discovery Grant for Computer Science (2016-2018). His
research interests include the areas of computational logics, model checking,
multi-agent systems, service computing, game theory, and software engineering.

Rabeb Mizouni is an associate professor in Electrical and Computer Engineering
at Khalifa University. She got her PhD and her MSc in Electrical and Computer
Engineering from Concordia University, Montreal, Canada in 2007 and 2002
respectively. Currently, she is interested in the deployment of context aware
mobile applications, software product line and cloud computing.

Omar Abdel Wahab is an Assistant Professor at the Department of Computer
Science and Engineering, Université du Québec en Outaouais, Canada. He holds a
Ph.D. in Information and Systems Engineering from Concordia University,
Montreal, Canada. He received his M.Sc. in computer science in 2013 from the
Lebanese American University (LAU), Lebanon. From 2017 to 2018, he was a
postdoctoral fellow at the École de Technologie Supérieure (ÉTS), Canada,
where he worked on an industrial research project in collaboration with Rogers
and Ericsson. The main topics of his current research activities are in the
areas of cybersecurity, data analytics, Internet of Things (IoT) and game
theory.

Gaith Rjoub received the B.S. degree in information technology engineering
from Arab Open University, Amman, Jordan, in 2008 and M.Eng. degree in Quality
Systems Engineering from Concordia Institute for Information Systems
Engineering (CIISE), Canada in 2014. He is currently pursuing his Ph.D. degree
in Information Systems Engineering at concordia University. His research
interests include cloud computing, machine learning, artificial intelligence
and big data analytics.

May El Barachi is a next generation networking expert holding Ph.D. and
master’s degrees in Computer Engineering from Concordia University (Canada).
She has 12 years’ experience in the field with a strong focus on smart and
resource efficient systems. During those years, she acquired academic
experience as associate professor and has worked as researcher with Ericsson
Research Canada. She co-founded and directed a cutting-edge research lab
aiming at investigating sensory, cloud, and mobile technologies. Presently,
she works as Associate Professor at University of Wollongong Dubai and is
involved in several research collaborations with international universities
and local industrial partners.