[论文翻译]云计算作为数据服务货币化平台：双边博弈商业模式

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原文地址：https://arxiv.org/pdf/2104.12762


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

云计算作为数据服务货币化平台：双边博弈商业模式

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 tobe 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 twosided market theory that takes into consideration the network effects among involved parties, while integrating the external i ties 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.

摘要-随着云计算作为存储当今大数据的支柱，我们前所未有地依赖它，本文认为，云的角色应从被动的虚拟市场转变为通过人工智能 (AI) 服务实现大数据货币化的主动平台。目标是使云成为一个主动平台，帮助大数据服务提供商接触到更广泛的客户，并使云用户（即数据消费者）接触到更丰富多样的数据以运行其数据分析任务。为实现这一愿景，我们提出了一种新颖的博弈论模型，该模型结合了合作与竞争策略。博弈的参与者包括大数据服务提供商、云计算平台和云用户。参与者的策略采用双边市场理论建模，考虑了各方之间的网络效应，同时将云资源与消费者需求之间的外部性整合到博弈设计中。使用 Amazon 和 Google 集群数据进行的模拟表明，与当前的商家模型相比，所提出的模型在云资源供应和货币利润方面提高了所有相关方的总盈余。

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

索引术语-云计算商业模式；博弈论；大数据；双边市场。

1. INTRODUCTION

1. 引言

N LOUD computing is witnessing a striking increase in the C 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 EC2 instances and generating $600,{\cal Z B}$ of data per year [2]. This explosive amount of data generated and stored on cloud resources forms the backbone for Artificial Intelligence (Al) 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.

云计算正见证着越来越多的企业和制造商依赖这一范式来存储和处理数据。例如，[1] 中报告的研究显示，有 100 万客户在 Amazon 上部署自己的企业，每年在 Amazon EC2 实例上花费 300 亿美元用于持久存储，并生成 $600,{\cal Z B}$ 的数据 [2]。这些在云资源上生成和存储的爆炸性数据量构成了人工智能 (AI) 服务的基础，并为新的云业务模式打开了大门，使其成为通过数据获利以支持 AI 服务的活跃平台。然而，云并不是这些大块数据的实际所有者，未经实际所有者同意，云无权交易和使用这些数据。

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. 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 demandsupply 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 frst 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.

受到将云作为数据服务货币化平台的愿景启发，本文提出了一种新颖的云商业模式，该模式允许数据消费者（如市场研究企业）在云上存储的大量多样化数据上运行其数据分析。这不仅为数据消费者提供了从多个数据提供商的海量数据中提取有价值模式的机会，还使他们免于为每种需要分析的特定数据类型搜索和发现合适的提供商。数据提供商除了倾向于访问基于云的基础设施而非购买自己的计算和存储平台外，还发现与云打交道的庞大且多样的数据消费者群体为他们提供了额外的动力，将数据存储在这一平台上以提高曝光率并增加市场份额。如图1所示，这间接使云计算平台成为数据提供商和数据消费者之间的中介，并在整个大数据分析过程中扮演主要角色。这为新的创新商业模式打开了大门，以利用这一场景增加所有相关方的利润，而不仅仅是将云视为通过互联网提供服务的被动虚拟市场的传统商业模式。具体而言，面向业务的数据交易文献可分为两大类，即纯商家方法和协作方法。纯商家方法下的提案，如[3, 4]和[2]，采用经典的经济方法，主要是供需模型和单边博弈论/拍卖定价，以模拟数据提供商、数据消费者和第三方平台（即信息服务提供商）之间的互动。在这种方法中，第三方平台旨在通过从数据所有者处购买数据、重新处理数据、提取有用信息并将这些信息出售给消费者来最大化其收入。这种方法在应用于云计算场景时存在几个局限性。第一个局限性涉及数据消费者兴趣的多样性，这导致第三方平台的处理成本更高（就为不同客户兴趣提取信息而言）。此外，在纯商家模型下，数据提供商旨在最大化其数据商品的使用收入，而第三方平台则旨在最小化从这些提供商处购买的原始数据的成本。同时，从数据消费者的角度来看，第三方平台旨在通过销售处理后的信息最大化其收入，而消费者则旨在最小化信息商品的成本，考虑到信息的最大可用质量和数量。这种不同参与方之间的激烈竞争导致总剩余的分配较少且粗糙。此外，数据与其他经济商品的不同之处在于其可以同时（重新）出售给多个消费者的潜力。在纯商家模型中，由于经济商品不能转售，市场的均衡位于供需曲线的交点。这意味着消费者所需的商品数量等于卖方提供的商品数量。然而，这在我们的情况下并不成立，因为同一数据可以同时与多个消费者共享，这导致数据提供商之间以更低的价格出售数据的激烈竞争。商家模型的缺点在[5]中得到了深入讨论，该文献提出了一种双边市场模型来货币化个人数据。更详细地说，Bataineh等人[5]提出了一种开放市场模型，其中个人（实际数据所有者）和数据消费者通过一个第三方平台进行数据交易，该平台帮助他们相互发现。作者表明，双边市场在最大化总剩余方面优于商家模型。然而，这种方法的主要局限性在于它基于对消费者需求和数据价格的静态分析，这使得它不适合动态云市场。


Figure 1: Overview of the new cloud business model

图 1: 新云业务模式概览

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 external i ties (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 external i ties 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.

在协作方法的框架下，一些提案，例如 [6] 和 [7]，尝试在面向业务的物联网 (IoT) 领域中建模三个实体之间的交互。在 [6] 中，作者提出了一种模型，其中客户端对等体有兴趣在云的帮助下共享视频内容。在 [7] 中，作者提出了物联网传感器、物联网服务提供商和数据消费者之间的博弈论模型。在这些博弈中，两个实体（即物联网传感器和物联网服务提供商）在一个博弈中合作，然后作为一个实体与数据消费者竞争。这种方法存在三个缺点：(1) 它没有考虑参与方之间的跨群体外部性（例如，一方的客户规模对另一方客户规模的相互影响），这使得它无法捕捉三方经济模型的整体、更具体和更现实的图景；(2) 不同参与者采用的合作和竞争策略受到跨群体外部性的高度影响，这可能并不总是为这些参与者带来最佳结果；(3) 它没有阐明合作实体如何分享其获得的收入。

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 he te rogen io us 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 fty-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.

在动态的云数据交易场景中，采用传统的博弈论概念（如Shapley值和纳什均衡）来分配不同合作方之间的收益存在一些局限性。具体来说，1）尽管这些概念在所有参与方都是理性的情况下可能非常高效，但在存在异质且倾向于偏离均衡点的参与方时，其有效性开始下降。例如，最近的研究表明，在合作博弈中，只有37%的玩家倾向于接受纳什均衡（感兴趣的读者可以查阅行为博弈和最后通牒博弈[8]以获取更多细节）；2）尽管Shapley值方法根据各实体的贡献公平地分配收益，但在无法衡量实体贡献的情况下（这适用于本文考虑的云场景），该方法变得不适用。具体来说，云提供商通过引入数据消费者的广泛社交网络为数据提供者提供了无形但重要的贡献。另一方面，数据提供者拥有构成这一新业务核心的数据。这导致数据提供者和云提供商之间持续存在关于谁对联盟贡献最大以及谁应获得最大收益份额的困境。所谓的“五五分成”是云提供商和数据提供者之间分配收益的一种方法。然而，如前所述，参与方（即云提供商和数据提供者）的理性和贪婪阻碍了这种策略的成功。这使我们得出结论，我们正在处理一种行为和最后通牒博弈，其中两个玩家（提议者和响应者）争论如何分配一定数量的收益。提议者被赋予一定数量的收益，并负责与响应者分配这笔收益。响应者可以接受或拒绝这笔收益。如果响应者接受，收益将按照提议分配；否则，双方都将一无所获。

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 external i ties, 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 external i ties 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.

贡献。为了解决上述问题，我们研究了双面市场模型 [9]，该模型因其在涉及经纪人和跨群体外部性的情况下的成功建模而受到赞誉，以研究基于云的数据交易问题。我们解决方案的主要思想是，云计算平台通过向数据消费者提供更多的计算资源来部署他们的数据分析任务，从而吸引数据消费者。这反过来又有助于吸引更多的数据提供商加入云的数据消费者网络。因此，数据提供商有动力向云计算平台提供更高比例的收入。双面市场为第三方平台连接其他两方的情况提供了有效的解决方案概念。然而，双面市场理论的主要局限性在于，它在需求静态的情况下建模有效，但在云计算这种需求动态和持续变化的弹性环境中效果较差。为了解决这个问题，我们在双面市场模型的基础上集成了一个新颖的博弈论模型，如图 2 所示。我们博弈的参与者是（多个）独立竞争的服务提供商（追随者）和云计算平台（领导者）。参与者选择混合合作和非合作策略，其中策略被建模为依赖关系的闭环。数据消费者和云平台之间表现出跨群体的外部性，消费者的更高需求导致云平台的收入增加，而云平台提供的更多计算资源则创造了更多的消费者需求。

In the first stage of the game, the leader (cloud platform) announces thedesired portionof 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.

在游戏的第一阶段，领导者（云平台）宣布希望从数据提供商的收益中获得的分成比例，然后在第二阶段，数据提供商决定他们对数据消费者的定价策略。由此产生的均衡迫使云平台提供更高且合理的计算资源供应，以确保最大化的收入水平，同时不会在数据提供商的收入分成上表现出贪婪行为。此外，根据我们的解决方案，数据提供商被迫向云平台提供更高比例的收入，以确保向数据消费者提供适当的服务质量（QoS）。在云平台表现出贪婪行为的情况下，我们的游戏采用了一种补贴机制。这种机制促使数据提供商增加向云平台提供的分成比例，以维持高且合理的计算基础设施水平，从而保证高水平的消费者需求。同样，在数据提供商表现出贪婪行为，向云平台提供较少收入分成的情况下，补贴机制会推动云平台增加基础设施单位，以提高消费者需求，从而确保尽可能高的收入分成水平。

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.

为了验证我们的解决方案，我们使用来自 Google 和 Amazon 的真实数据进行了实证实验。实验结果表明，通过遵循我们的解决方案，所有相关方（即云平台、数据提供商和数据消费者）都实现了比传统云计算商业模式更高的收入。


Figure 2: Overview of the proposed two-sided game

图 2: 提出的双面游戏概览

I1. RELATED WORK

I1. 相关工作

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.

在本节中，我们对云计算商业模式进行了文献综述。现有的提案可以分为两大类：经典市场和基于博弈论的定价模型。经典市场类别下的提案，如 [10, 11, 12]，使用简单的定价模型来解决云服务的定价问题，包括基于成本的定价、差异化定价、拉姆齐定价和需求曲线函数。他们将云计算资源的定价建模为多个云提供商和云用户之间的优化问题。然而，这些方法的主要缺点在于其静态定价策略，不适合云计算高度变化和动态的环境。

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 Stack el berg 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 Stack el berg 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.

另一方面，博弈论模型考虑了参与实体之间可能发生的瞬时互动及其对各参与方福利的影响。其目标是动态捕捉云计算资源的最优价格和分配。许多提案如 [13, 14, 15, 16, 17] 应用了不同的方法，包括博弈和机器学习 [18]，来解决云资源分配和定价问题。在 [13] 中，作者提出了一种基于 Stackelberg 博弈的经济模型，用于在云平台上交易视频内容和电影。该模型描述了服务提供商（如 Netflix）与终端用户之间的互动。服务提供商作为博弈的领导者，旨在最小化云带宽消耗，同时保证用户的满意度。[19] 中的工作将多个软件即服务 (SaaS) 提供商和基础设施即服务 (IaaS) 提供商之间的互动建模为一个两阶段的 Stackelberg 博弈。在博弈的第一阶段，SaaS 提供商确定所需的虚拟机实例数量，同时考虑向其用户提供的服务质量 (QoS) 和相关成本。在第二阶段，IaaS 提供商根据 SaaS 提供商的出价寻求最大化其收入 [20, 21]。在 [6] 中，作者提出了一种经济模型，其中云用户寻求通过云与其他用户共享视频内容。该模型通过云与其用户之间的合作和非合作博弈来解决。[7, 16] 中对不同的云应用进行了类似的研究。[22] 中的作者提出了一种博弈论模型，用于提供一组互补的物联网 (IoT) 服务。该解决方案研究了商家-消费者场景，其中 IoT 服务直接在服务提供商和服务消费者之间交易，无需任何第三方的干预。然而，该解决方案无法适用于我们的情况，因为云计算并不是实际的数据所有者，因此无法直接为消费者将数据货币化。尽管如此，云计算（本文中的第三方）被视为一个全球市场，数据服务和数据消费者在此相遇，从而增加了他们的市场份额。[23] 和 [24] 中的作者引入了一种用于管理、交易和定价大数据服务的市场模型。这两个提案都使用双边市场理论，为云提供商和用户提供激励，以增加他们的数据份额。[5] 中的工作扩展了 [23] 中提出的工作，并全面研究了双边市场模型作为个人数据货币化的成功模型。然而，这些提案考虑了一个静态环境，其中对云资源的需求是以静态方式计算的，这使得它们无法适应云的弹性特性。

To the best of our knowledge, the proposed work is the first that addresses big data services monet iz ation, while considering the cross-group external i ties 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.

据我们所知，所提出的工作是第一个解决大数据服务货币化问题的，同时考虑了参与实体之间的跨群体外部性。与经典的云计算商业模式（其中主要挑战是如何在仅考虑运营成本和QoS指标的情况下优化云利用率）不同，我们的方法：1) 支持并帮助初级大数据服务提供商，特别是那些资金预算有限的提供商；2) 使用双边市场理论来建模参与方之间的互动，而上述所有提案都使用经典的商家模型；3) 包含一种补贴技术，以推动结果均衡向帕累托最优点发展。另一方面，上述提案采用的公平标准是根据各方的贡献来奖励他们。我们还与其他采用双边市场理论的提案不同，提供了一种动态定价方法，而不是基于静态博弈论的定价策略。

III. PROPOSED BIG DATA SERVICES MONET IZ ATION MODEL OVER THE CLOUD: A TWO-SIDED GAME MODEL We explain in this section the details of our proposed Big data services monet iz ation.

III. 基于云的大数据服务货币化模型：一种双边博弈模型

本节详细阐述了我们提出的大数据服务货币化模型。

A.Solution Architecture and Game Formulation

A. 解决方案架构与游戏公式化

The proposed cloud market platform, depicted in Figure 3, consists of three entities: consumers of services CS （ $C S_{i}$ denotes Consumers of Service $i)$ , big data service providers $S P$ (a Service Provider providing service $i$ is denoted $S P_{i}$ and a typical Cloud Platform $(C P)$ . 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 $S P_{i}$ 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 $C P$ 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 $C S_{i}$ S demand, denoted by $D_{c_{i}}$ , and the computing and storage resources $D_{s_{i}}$ supplied to $C S_{i}$ is modeled using the two-sided market model as cross group external i ties $\alpha$ 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.

图 3 所示的云市场平台由三个实体组成：服务消费者 CS（$C S_{i}$ 表示服务 $i$ 的消费者）、大数据服务提供商 $S P$（提供服务 $i$ 的服务提供商表示为 $S P_{i}$）以及典型的云平台 $(C P)$。云平台（如 Google 和 Amazon）是市场领导者，拥有巨大的计算和存储能力、资本以及社交消费者网络。在我们的模型中，提供特定服务 $i$ 的大数据服务提供商 $S P_{i}$ 将其服务部署在云上，并在每个消费者访问其服务 $i$ 时获得 $P_{i}$ 的货币价值。云平台 $C P$ 负责通过提供所需的计算和存储基础设施（包括硬件、软件和安全服务）来维持消费者访问。消费者 $C S_{i}$ 的需求（表示为 $D_{c_{i}}$）与提供给 $C S_{i}$ 的计算和存储资源 $D_{s_{i}}$ 之间的关系使用双边市场模型建模为跨组外部性 $\alpha$ 和 $\beta$。其中，$\alpha$ 表示当向 $D_{s_{i}}$ 添加新的计算和存储资源时消费者获得的收益，$\beta$ 表示当向 $D_{c_{i}}$ 添加更多新消费者时云平台获得的收益。参数 $\alpha$ 和 $\beta$ 取决于服务 $i$。然而，为了简化方程，省略了索引 $i$，因为服务 $i$ 可以从上下文中理解。同样的简化也适用于出现在方程中的其他参数（作为指数）。


Figure 3: Two-sided model

图 3: 双面模型

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

$S P$ 和 $C P$ 之间的互动被建模为一个两阶段博弈，其中 $C P$ 作为博弈的领导者，$S P$ 作为跟随者。在博弈的第一阶段，每个提供服务的服务提供商 $i:S P_{i}$ 观察到 $C P$ 要求的资金回报 $\chi_{i}$，以便调整向 $C S_{i}$ 收取的价格。在 $S P_{i}$ 指定的价格下，$C P$ 确定应向 $C S_{i}$ 提供的最优计算和存储资源量 $D_{s_{i}}$。该模型形成了一个依赖关系的闭环，涉及 Stackelberg 和 Ultimatum 博弈论技术以及补贴技术。

In the Stack el berg game, the interactions take place in two stages where the leader $(C P)$ makes the first move and then does each follower $(S P_{i})$ after having observed the leader's move. In the ultimatum game, the first player $(C P)$ proposes a strategy to divide the amount of returned revenue with the second player $(S P_{i})$ . In case $S P_{i}$ 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, $S P_{i}$ may chose to subsidize $C P$ by an extra amount of payment that exceeds the contribution of this $C P$ . The objective is to keep an optimal level of $D_{s_{i}}$ that maximizes the return revenues $P_{i}*D_{c_{i}}$ . Alternatively, $C P$ may subsidize $S P_{i}$ 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.

在 Stackelberg 博弈中，交互分为两个阶段进行，领导者 $(CP)$ 首先行动，然后每个跟随者 $(SP_{i})$ 在观察到领导者的行动后采取行动。在最后通牒博弈中，第一个玩家 $(CP)$ 提出一个策略来分配返回的收入与第二个玩家 $(SP_{i})$。如果 $SP_{i}$ 拒绝提议，双方都不会获得任何收益。否则，第一个玩家获得其请求的金额，第二个玩家获得剩余部分。在补贴技术中，$SP_{i}$ 可以选择通过支付超过 $CP$ 贡献的额外金额来补贴 $CP$。目标是保持 $D_{s_{i}}$ 的最优水平，以最大化返回收入 $P_{i}*D_{c_{i}}$。或者，$CP$ 可以通过将部分收入补贴给 $SP_{i}$ 来保持 $P_{i}$ 的最优水平。我们提出的解决方案中使用的不同参数和符号如表 I 所示。

模型参数 描述
SP 提供服务的服务提供商。
CP 典型的云平台。
CS 服务的消费者。
Dci 消费者的需求。
Dsi 提供给消费者的IT基础设施供应。
P 服务的价格。
Ds对Xi的弹性。
Xi 云平台从服务提供商处要求的收入份额。
De对Pi的弹性。
β 网络效应对Ds的影响。
Ds对Pj的弹性。
网络效应对De的影响。
fc 每个服务消费者的相关成本。
k1, k2 常数乘数。
元 服务提供商的收益。
fs 每个IT基础设施单位的相关成本。
π 云平台的收益。
a1 -=
a2 =1-αβ。
a3 =Y-yβ。
a4 Φ∞=

B. Players’ Demand and Utility Functions

B. 玩家的需求与效用函数

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).

准确估计所需的计算和存储资源需要一个价格估计机制，该机制需要考虑消费者数量及其需求相对于提供的服务质量 (QoS) 的变化。为此，我们使用 Cobb-Douglas 函数定义了消费者的需求和供给，该函数有效地捕捉了计算和存储资源供给 $(D_{s_{i}})$ 的弹性及其对每个特定用户需求的变化。这种弹性是云计算环境的特征属性。我们使用的需求函数是连续的、凹的或凸的，并捕捉了每个输入参数的弹性。使用了两个弹性参数 $\gamma$ 和 $\psi$（见表 I）。这两个参数依赖于服务 $i$，为了简化起见，如前所述，符号中省略了这一点。在我们的模型中，消费者的需求 $(D_{c_{i}})$ 是 $P_{i}$ 和 $D_{s_{i}}$ 的函数，如公式 (1) 所示。

D_{c_{i}}=k_{1}P_{i}^{-\gamma}D_{s_{i}}^{\alpha}```


\$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  \$C P\$   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  \$C P\$   and  \$S P_{i}\$  . In fact, it reflects the level of perfect/imperfect information that  \$C P\$   and  \$S P_{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  \$C P\$   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  \$C P\$   and  \$S P_{i}\$   strategies with each other, which captures the sensitivity of  \$C P\$  to  \$S P_{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}}\$ 由公式 (2) 给出。显然，消费者需求的增加会影响供应资源的数量。云平台 \$C P\$ 使用更多的计算和存储资源以应对不断增加的消费者访问量，从而保持高质量的服务水平。参数 \$\chi_{i}^{\phi}\$ 代表云平台的偏好（即期望利润），并隐式地捕捉了 \$C P\$ 和 \$S P_{i}\$ 的理性行为。实际上，它反映了 \$C P\$ 和 \$S P_{i}\$ 彼此之间信息的完整/不完整程度。高弹性 \$\phi\$ 可能是由贪婪的垄断云平台或资本较少、接受较小利润回报的弱势服务引起的。参数 \$\phi\$ 依赖于服务 \$i\$，但如前所述，当上下文明确时，索引 \$i\$ 会被省略。收费价格 \$P_{i}\$ 也对 \$D_{s_{i}}\$ 有正向贡献。我们可以认为，向消费者收取更高的价格 \$P_{i}\$ 会迫使 \$C P\$ 提供更多的计算和存储资源，以满足消费者的需求。将 \$D_{s_{i}}\$ 建模为 \$\chi_{i}\$ 和 \$P_{i}\$ 的函数，并考虑不同的弹性值，将 \$C P\$ 和 \$S P_{i}\$ 的策略相互联系起来，这捕捉了 \$C P\$ 对 \$S P_{i}\$ 策略（即收费价格和共享部分的结构）的敏感性，并突出了补贴技术的重要性。这一方面在模拟部分（第 IV-D 节）中进一步说明和讨论。

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

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

将方程 (2) 代入方程 (1) 并反之，我们可以将 $D_{c_{i}}$ 和 $D_{s_{i}}$ 表示为 $P_{i}$ 和 $\chi_{i}$ 的函数，如下所示：

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


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


Each big data service provider  \$S P_{i}\$  is subject to a fixed cost  \$f_{c}\$  per each consumer access.  \$S P_{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).

每个大数据服务提供商 \$S P_{i}\$ 在每个消费者访问时都会产生一个固定成本 \$f_{c}\$。\$S P_{i}\$ 的目标是最大化其收益，如公式 (5) 所示。我们将服务提供商的收益 \$\pi_{i}\$ 表示为 \$P_{i}\$ 和 \$\chi_{i}\$ 的函数，通过将公式 (3) 代入公式 (5) 并对两边取对数，如公式 (6) 所示。

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


\begin{array}{r}{\log\pi_{i}=\log(P_{i}(1-\chi_{i})-f_{c})+(1/a_{2})(\log k_{1}k_{2}^{\alpha}\qquad\qquad}\\ {-a_{1}\log P_{i}+a_{4}\log\chi_{i})\qquad\qquad\qquad\qquad}\end{array}```


The cloud platform  \$C P\$  is subject to a fixed cost  \$f_{s}\$   per each unit of computing and storage resources. The  \$C P\$  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).

云平台 \$C P\$ 每单位计算和存储资源需承担固定成本 \$f_{s}\$。云平台的目标是最大化其收益，如公式 (7) 所示。我们将云平台的收益 \$\pi\$ 表示为 \$P_{i}\$ 和 \$\chi_{i}\$ 的函数，通过将公式 (3) 和 (4) 代入公式 (7)，如公式 (8) 所示。

\pi=P_{i}\chi_{i}D_{c_{i}}-f_{s}D_{s_{i}}```


\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}}})```


# C. Game Equilibrium

# C. 游戏均衡

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  \$S P_{i}\$   determines its optimal decision  \$P_{i}^{*}\$  while considering the  \$C P\$  's optimal decision  \$\boldsymbol{\chi}_{i}^{*}\$  as an input parameter. The players’ best responses are discussed in the following.

上述博弈的均衡采用逆向归纳法求解。因此，首先求解追随者（服务提供者）的子博弈，以获得他们对服务消费者的响应 \$P_{i}\$。然后，考虑所有追随者可能的反应，计算领导者（云平台）的子博弈，以最大化其收益 [25]。每个服务提供者 \$S P_{i}\$ 在将 \$C P\$ 的最优决策 \$\boldsymbol{\chi}_{i}^{*}\$ 作为输入参数的情况下，确定其最优决策 \$P_{i}^{*}\$。下文将讨论参与者的最佳响应。

Theorem 1. The best responses in the two-sided game are as follows:

定理 1. 双边博弈中的最佳响应如下：

1） The best response of the service provider  \$S P_{i}\$  isgiven by：

1） 服务提供商 \$S P_{i}\$ 的最佳响应为：

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


\begin{array}{r l r}{i f\!\!\!:}&{{}}&{\frac{a_{1}}{a_{1}-a_{2}}>0\;\;\;a n d\;\;\;\frac{a_{1}}{a_{2}}>1}\end{array}```


2) The best response of the cloud platform with respect to aservice  \$i\$  is givenby:
3) 云平台对于服务 \$i\$ 的最佳响应由以下公式给出：

\begin{array}{r l}&{\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}})}\ &{\qquad\qquad\qquad\times(\displaystyle\frac{k_{2}k_{1}^{\beta}}{k_{1}k_{2}^{\alpha}})^{\frac{1}{a_{2}}}\times(\frac{a_{1}f_{c}}{a_{1}-a_{2}})^{\frac{a_{1}+a_{3}}{a_{2}}-1}}\ {i f{:}}&{a_{4}+a_{2}-\phi<0}\end{array}```

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:

证明。考虑由方程 (6) 给出的服务收益，最优价格 $P_{i}^{*}$ 由 $\partial\pi_{i}/\partial P_{i}=0$ 定义如下：

\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```


→

→

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

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

由于 $P_{i}^{*}$ 始终为正，因此

\frac{a_{1}}{a_{1}-a_{2}}>0```

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

为了验证 \$P_{i}^{*}\$ 的最优性类型（即最大值或最小值），我们通过对公式 (5) 求导来计算二阶导数测试：

\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}}```
By deriving Equation 3, then

通过推导方程 3，然后


\frac{\partial D_{c_{i}}}{\partial P_{i}}=\frac{-a_{1}}{a_{2}P_{i}}D_{c_{i}}```


7）By substituting Equation 15 into Equation 14, then

7）将公式 15 代入公式 14，然后

\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}}```

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

通过使用方程 (5) 重写方程 (16)，然后

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

\frac{\partial^{2}\pi_{i}}{\partial P_{i}^{2}}=\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_{i}^{2}}\pi_{i}```

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

通过简化方程 (18) 并代入方程 (12)，我们得到：

\frac{\partial^{2}\pi_{i}}{\partial P_{i}^{2}}=\frac{D_{c_{i}}}{P_{i}}\big(1-\frac{a_{1}}{a_{2}}\big)\big(1-\chi_{i}\big)```


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

由于 \$D_{c_{i}}\$ 和 \$P_{i}\$ 始终为正，因此

\frac{\partial^{2}\pi_{i}}{\partial P_{i}^{2}}<0\Rightarrow\bigl(1-\frac{a_{1}}{a_{2}}\bigr)<0\Rightarrow\frac{a_{1}}{a_{2}}>1```

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

同样，为了获得最优的 $\boldsymbol{\chi}{i}^{*}$，我们对 $\chi{i}$ 求导，得到方程 (8)，如方程 (21) 所示：


\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_{i}^{\frac{a_{4}}{a_{2}}}-(\frac{\phi f_{s}(k_{2}k_{1}^{\beta})^{\frac{1}{a_{2}}}}{a_{2}})P_{i}^{\frac{a_{3}}{a_{2}}}\chi_{i}^{\frac{\phi}{a_{2}}-1}=0```

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


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

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

将方程 (12) 代入方程 (22)，我们得到：

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

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

为了验证 $\boldsymbol{\chi}_{i}^{*}$ 的最优性类型，我们通过推导方程 (21) 来计算二阶导数检验，如方程 (24) 所示：


\begin{array}{c}{{\frac{\partial^{2}\pi}{\partial\chi_{i}^{2}}=(k_{1}k_{2}^{\alpha})^{\frac{1}{a_{2}}}(\frac{a_{4}\left(a_{4}+a_{2}\right)}{a_{2}^{2}})P_{i}^{\frac{a_{2}-a_{1}}{a_{2}}}\chi_{i}^{\frac{a_{4}}{a_{2}}-1}}}\\ {{-(\frac{f_{s}\phi\left(\phi-a_{2}\right)\left(k_{2}k_{1}^{\beta}\right)^{\frac{1}{a_{2}}}}{a_{2}^{2}})P_{i}^{\frac{a_{3}}{a_{2}}}\chi_{i}^{\frac{\phi}{a_{2}}-2}<0}}\end{array}```

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

将方程 (22) 代入方程 (24) 中，我们得到：

a_{4}+a_{2}-\phi<0```

IV. SIMULATIONS AND EMPIRICAL ANALYSIS

IV. 模拟与实证分析

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 $\grave{\mathbf{a}}_{}$ -vis the current cloud computing business model (i.e., the pay-as-to-go model); 2) study the equilibrium of the twosided 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.

在本节中，我们评估了所提出的双边博弈解决方案与五五分成和按需付费方法在涉及各方的总盈余（即云平台、服务数据提供商和服务数据消费者的收益）方面的表现。具体来说，我们旨在：1）验证所提出的博弈相对于当前云计算商业模式（即按需付费模型）的有效性；2）研究在五五分成选择（即最后通牒博弈中的平等选择）存在的情况下双边博弈的均衡，这是此类博弈的典型解决方案；3）研究模型参数对我们解决方案性能的影响。图4展示了我们模拟设置的概述，包括输入、场景和结果。模拟输入和场景分别在IV-A和IV-B节中描述，而模拟结果在IV-C、IV-D和IV-E节中详细讨论。


Figure 4: Simulation overview

图 4: 模拟概览

A. Simulation Setup

A. 模拟设置

In this section, we conduct a simulation analysis grounded on statistical observations fromBMR[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 10,0oo 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 EC 2 where each instance includes 16 VMs, 30 GB of Memory, and $1000,\mathrm{GB}$ 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 EC2 instances are represented by $S P_{i}$ (service data provider) and $D_{s_{i}}$ respectively. The mean of the supply function $D_{s_{i}}$ consists of $32\ \mathrm{EC}2$ 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 EC2 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 $53\ \mathrm{EC2}$ 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 external i ties $\alpha$ 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 external it y factor $\alpha$ which means that $\alpha$ ranges from 0.1 to 0.7. According to the assumption presented in [9], the cross group external i ties factor should be bounded by O and 1, i.e., $0<\alpha\beta<1$ . Hence, the external it y factor $\beta$ would range from O to $1/\alpha$ .A consumer's demand $D_{c_{i}}$ on each enterprise ranges from $0.1\times1$ to $0.7\times53$ 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 elastic i ties are set up between $0.1-0.35$ (i.e., Y), 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 $\left(k_{2}=1\right)$ 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 $C S_{i}$ 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.

在本节中，我们基于BMR[1]的统计观察和[26]的真实数据进行模拟分析。根据[1]，2019年，Amazon Web Services (AWS) 从100万活跃客户中获得了300亿美元的收入，净收入约为100亿美元，这些客户每月在Elastic Compute Cloud (EC2) 的自定义实例上运行7000万小时的企业业务。因此，1) 企业客户平均每年花费30,000美元，每月租用70小时的云资源；2) 云平台的边际运营成本为收入的66%（亚马逊从每个客户中获得10,000美元的净收益）。通过将这些数字输入亚马逊计算器[27]，我们可以得出结论，客户平均每月租用32个Amazon EC2实例的70小时，每个实例包括16个虚拟机、30 GB内存和1000 GB硬盘存储，每小时价格为36美元。价格率（36美元/小时）用$P_{s}$表示，稍后将用于计算按需付费模型中云和数据提供商的收益，如第IV-B节所述。云提供商（亚马逊）承担实例价格（36美元/小时）的66%作为运营成本，即23.7美元/小时。在我们的模型中，运营成本用$f_{s}$表示。事实上，40%的收入作为利润，60%作为运营成本在商业中很常见。因此，我们假设数据消费者$(f_{c})$由数据提供商承担的边际成本与$(f_{s})$具有相同的分布。企业客户及其对EC2实例的消费分别用$S P_{i}$（服务数据提供商）和$D_{s_{i}}$表示。供应函数$D_{s_{i}}$的平均值包括32个EC2实例。然而，企业客户有不同的业务类型，因此在所需的云资源数量上有所不同。为了在模拟中建模这种变化，客户对EC2实例的需求围绕平均值呈正态分布，标准差为10。这意味着供应函数$D_{s_{i}}$的共域范围从1到53个EC2实例。真实数据集[26]记录了由大量企业客户在类似EC2实例上执行的计算大数据作业的日志文件。该数据集帮助我们提取了消费者需求$D_{c_{i}}$以及外部性$\alpha$和$\beta$的可靠范围，如下所述。每个实例的计算能力，从同一数据集[26]中提取，呈正态分布，平均值为每秒0.38个作业，标准差为0.1。平均计算能力在提出的模型中用外部性因子$\alpha$表示，这意味着$\alpha$的范围为0.1到0.7。根据[9]中提出的假设，跨组外部性因子应限制在0和1之间，即$0<\alpha\beta<1$。因此，外部性因子$\beta$的范围为0到$1/\alpha$。消费者对每个企业的需求$D_{c_{i}}$范围从$0.1\times1$到$0.7\times53$，即每秒0.1到37个请求。服务价格$P_{i}$通过观察AWS市场[28]中150个商业智能计算服务（包括大数据和物联网服务）的价格来估计。根据观察到的价格，$P_{i}$呈正态分布，平均值为1.7美元/小时，标准差为0.5美元。这意味着服务价格范围从0.2美元/小时到3.2美元/小时。参数$\phi$表示云平台对服务提供商的贪婪程度。补贴因子$0<\phi<1$表示云的理性行为（补贴行为），而$1<\phi$表示云平台的贪婪行为。价格弹性设置在$0.1-0.35$之间（即Y），类似于文献[29]中显示的移动/电信服务价格的敏感性。我们假设在模拟中$k_{2}=1$。通过将$\alpha$、$D_{s_{i}}$、$D_{c_{i}}$、$\gamma$和$P_{i}$的期望值代入方程(1)并考虑假设$\left(k_{2}=1\right)$，我们发现乘数$k_{1}$的范围为0.1到0.99。值得一提的是，消费者需求$(D_{c_{i}})$和供应给$C S_{i}$的云资源（即计算和存储资源）$D_{s_{i}}$仅在模拟设置下估计，以提取乘数$k_{1}$的合适范围，但它们不作为模拟输入。模拟计算了预期的消费者需求和云资源的最优供应，如第IV-B节所述。所有相关参数的值总结在表II中。

B.Simulation Scenarios

B. 模拟场景

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.

我们考虑在云端的300个数据服务提供商在三种场景下的情况：1) 提出的双边博弈；2) 五五分成场景，除了云平台和数据提供商同意平等分享收入外，其余遵循我们的模型；3) 按需付费场景，这是Amazon和Google等主要云提供商目前采用的商业模式。

Table II: Simulation parameters values

表 II: 仿真参数值

系统参数 值
Pi 0.2 - 3.2 美元/小时
中 0-5
α 0.1 - 0.7
β 0 -1/α
0 -0.35
Ps 36 美元/小时
k1 0.1 - 0.9
  1. Two-sided scenario: The two-sided model, explained in details in Section II-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.
  2. 双边场景：双边模型在算法 1 中进行了描述，详细解释见第 II-A 节。给定数据服务价格 $P_{i}$，云平台确定最优的收入分成比例 $\chi_{i}$ 以及所需的云资源量，以最大化其收益。

Algorithm 1 Two-sided scenario

算法 1 双边场景

8: end for

8: 结束循环

  1. Fifty-fty scenario: The egalitarian (fifty-fifty) scenario follows the two-sided market model in terms of consumer demand and supply function, thus considering the external i ties 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 p