I Introduction
Ia Background
With the spreading and application of smart mobile terminals, the global mobile data traffic grows explosively [1]. According to the prediction of Cisco, the global mobile data traffic is projected to achieve 49 exabytes/month by 2021, video streaming will occupy almost 78% of the mobile traffic and the average mobile connection speed will exceed 20 Mbps[2]. Meanwhile, the developments of recent communication technologies such as HighDensity Network, Massive MIMO, MillimeterWave Communication and Local Caching, etc [3, 4, 5, 6] accommodate the requirements of data traffic explosion and data rate increment.
Under this context, the content providers are providing more and more of their services on the platform of the mobile device. Take video websites for example, in the past, we have to watch live or recorded videos on PC by visiting video websites; nowadays, we can watch videos through the APPs on smart mobile devices. Since the content providers (e.g., video websites) are profitoriented entities, their objectives are to maximize their own revenues in addition to compensating for operational cost and the payment of video copyright. Therefore, a new business model which is adapted to the mobile useroriented network model is urgently needed for content providers to create more revenues [7].
IB Motivations
Recently, a variety of works have applied several gametheoretic approaches to study the business models of network resource allocation. The literature can be categorized into several lines of works: 1) for cache resource allocation, references [8, 9] respectively applied the Contract model and Stackelberggame model to study the optimal pricing strategy of operators and the optimal caching strategy of content providers in a smallcell system, and reference [10] proposed the pricing and caching scheme in an information centric network. 2) For data offloading, reference [11] utilized a distributed market framework to analyze the interactions between the offloading service providers (access points) and the offloading consumers (data traffic), reference [12] proposed a threestage Stackelberg game model to formulate the data offloading problem among mobile network operators and access point owners. References [13, 14, 15, 16] adopted different game approaches to investigate the physical parameters (e.g., power, bandwidth, SINR and average achievable rate) allocation problems, where [13] studied the relay nodes selection and power allocation problems in cooperative relay model by the Stackelberg game approach, [14] analyzed the pricebased power allocation strategies for twotier spectrumsharing femtocell networks, [15] investigated the wireless service provider selection problem and the corresponding bandwidth allocation problem in multitier heterogeneous cellular networks by evolutionary game and multileader multifollower Stackelberg game, respectively; and [16]
modeled multiple small cells by stochastic geometry and utilized evolutionary game theory to analyze the average SINR and the average achievable rate. In addition, some works have also applied varieties of game theories to study the resource allocation problems in the fields of WIFI & LTEU
[17, 18, 19, 20], distributed computing [21, 22], cloud computing & softwarized network[23, 24], and rollover data [25, 26], etc. Although the above literatures have not directly considered the business model among content providers and mobile users, they have given us great insights for the business modeling of new scenarios and the analysis of the interactions among all the entities.Consider the relationship among content providers and mobile users, and take video websites for example, Membership mode is an effective business mode to create revenues [27]. More specifically, Membership mode refers to an operational mode where the video website generates revenue from the mobile users through selling access rights of video resources to mobile users.
In addition to membership mode, Advertising Mode, an emerging business mode, provides another good solution for the content provider (e.g., video websites) monetization [28, 29, 30, 31, 32]. In this mode, the video websites can create revenues from the advertisers via embedding the advertisements on their platforms in the form of text, picture or video. Meanwhile, the advertisers can raise the brand awareness and further increase the sales of commodities via video advertising on video website, which is beneficial to increase the advertisers’ revenue. Several works have been conducted to study the field of advertising [33, 34, 35, 36, 37, 38, 39, 40]. More specifically, references [33, 34, 35, 36] mainly focused on the study of the impact of targeting technology on advertising markets, references [39, 38] analyzed the competitions among advertising companies in vehicular adhoc networks, reference [37] investigated the advertising targeting and monetization problem of mobile locationbased user in a venue (e.g., shopping mall or airport), and [40] applied advertising to study the monetization model of the monopoly wifi business market.
Combining the above two business modes together, we can build a new mode called MembershipAdvertising Mode. More specifically, the video website provides two types of services for mobile users: member service(s) (one or more) and nonmember service. The website members need to pay the video website for enjoying the high quality, adfree video services, while the nonmember can watch the low quality, adcontaining video services for free. In this mode, the video website can create revenues from mobile user members as well as advertisers, and is thus a more flexible business mode than membership mode or advertising Mode. In practice, some popular video websites in China, such as TENCNET, IQIYI, YOUKU and SOHU, have adopted the MembershipAdvertising Mode in their major business model. However, we notice that few literature has studied the interactions among all interest entities of this model (e.g., advertiser, video websites and mobile users) as well as the designs of the corresponding policies. Motivated by this, we conduct the study in this paper.
IC Contributions
In this paper, we investigate the economics of the video websites with the MembershipAdvertising Mode in the wireless network. More specifically, video websites provide three video services for mobile users: VIPMember service, RegularMember service and NonMember service. For VIPMember and RegularMember services, the video websites charge the subscribed mobile users a fee according to their pricing mechanisms, where the price of the VIPMember service is higher than that of RegularMember service. Correspondingly, VIPMember service subscribers can enjoy the high rate adfree video service for unit period, and the RegularMember service subscribers can enjoy the middle rate adfree video service for unit period. For NonMember services, although no membership fee is paid, the mobile users can only enjoy the low rate adcontaining video service. According to the websites’ pricing mechanisms, mobile users choose one of these three video services as their watching strategies based on their own preference of the video QualityofExperience (QoE). Since the NonMember mobile users are the potential consumers of the advertiser, to promote the sales of its commodities, advertiser offers a certain budget for purchasing the advertising spaces among all video websites to display its commodities’ advertisements. Meanwhile, the advertising budget attracts each video website to sell its own advertising spaces to the advertiser. Each video website decides the selling number of the advertising spaces with the consideration of the advertising budget, its own advertising space maintenance cost and other websites’ advertising spaces selling strategies.
The main contributions of this paper can be summarized as follows:

Novel Video Website’s Business Model: To the best of our knowledge, this is the first work that proposes and analyzes the network model consisting of multiple video websites, multiple mobile users and an advertiser. In this network model, we propose a novel MembershipAdvertising Mode in the monetization model.

Equilibrium Analysis: We model the interactions among advertiser, video websites and mobile users as a threestage Stackelberg game, and study the behaviour of each entity of interest as well as the corresponding subgame equilibrium systematically. In particular, we derive the unique closedform solutions of each mobile user’s optimal watching strategies and each video website’s optimal membership pricing strategy. We then determine the unique optimal subset of those video websites participating in the advertising budget game by exploiting the special structure of the advertisement (AD) space maintenance cost in the subset, and further derive the closedform of the unique optimal ADspaces selling number strategy for each website. Moreover, we analyze the piecewise structure of the advertiser’s utility and propose an efficient algorithm to obtain the optimal advertising budget.

Analysis of Key Parameters’ impacts: We analyze the relationship among the preference factor thresholds with different values of VIPMember price coefficient, and further investigate the coefficient’s impact on mobile users’ optimal watching strategies. Meanwhile, we also find that the subset of video websites that participate in the adverting budget game only depends on the ADspace maintenance cost rather than the advertising budget.

Performance Evaluation: Extensive simulation results show that: 1) the increasing of VIPMember price coefficient is not beneficial for both video websites and advertiser to create revenues; 2) The impact of popularity concentration level on each utility is in connection with the popularity of the subset of the video websites that participate in the advertising budget game; 3) The utility of video website (advertiser) increases (decreases) in the ADspace maintenance cost; 4) The utility of video website (advertiser) increases in visiting frequency if the website’s ADspaces are saturated, when visiting frequency is sufficiently large, the utility of video website (advertiser) is independent of visiting frequency.
ID Organization
The remainder of this paper is organized as follows. Section II introduces the system model and presents utility functions. Section III presents the threestage stackelberg game to formulate the interactions of the utility function maximization problem and provides the game equilibrium. Section IV proposes the numerical computation to validate the results in this paper. Finally, section V concludes this paper.
Ii system model
Before introducing the system model, we first list all the symbols in Table I for convenience of reading.
Parameters  Description 

Video websites number.  
Mobile users number.  
Advertisements number.  
VIP Member service quality.  
Regular Member service quality.  
Non Member service quality.  
The preference for QoE .  
VIP Member price coefficient.  
Concentration level.  
Video website ’s popularity.  
Mobile user’s visiting frequency. 
Variables  Description 

AD space maitenance cost.  
Membership price.  
AD space selling number.  
The advertising budget. 
Functions  Description 

VIP Memberprobability.  
Regular Member probability.  
Non Member probability.  
Mobile user’s watching strategy set.  
AD Watching Probability.  
Mobile user’s utility.  
Video website’s membership utility.  
Video website’s advertising utility.  
Video website’s total utility.  
The utility of the advertiser. 
In this paper, we consider a network ecosystem which consists of an advertiser, video websites and mobile users, as show in Fig. 1. We focus on the interactions among them via a threestage Stackelberg game.
Iia Network Model
IiA1 Advertiser
The advertiser has total advertisements (ADs) which seek to display on video websites. The advertiser has total advertising budget to buy the advertisement (AD) spaces from video websites. Here, the unit ADspace refers to the time segment (e.g., 30 seconds) at the beginning of a video which is specially used for displaying video AD.
IiA2 Video Website
There are total video websites in the network, and we denote as the website set. There exists twofold interactions for each video website: one is the interaction between the video website and the advertiser: under the motivation of the advertising budget , all video websites compete with each other through selling the AD spaces ; the other is the interaction between the video website and the mobile users: each video website provides three video services for mobile users: VIPMember service, RegularMember service and NonMember service. We let , and respectively denote the corresponding video service quality of website . More specifically, for the VIPMember service, the website charges its subscribed mobile user (), where is the VIPMember price coefficient, and provides the video service with video rate per unit period (e.g., /month), and the service quality is measured by [41]; for the RegularMember service, the website charges its subscribed mobile user , and provides the nonadvertising video service with video rate per unit period, and the service quality is measured by [41]; for the NonMember service, although it is free of charge, the webwite only provides the advertisingcontaining video service with video rate , and the service quality is measured by [41]. Without loss of generality, we assume that , naturally, we have .
IiA3 Mobile User
We denote as the total number of mobile users browsing the video websites within an unit period. We let a positive denote each user’s preference for QualityofExperience (QoE) for website browsing, and further assume
follows the uniform distribution over
. The preference factor reflects the user’s requirement and willingness for video watching experience, namely, a larger implies that the user is sensitive to the video QoE, while a lower means the user is relatively QoEtolerant. Note that since different users may have different preference factor values, they have different watching strategies when browsing one video website , .According to the video service types of each video website, we denote as a mobile user’s corresponding watching strategy when browsing video website , and denote as the mobile user’s watching strategy set for all the websites. Specifically, , and denote that an mobile user chooses to be an VIPMember, RegularMember and NonMember of website , respectively.
IiB Mobile User’s Utility
IiB1 Mobile User’s Payoff
Based on mobile user’s three different watching strategies, for a type user browsing website , the payoff over an unit period is defined as follows:
(1) 
Each mobile user will choose one strategy which maximizes the payoff as the utility function.
IiB2 Strategy Probability, Visiting Frequency and Websites Preference
Given price , we denote , and as the probability that a mobile user chooses to be VIPMember, RegularMember and NonMember
, respectively. In addition, we assume that each mobile user’s visiting frequency for each video website per unit period follows the Poisson distribution with mean
. Meanwhile, due to different influence factors such as individual willingness, QoS, charge standard, video content popularity and so on, mobile user has different level of preference for all the video website. We let denote each mobile user’s preference of video websites, where follows the Zipf distribution, i.e.,(2) 
for . Note that this assumption is also made in [9, 8]. The parameter is a positive real number which characterizes the concentration level of the website’s popularity distribution. A larger implies that the polarization of popularity is more obvious, that is, the popularity of those websites with smaller index is much higher than others.
IiC Video Website’s Utility
Since each video website has the interactions with both mobile users and advertiser, its utility comes from two aspects.
One is the utility comes from the mobile users’ payments for membership and we denote it by , :
(3) 
Recall that is the mobile user number, is the popularity of video website , and are respectively the VIPMember probability and the RegularMember probability of website under price , thus and are respectively the expected number of the VIPMember and the RegularMember of website .
The other is utility comes from selling AD spaces to the advertiser. We assume the reward that video website receives is proportional to , and denote as the maintenance cost of unit AD space, then, the utility of website in terms of selling AD space can be expressed as follows:
(4) 
where .
To sum up, the utility of video website , , is given by:
(5) 
IiD Advertiser’s Utility
IiD1 AD Watching Probability
We assume the total number of AD spaces that video website sells to the advertiser under advertising price is . Meanwhile, we assume that the AD spaces allocation among all the ADs follow equal allocation principle. Since each website needs to display total ADs, the total display number of each AD over unit period is . In addition, the expected number of mobile users who watch the advertisingcontaining video of website is . Since the average visiting frequency of each mobile user per unit period is , the total visiting number of the advertisingcontaining video of website per unit period is . Therefore, if a mobile user watches an advertisingcontaining video of website , the probability that the user can watch a specific advertisement is given by:
(6) 
Note that each mobile user’s website visiting frequency is a random discrete variable which follows Poisson distribution with mean , and its probability mass function (PMF) is given by [42]:
(7) 
According to the complementary advertising assumption [43, 33, 44], we know that the advertiser can receive the reward of an advertisement on video website only if the specific advertisement has been watched by the mobile user at least one time. We further define the probability that a specific advertisement on video website which has been watched at least one time as AD Watching Probability, i.e., , which is given by:
(8) 
where (a) is obtained by the Taylor expansion for exponential function .
IiD2 Advertiser’s Payoff
Based on the AD Watching Probability , , the payoff of the advertiser is given by:
(9) 
where is the reward coefficient that the advertiser display ADs on website , is the total ADs number, is the expected NonMember number of website , is the AD Watching Probability, is the advertising budget, is the set of RegularMember price and is the set of selling number of AD spaces.
Iii ThreeStage Stackelberg Game
In this section, we will utilize a threestage stackelberg game to formulate the interactions among the advertiser, video websites and the mobile users. Specifically, in Stage I, the advertiser decides its total advertising budget ; in Stage II, each video website specifies the selling number of AD spaces and the RegularMember price ; in Stage III, each type mobile user chooses the video website watching strategies . We use backward induction to analyze the threestage Stackelberg game.
Iiia Stage III: Mobile User’s Optimal Video Watching Strategy
IiiA1 Preference Factor Threshold
For a specific video website , the goal of each mobile user is to choose one video watching strategy that maximizes its payoff in (1). Since the Regular Member price in (1) is given in Stage II, each mobile user’s video watching strategy only depends on the preference factor . Before we proceed, we first give some definitions about the preference factor threshold.
Definition 1.
We define as the preference factor threshold such that , then, .
Definition 2.
We define as the preference factor threshold such that , then, .
Definition 3.
We define as the preference factor threshold such that , then, .
Based on the preference factor threshold of video website (), the optimal video watching strategy of a type mobile user is given by:
(10) 
IiiA2 The impact of on
Next, we will analyze the relationship among , and , and rigorously describe it in the following lemma.
Lemma 1.
For ,

when , then, ;

when , then, .
Proof:
Please refer to Appendix A. ∎
Remark 1.
Firstly, it is obvious that both and are the linear increasing function of since both and are two positive constants under price . Moreover, since , the slope of straight line , i.e., , is larger than that of straight line , i.e., ; Secondly, is a independent positive constant; Thirdly, since these three straight lines intersect at , in the domain , we have , and in the domain , we have . Here, we present the graphical visualization of the relationship among , and stated in Lemma 1 in Fig. 2.
When taking into consideration, there are total five possibilities of the optimal video watching strategy to discuss.
Case 1–: Combining Definition 13 and Lemma 1, it is not difficult to find out that the inequality holds for any positive ^{1}^{1}1According to Definition 13, when , we have ; when , we have , , thus ; when , we have , , , thus ; when , we have .. Therefore, the optimal video watching strategy of a type mobile user in (3) can be reduced to:
(11) 
Case 2–: Similar to the analysis of the footnote in case 1, the inequality holds for any positive . Therefore, the corresponding optimal video watching strategy in (3) can be further reduced to:
(12) 
In addition, The graphical illustration of all the five possibilities of the optimal video watching strategy stated in (11) and (12) is presented in Fig. 3.
IiiA3 Watching Strategy Probability
Note that follows the uniform distribution over , therefore, under and coefficient , the probability that a mobile user chooses to be VIPMember, RegularMember and NonMember of website can be respectively given by:
(13)  
(14)  
(15) 
IiiB Stage II: Video Websites’ Optimal Membership Pricing and Optimal Selling Number of AD Spaces
In this subsection, we consider the video Websites’ optimal membership pricing strategies for mobile users and the optimal selling number of AD spaces for advertiser in stage II. Each video website decides its optimal member pricing by anticipating the mobile user’s watching strategy in stage III, and makes its decision on optimal selling number of AD space not only by responding to the advertising budget in stage I, but also depending on the AD spaces selling strategies of other websites .
IiiB1 Optimal membership pricing
Substituting (13) and (14) into (3), the optimization problem of maximizing the utility of video website in terms of mobile users’ payments for membership can be formulated as:
(16)  
(17) 
where the first constraint in (17) means the membership price is nonnegative, and the second constraint in (17) means the preference factor threshold should no larger than to guarantee nonempty feasible domain of each mobile user’s video watching strategy (i.e., ).
Theorem 1.
The unique optimal membership price of video website , i.e., , for problem in (16) is given by:
(18) 
where .
Proof:
Please refer to Appendix B. ∎
IiiB2 Optimal Selling Number of AD Spaces
In this part, we will determine the optimal selling number of AD spaces . From the utility function of each video website in (4), we can see that the optimal selling number of the AD spaces of website , i.e., , not only depends on the total advertising budget , but also depends on the AD spaces selling strategies of other websites, i.e., . Therefore, the process of determining the optimal for each website is the noncooperative game, and the utility maximizing problem of each website in terms of selling AD spaces can be formulated as follows:
(19)  
(20) 
for . The first term in (19), i.e., , represents the reward of video website , and the second term in (19), i.e., , means the corresponding total ADs maintenance cost. The constraint in (20) indicates that the selling number of AD spaces for each video website is nonnegative.
Assumption: we consider the case , i.e., all other websites except website don’t participate in the advertising budget game, then, the utility in (4) is reduced to . In this case, there exists no optimal solution (equilibrium) for problem in (19) since the utility can be infinitely tending to when we choose a sufficiently small positive . Therefore, we here assume that in this paper.
We note that the objective function in problem (19) is concave since holds, and the constraint in (20) is linear. Therefore, the problem in (19) is convex, and the KarushKuhnTucker (KKT) conditions are the necessary and sufficient conditions of optimality [45]. We thus derive the KKT conditions of problem in (19) as follows: we let , , denote the the lagrange multiplier associated with the constraint in (20). The Lagrangian function of problem (19) with nonnegative , , can be given by:
(21) 
Denote as the optimal the optimal Lagrange multiplier for the corresponding dual problem. Therefore, the KarushKuhnTucker (KKT) conditions [45] are given by:
(22) 
Moreover, the nonnegative Lagrange multiplier, i.e., , should satisfy the the complementary slackness conditions [45]:
(23) 
Combining (22)(23) and simplifying, we have
(24) 
for , where .
We can see from (24) that: if , we have ; else if , we have . Thus, we can further divide the optimal selling number of AD spaces into two subsets. Specifically, one is the subset where the optimal strategy of each video website is participating in the advertising budget game, in other words, the optimal selling number of AD spaces is positive. We further denote this subset as , and denote the corresponding size as . The other is the subset where the optimal strategy of each video website is not participating in the advertising budget game, namely, the optimal selling number of the AD spaces is zero. Similarly, we denote this subset as