Pricing and Revenue Sharing in Secondary Market of Mobile Internet Access

Transcription

1 Pricing and Revenue Sharing in Secondary Market o Mobile Internet Access Hengky Susanto,3, Benyuan Liu, ByungGuk Kim, Honggang Zhang, Xinwen Fu Department o Computer Science, University o Massachusetts Lowell Engineering Department, University o Massachusetts Boston 3 Department o Computer Science and Engineering, Hong Kong University o Science and Technology {hsusanto, bliu, kim, xinwenu}@cs.uml.edu, honggang.zhang@umb.edu Abstract There is a ast growing number o public spaces oering Wi-Fi access to meet the rising demands or Internet access. It is common or such service to be oered to users at no charge or or a lat ee. Both situations provide very little incentive or Wi-Fi providers to oer better service to the users. Similarly, Wi-Fi providers pay a monthly lat rate to or Internet access and, this too does not incentivize to oer better service to Wi-Fi users. As a result, Wi-Fi users may experience poor connection when network becomes congested during peak hours. In this paper we propose a dynamic pricing scheme or Internet access and a revenue sharing mechanism that provides incentives or both and Wi-Fi providers to oer better service to their users. We build our revenue sharing model based on Shapley value mechanism. Importantly, our proposed revenue sharing mechanism captures the power negotiation between and Wi-Fi providers, and how shits in power inluences revenue division. Speciically, the model assures that the party who contributes more receives a higher portion o the revenue. In addition, our simulation demonstrates that our model captures the bargaining power shits between Wi-Fi providers and, and shows that the division o revenue asymptotically converges to a percentage value. I. INTRODUCTION In the recent decade, wireless local area network technology (e.g. Wi-Fi) has become essential to our everyday activities including communication, commerce, entertainment, education, etc. To cater to the rising demand or Internet access, there is a growing number o public spaces oering Internet access, such as malls, airports, coee shops, libraries, parks, etc. They are reerred to as Wi-Fi providers (). As this paper is written, s commonly oer Internet access service ree-o-charge or or a lat price. For example, a hotel charges their guest $5 per day or Internet access. Both ree-o-charge or lat ee arrangements oer little economic incentives or s to oer additional bandwidth to their users, when they need more bandwidth. This is because s do not gain additional reward or providing better service to their users and this may result in users being stuck with the deault service oered by. s rely on Internet Service Providers () or the Internet access and pay s a monthly lat rate or the service. This means s are also responsible or the traic generated by Wi-Fi users through s. Similarly, due to the arrangement o monthly lat rate, there is also very little incentives or s to provide additional bandwidth to Internet users o s. Study [] reports that Starbucks customers experience poor connection whenever there is a high volume o customers in a coee shop using the Internet at the same time. While the customers enjoy their drinks, they may be dissatisied with their Internet service. To address these issues, we propose a pricing scheme and a revenue sharing mechanism that provide incentives to both s and s to oer better service to s users. In other words, we propose a mechanism that allows Wi-Fi users to pay more i they wish to attain more bandwidth. Otherwise, they can use the service that is available to them. Our contributions are the proposed pricing model and revenue sharing mechanism collectively address the rising concerns on network traic load and price rom s, s, and end users. Importantly, the revenue sharing mechanism assures economic incentives or both and while providing acceptable service to their users. In this paper, we propose and develop a revenue sharing mechanism where the revenue rom providing Internet access to users is shared between an and a. We build our revenue sharing model based on Shapley value mechanism [6,7] because o its capacity to divide the revenue airly between parties involved. Our study shows that the cooperative scenario brought by our revenue sharing mechanism provides incentives to both an and a to oer additional bandwidth to the s users. That is, our cooperative revenue sharing model ensures that an receives a portion o the revenue collected by a. This way, the s revenue share increases as the generates higher revenue. In addition, our revenue sharing model also discourages s users rom transmitting more data when an is experiencing congestion at its end. Another important observation is that our sharing model also captures the shit in bargaining power between an and a according to the amount o revenue generated. Speciically, the revenue sharing model apportions a larger share o the revenue to an when a generates lower revenue, and this is reasonable because the has to incur a minimum inrastructure overhead cost at all times. When a generates higher revenue rom its users, our model attributes a higher portion o the revenue in recognition o its more signiicant contribution. However, the division o revenue between a and an converges to a percentage value even when the generates most o the revenue. The above outcomes conirm that our revenue sharing model /4/$3. 5 IEEE

2 achieves air compensation to both a and an according to Shapley value characteristics. We also demonstrate that our revenue sharing also assures that both and have incentive to oer additional service even with dynamic number o users. At last, we also demonstrate a best practice or a and an to achieve higher shared revenue, while keeping users happy at the same time. Next, we argue that dynamic pricing (other than lat rate and ree service) is able to provide economic incentive to both and or oering additional bandwidth to their users. Following this argument, we design a dynamic pricing model that incentivizes both and to provide additional bandwidth. Our pricing model is built upon two considerations. The irst consideration is that a dynamic pricing should adapt to the luctuation o the level o bandwidth demand. Thus, an needs to decide the minimum sale price by considering the total traic load generated by the as well as those generated by the s other subscribers. Similarly, the computes the price to its users according to the level o demand, i.e., price should increase as the level o demand increases. The second consideration is that the inal price charged to a s users must be equal or higher than the minimum price set by an. This is because the inal price should cover at least the s minimum price. For instance, when the minimum price set by the is higher than the price set by the, then the charges its users with price set by the. Importantly, our study shows that this pricing model provides incentive or both an and a to oer additional bandwidth to their users. This pricing model ollows the economic concept o demand and supply, where a charges higher price or service when demand or access increases. We ormulate our pricing scheme as a Network Utility Maximization (NUM) problem [,3,4], and solve it using a subgradient based algorithm. The s and the s price are obtained rom the solution to the NUM. The rest o this paper is organized as ollows. We begin by ormulating our research problem in section II where we discuss the impact o pricing and revenue sharing on, dierent types o pricing and revenue sharing approaches, and related works. In section III, we present our proposed revenue sharing mechanism between and. Following that, we present the dynamic pricing mechanism or both and in section IV. Our simulation results are presented in section V, ollowed by concluding remarks. II. BACKGROUND A. Impact o s traic on In order to design suitable pricing and sharing mechanisms, the impact o traic generated through s on an must be considered. Providing a Wi-Fi service in a public space may increase the amount o data being injected into the network. With the additional traic rom s during peak hours, network may become even more congested, increasing the burden on an. Moreover, a higher traic load may also negatively aect the connection quality o users at the s end and degrade network perormance. From a commercial perspective, while an s users may gain Internet access and the that charge users may receive some monetary gain, the may have to incur higher cost to support the additional traic without additional inancial beneits. B. Free Service, Flat-rate, and Dynamic Pricing To decide an appropriate pricing mechanism or providing additional bandwidth, we irst explore the tradeos between ree service, lat rate, and dynamic pricing. Free Internet access is commonly employed by s to entice customers to boost their business sales. For example, a coee shop oers ree Wi- Fi to attract more customers to come and linger, in order to achieve higher sales per customer. A has very little incentive to provide additional bandwidth because it does not gain additional beneit rom users enjoying good service, especially when good service has little direct impact on increasing the sale o their primary product/service. Similarly, lat-rate pricing strategy or Internet access also provides little incentive or a to oer additional bandwidth. For example, a hotel guest may pay a daily lat rate ($ per day) during his/her stay, and providing better service does not increase the hotel s revenue because the guest still pays the same rate regardless o the quality o the connection. By the same token, there is little incentive or an to oer additional bandwidth i a pays a lat rate to the. As a result, without the s support or providing additional bandwidth, the may not be able to oer additional bandwidth even i it desires to. Dynamic pricing is a usage-based pricing strategy where users pay according to the amount o bandwidth they use. This pricing model may provide more incentive to a to oer additional bandwidth because users must pay more or a better connection quality, which leads to higher earning or the. This pricing strategy can also be used to avoid congestion when there is more demand than available bandwidth in network. In such a situation, a increases the price to reduce traic load. Thereore, dynamic pricing not only oers more opportunities or higher revenue, it also gives a better control over traic. Similar arguments apply to an on the employment o dynamic pricing to provide additional bandwidth to its s users. C. Cooperative Versus Non-Cooperative Strategies In order to investigate what kind o sharing mechanism may provide incentive or an to support its s through additional bandwidth, we explore both cooperative and noncooperative strategies. Assumption. Price charged by a to users, denoted by λ, is no less than the price charged by its, denoted by g. In a non-cooperative setting, an determines and charges its s with a price g. Then, a sells bandwidth to users at price λ and pays the at price g, where g λ. Here, the gets to keep the dierence between λ and g. In all circumstances, the will not know the s inal sale price λ to users. This scenario may not be avorable to the when the earns signiicantly higher revenue, and the may want a higher share in the revenue. The non-cooperative setting may not be avorable to users either because the may not gain any additional inancial beneit rom allocating more resources or better service. As a result, users may experience poor perormance during peak time even ater paying a high price to their. Thus, non-cooperative model is not supportive to user demand or additional bandwidth. In a cooperative setting, an decides the minimum selling

3 price g to its and the sets the inal sale price λ to end users, and the and the share the total revenue received at price λ. In this setting, the is inormed o the inal sale price λ to the users, and its portion o the revenue corresponds to the inal price. Because it knows the inal sale price to users, the is able to monitor and assess the actual demand and the value o the service. Based on this reasoning, we propose in this paper a revenue sharing mechanism based on Shapley value [6]. This mechanism is desirable because it exhibits several airness properties that ensure revenue sharing is proportional to each party s contribution to the total revenue. D. Related Work In [], the authors propose a pricing strategy based on online mechanism design (OMD) to provide Wi-Fi service to Starbucks customers. Their pricing strategy is designed on the basis o users dynamically arriving at and leaving the coee shop in a period o time, and considers that users make certain decisions based on certain outcomes as time progresses. For instance, a customer may decide to leave the shop ater he/she has inished his/her drink, or to stay longer or more drinks. In addition, their pricing strategy also requires users to reveal their true valuation on the Internet access and their arrival time at the coee shop. Our proposal, on the other hand, does not require users to reveal their valuation o the service to, and Wi- Fi price is determined according to network traic and is available ater users start transmitting data. Our approach provides more lexibility and the price can be updated dynamically in real time setting. Furthermore, the role o is not incorporated in their design. Our model, on the other hand, allows to inluence s pricing, especially when is experiencing high traic demand. Revenue sharing between s utilizing Shapley value has been studied in numerous literatures. For example, [8] has studied Shapley value to model s routing and interconnection decision. Similarly, [9] explores the design o proit sharing mechanism using Shapley value that allows the revenue to be decided airly among participating s. In [], the authors examine the bilateral prices that can achieve the Shapley-value solution in peering. These literatures primarily ocus on revenue sharing between s that are at par or almost equal. In other words, multiple s are partnering and collaborating at equal or almost equal level to deliver massive amount o data rom content providers (like Google, CNN, ESPM, etc) to a very large pool o users. Moreover, s inrastructure is very complex and expensive which increases the complexity o the collaboration between s. Our paper is mainly concerned with revenue sharing between and, the latter a customer o, where relies on and pays or Internet access. Also, s network inrastructure is made up o only consumer level routers, and it serves a much smaller pool o users. Thus, equal partnership between and is not possible in this setup. In [], Shapley value is also incorporated in the revenue sharing mechanism between cellular network providers and wireless data plan subscribers (reseller) who resell their unused bandwidth to provide ad hoc Internet access or monetary rewards. The revenue sharing mechanism in [] is targeted at low usage subscriber resellers, such that resellers portion is only suicient to oset their monthly subscription ee. There is however no restriction on the amount o revenue that can be generated by and to be shared with. [5] proposes auction based secondary market or ad-hoc Internet access, where the provider keeps the dierence between the bids rom users and the actual price. Other than Shapley value based models, [] proposes asymmetric Nash Bargaining Solution revenue sharing model between dierent types o s. In this study, Stackelberg game, a non-cooperative game model, is considered in their pricing scheme, where a group o s decide their prices according to the prices being oered in the market by other s. However, Shapley value based revenue sharing model is is a cooperative based game theory [6]. In our discussion later, we show that the cooperative model is more avorable or, and yields higher revenue or both and. The authors o [3] propose a revenue sharing mechanism between global s (Skype) and local s (coee shops, hotels, etc.) and the mechanism to incentivize local to support Skype. In this setup, Skype users completely rely on to provide the additional bandwidth. Our model, in contrast, requires collaboration between and to provide additional bandwidth. Furthermore, our proposed revenue sharing model divides the revenue according to the contribution o the participating parties. III. REVENUE SHARING In this section, we introduce a revenue sharing model to address how the revenue gained rom selling bandwidth to users is shared between a and an, by using revenue sharing mechanism based on Shapley value [6]. Figure illustrates how revenue R is shared: φ w apportioned to w and φ i to i, depending on their relative contribution. φ w Total Revenue R({w, i}) Fig.. Shapley value based revenue sharing. A. Desirable Sharing Properties We next list a set o properties that our revenue sharing mechanism should satisy. Let R(. ) be the revenue unction and variable φ denote a vector o Shapley value. Let R({w, i}) denote the total revenue received rom providing network service by w which subscribes or bandwidth rom i. The Shapley value has the ollowing desirable properties [6,7]: Property (eiciency): φ w + φ i = R({w, i}). The eiciency property requires that the total shared revenue equals the revenue received by providing service. In other words, the mechanism does not contribute or receive extra revenue. Property (symmetry): I R(Z i) = R(Z w) (where Z = ), then φ w = φ i. The symmetry property requires that when an and a each renders the same contribution, both should receive the same portion o the revenue. Property 3 (dummy player): I w is a dummy, R(w i) = R(i) and φ w =. This property assures that when w does not contribute, φ i

4 then it receives zero share. Since w relies on an s inrastructure to sell bandwidth to users, the always has a contribution in supporting the network service, but not necessarily w. Property 4 (airness): For w and i, the portion o revenue share is proportional to their respective marginal contributions to the total revenue gained rom the sale. This property addresses the airness o revenue sharing between any pair o w, i. Property 5 (additivity): Lets separate a transaction into two parts, such that T = T + T. For any two transaction T and T, φ i (N, T + T ) = φ i (N, T ) + φ i (N, T ), where N = {w, i} and (N, T + T ) is deined by (T + T )S = T (S) + T (S) or every coalition o S. The additivity property addresses the process o getting the Shapley value. The premise is that the outcome rom transaction (N, T + T ) should be equal to the addition o two dierent transactions o (N, T ) and (N, T ). To illustrate the idea, imagine a receives revenue according to transaction (N, T ) on the irst day and (N, T ) on the second day. Assume that T and T are independent. Then, the s share rom both days should be the summation o the revenue received rom both transactions. In other words, this property guarantees that i the revenue o the service provided by the is additive, then the distributed revenue is the sum o the revenue generated or providing the service. B. Revenue Sharing Model In this subsection, we propose a revenue sharing scheme between an and a and its implementation. Deinition. Shapley value φ is deined by φ j = N! i(r, Z(π, i)), j N, () π Π where N = {w, i}, Z N, and j (R, Z(π, j)) = R( Z {j} R(Z) ), () where j N. Remark: Given (N, R), consider a permutation on π on the set N. Members o set N appear to collect their revenues according to the ordering all possible permutation π. For each member in N, let Z j π be the set o members preceding member j, where Z j π N. The marginal contribution o member j according to all possible permutation π is j (R, Z(π, j)) = R (Z j π {j} R(Z j π )). Here, the Shapley value can be interpreted as the expected marginal contribution j (R, Z), where Z is preceding j in an uniormly distributed random ordering. Since in this model N =, that is N = {w, i}, the Shapley value or w and i can be obtained by the ollowing approach: φ i = R({i}) + (R({w, i}) R({w})), (3) φ w = R({w}) + (R({w, i}) R({i})), (4) where R({w, i}) = φ i + φ w. Here, i will keep the revenue o φ i amount, while w will receive φ w o the total revenue R({w, i}), as illustrated in Figure. Total revenue R({w, i}) earned at the s end is deined as ollows. R({w, i}) = x s λ s s w. (5) Here x s and λ s denote bandwidth allocation and the inal price charged by w to user s respectively. Thereore, R({w, i}) = x s λ s s w = φ w + φ i, where the term s w denotes that user s receives Internet service provided by w. Additionally, in Shapley value methodology, R({w}) and R({i}) are the contributions o the Wi-Fi provider and the to revenue R({w, i}) respectively, but they also can be interpreted as the revenue that they will gain i they do not collaborate. Here, the revenue R({i}) is determined by solving the ollowing equation R({i}) = x s g s, (6) where g s denotes the price determined by the to provide service to user s. Revenue R({i}) can be interpreted as the cost charged by the to the at price g s or providing service to user s. Equation (6) indicates that the charges dierent prices to dierent users. However, since the relies on the to provide the network access, when R({w}) =, then R({i}) = R({w, i}), which means keeps the entire revenue o R({w, i}). Thus, φ i, R({w}) > R({i}) = { x s λ s, R({w}) =. s w Next, given that the provides Internet access to the, the s contribution R({w}) to R({w, i}) is determined as ollows. R({w}) = (λ s g s )x s max(log(g w ), β), (8) where g w = g s and β is a positive constant to guarantee the denominator is greater than. To assure that apportion o the share is allocated to the, the denomination actor in (8) is concave and lattened as g w increases. Moreover, the gap between λ s and g s is considered in equation (8) to assure that the receives more i λ s increases. However, without Internet access provided by the, the contribution o the is R({w}) =. In our design o R({w}), the s marginal contribution is inluenced by the cost incurred by the to provide the access but the inluence diminishes as the cost increases. A higher cost g w o access results in a lower contribution to the total revenue to a certain point, which may allow the to achieve higher proit rom the sales ater the s cost is covered. Next, we show that the property o our revenue sharing mechanism. Theorem. The revenue sharing mechanism assures that an s revenue portion at least covers the cost o providing service to its, i.e. φ i x s g s. The Proo o theorem is provided in the appendix. Additionally, by deinition, a s minimum revenue share (7)

5 is described by equation (8). Naturally, a and an may want to maximize Shapley value in order to maximize their earnings. However, it is very diicult or s to determine their maximum earnings because maximizing Shapley Value is conp-hard [7]. The solution to Shapley Value maximization problem is discussed in [7]. The amount o revenue or an and its is clearly determined by the price charged to users. In line with the objective o our revenue sharing mechanism to incentivize an and its to oer additional bandwidth to users, we also introduce a dynamic pricing strategy in next section. IV. PRICING MECHANISM In this section, we propose an s pricing strategy to its and the s pricing to user. Figure illustrates the overview o a transaction: ater a user s makes his/her request or connection, the presents the with the minimum price g s. At the same time, the computes its price λ s, and determines the inal sale price λ s, ormulated as λ s = max(λ s, g s + ρ), (9) where ρ denotes a constant minimum proit decided by the, or ρ. Then, the presents price λ s to user s and user s pays the at price λ s. Min. price g s Final sale price λ s Fig.. Pricing mechanism. Moreover, Figure 3 gives an overview o the pricing ormulation in which the decides the minimum sale price g s to support user s and at the same time the also decides the its own price λ s to user s. Then, user s pays the service at price λ s (the maximum between the two prices according to e.q ()). Fig. 3. Pricing Formulation. The pricing mechanism also considers multiple users at any point o time. We begin by irst addressing an s price to user. A. Wi-Fi Provider s Price Let S w denotes a set o users who access the Internet, through w. For any s S w, the objective o user s is to solve max U(x s, λ s ), or x s, λ s, () where x s denotes the amount o data usage by user s and λ s t denotes the price to be paid by user s or Internet access at time t. The price is dynamically determined according to the level o demand or network service. The utility unction o the user is deined as ollows. user U(x s, λ s ) = U bw (x s ) + U cost (x s, λ s ), where U bw (x s ) and U cost (x s, λ s ) denote the utility o user s in terms o bandwidth consumption x s and service cost, respectively. Considering that the operates at requency band B s, the utility unction o bandwidth usage is deined as ollows U bw (x s ) = W s log (x s ( + P s c s )), s B s where P s is the transmission power o user s mobile device, c s is the channel gain rom w to user s, and s is the Gaussian noise variance or the channel between w and s [4]. In other words, U bw (x s ) is inluenced by the channel quality and the amount o bandwidth. Additionally, U bw (x s ) ollows the law o diminishing return. This is because more bandwidth does not always mean higher satisaction and SNR measurement or wireless is concave [4]. Utility unction U cost (x s, λ s ) represents user satisaction or monetary surplus when the cost paid or Internet access is less than the budget, which is deined as ollows. U cost (x s, λ s ) = x s λ s, m s where m s denotes the budget that user s is willing to spend or bandwidth x s. Note that x s λ s t can be interpreted as the price that user s must pay or the service. Thus, ideally, user s budget matches the price that he/she must pay or the service, such that x s λ s m s = and hence U cost (x s, λ s ) =. Thereore, given inal price λ s, user s utilizes m s to inluence the amount o bandwidth x s allocated to him/her. The objective o w is to maximize its own revenue without exceeding its monthly bandwidth capacity. The maximization problem is expressed as ollows. max x s λ s, () s. t. x s C w, over x s, s w, where denotes user s receives rom w, capacity C w is amount o the s bandwidth capacity. Considering the respective objectives o users and the at the system level, the problem can be ormulated into network utility maximization (NUM) []. max U(x s, λ s ) s. t. x s C w, over x s, s w. () In this setup, the solution or problem () also solves problem (9) and (). The Lagrangian optimization problem is ormulated as

6 Shared Revenue Shared Revenue Ratio Shared Revenue L(x s, λ s) = U(x s, λ s ) x s λ s + λ s C w, where L(. ) is the Lagrangian orm and λ s is known as the Lagrangian multiplier, which is oten interpreted as the link price, and x s is a vector o x s, or, and λ s is a vector o λ s. The common solution to NUM problem is the subgradient based method [3]. Typically, the dual problem D to the primal problem o () is constructed as ollows min D(λ s ), s. t λ s, where the dual unction D(λ s) = max x s x max L(x s, λ s). To solve D(λ s ), user s maximizes over x s given λ s. That is x s = arg max (U(x s, λ s )). (3) x s xmax s However, since e.q. () assures the minimum price charged to users. Thus, e.q. (3) can be expressed as ollows. x s = arg max (U(x s, λ x s xmax s )) s Next, L(x s, λ s) is minimized with subgradient projection method in an iterative solution given by λ s = [λ s σ t (C s x s ) ], (4) where C s sεs x s is a subgradient o D(λ s ) and σ t denote the step size to control the tradeo between a convergence guarantee and the convergence speed, such that σ t, as t and σ t =. (5) Next, ater solving λ s, then we solve or λ s with (). Notice that in (), g s + ρ serves the minimum price charged to user s, such that λ s g s + ρ. Generally, the subgradient-based solution relies on eedback loop mechanism. That is, the user determines the transmission rate according to the price set by the by solving (3) and the price is adjusted according to the traic load by solving (4). It is repeated until it converges to an optimal solution. Price λ s is also an indication o the demand or service. However, beore determining the inal sale price, the must consider the minimum price charged by the as described in (). It is because the depends on the s inrastructure to provide the service. The discussion on the minimum price is addressed in the next section. Proposition : I the step size σ in (5) satisies (4), then the subgradient-based algorithm converges to the optimal solution o problem (). [5] B. Minimum Price by Here, we address how an determines the minimum price or bandwidth. Consider a network managed by an with a set o links L, and a set o link capacities C over the links in L. Given a utility unction U s (x s, λ s ) o data user s with bandwidth usage o x s and traic generated by users in S, the maximization problem can be ormulated as ollows. t= max U(x s, λ s ) s S + (6) s. t. x s C l, sεs over x s. Here, users in set S include all users who get Internet service rom s that supported by the. To solve problem (6), users in S solve eq. (3) and the determines the minimum price to sell on each link l by solving g l = [g l σ t ((C l x s ) x s ) ]. (7) s S s l Here, s l denotes user s who transmits data through link l. The total minimum price to sell to user s is g s = g l, s,. s l Proposition : I the step size σ in (5) satisies (7), then the solution converges to the optimal solution o (6). [5] Since the speed o convergence is determined by step size σ, the running time required to obtain convergence also depends on the value o σ. Higher value o σ increases the speed o convergence but it may have the risk that the algorithm does not converge. Similarly, lower value o σ decreases the convergence speed but increases the convergence guarantee. V. SIMULATION AND DISCUSSION The objective o our simulation is to understand the behavior o revenue sharing between an and a using the Shapley Value model. More speciically, we investigate how the dierence between the inal sale price paid by users and the minimum price set by inluences revenue sharing, and whether the outcome is avorable to or. In the simulation setup, we have a subscribing Internet access rom an to provide Wi-Fi to users. In this setup, the provides to users bandwidth o MB/sec and the initial minimum price charged by the is units currency and the total minimum proit desired by the is 5 units currency. Thus, the initial price charged to users is 5 units currency. This set-up applies to the two scenarios we are investigating: irst, congestion occurs at the s network, and second, there is a high demand at the WSP s end but low traic load in the s network. In each scenario, either the s or the s price is raised incrementally by one unit up to 3 increments. a) Price Increment c) Price Increment Fig. 4. Revenue sharing when increases the price. (a) The revenue division between and in unit currency (e.g., dollar). (b) The revenue division between and in percentage. (c) The revenue that is apportioned to in unit currency. b) Portion Price Increment +

7 Shared Revenue Shared Revenue Ratio Shared Revenue Price charged to users Price Chared to Users Ratio Shared Revenue Bandwiidth usage Bandwidth usage User Utility User Utility First scenario. During the peak hours o an s network, the increases price to reduce the amount o demand. In this scenario, there are ten users getting Internet access rom a Wi- Fi provider, where each user receives equal amount o bandwidth allocation. Figure 4(a) and 4(b) illustrate that our proposed revenue sharing mechanism avors the during its peak hours, at the same time the model also assures that the receives some portion o the revenue. In other words, the majority o the revenue is allocated to the during peak hours. The y-axis o igure 4(a) depicts the portion allocated to the and the in unit currency and the y-axis in Figure 4(b) is the percentage o revenue apportioned to the and the, totaling to %. Thereore, there is little incentive or the to provide additional bandwidth during peak hours. However, as Figure 4(c) demonstrates, regardless how much charges, always receives some portion o the revenue as s portion converges to a value even when s price continues to grow. In essence, the outcome rom this scenario implies that during peak hours receives most o the share o the revenue, regardless how much charges users intersect a) Price Increment b) Price Increment Fig. 5. Revenue sharing when increases the price and the bargaining power shit between and. (a) The revenue division between and in unit currency (e.g., dollar). (b) The revenue division between and in percentage. Second scenario. The receives a high level o demand rom users, causing the to increase its price. However, there is low traic at the s end, where the minimum price decided by the is much lower than the s inal price. In this second scenario, there are initially ten users getting Internet access but eventually the number o users is increased by ive in each iteration. Moreover, the amount o bandwidth is divided equally among users, which results in a smaller allocation to each user as the number o users increases. Figures 5(a) and 5(b) illustrate the division o revenue between the and the as the s price is incrementally raised by unit currency up to 3 increments. Figure 5(a) depicts the division o revenue in unit currency and Figure 5(b) in percentage value. Figure 5(a) shows that in this scenario both the and the receive a higher revenue rom the high demand. The higher revenue received by the should provide an incentive or the to provide additional bandwidth. From the irst to the nd price increment, as shown in igure 5(a), receives a higher share o the revenue. Up to this point the revenue is still relatively low. This can be interpreted as because the provides and manages the inrastructure, a higher portion o the revenue is allocated to the to cover the cost o providing the access and managing the traic rom the. At nd price increment, the two lines intersect (Figure 4) at price incremental at. The intersection can be interpreted as when the bargaining power is balanced and revenue is equally Intersect shared between the and the. However, as the generates higher revenue and the traic at the s end remains low, the bargaining power progressively shits toward the. As the price increases, its bargaining power also increases because o its higher contribution to the transaction. The s portion o revenue eventually converges to a region o 7% o the total revenue (igure 5(b)), and the s percentage share converges to 3%. Generally, the convergence to a speciic value shows asymptotically that there is a predictable region o revenue sharing. Importantly, this convergence also provides the upper celling o the portion allocated to the, i.e. 7%, and the bottom limit o the portion allocated to the, i.e. 3%. The existence o these upper bounds or revenue sharing can become the basis or both the and the to evaluate and negotiate the risk and gain in such trade agreement or mutual beneits. a) Number o Users 5 c) number o users Number o Users d) Fig. 6. Revenue sharing when bandwidth demand is low with up to users. (a) Ratio shared revenue o over. (b) Average user utility. (c) The price that users pay or the service. (d) Amount o bandwidth sold to users. a) Number o Users 5 c) Number o Users d) Number o users Fig. 7. Revenue sharing when bandwidth demand is high with up users. (a) Ratio shared revenue o over. (b) Average user utility. (c) The price that users pay or the service. (d) Amount o bandwidth sold to users. Third scenario: we investigate the correlation between revenue sharing, pricing, users utility, and bandwidth usage. The simulation setup includes an providing MB/sec to users with initial minimum price charged by an o units currency, minimum proit desired by the is 5 units currency, users maximum willingness to pay is units currency, and user utility and price are measured and determined using eq. () and (4) respectively. In this scenario, we consider two case studies: (i) When the experiences lower and (ii) higher demand or bandwidth. Case (i): There are to users acquiring service rom. b) b) Number o Users 5 5 Number o Users 5

8 Figure 6(a) illustrates that shared revenue ratio o shared revenue increases as the number o users increases, shared revenue which conirms our previous simulation results. Figure 6(b) and Figure 6(c) demonstrate that users average utility and price are stable when there is suicient bandwidth or users. That is when the total bandwidth usage o users described in Figure 6(d) is only 7 MB/sec < MB/sec. Case (ii): There are to users subscribing rom the. The steep incline depicted in Figure 7(a) shows that the rapidly achieves higher shared revenue as demands or bandwidth increase, and the quickly attains near equal share as the. In addition, the behavior o shared revenue illustrated in Figure 7(c) is also a relection o price movement caused by the hiking the price up when the total demands exceeds the capacity limit. This leads to the bandwidth luctuation illustrated in Figure 7(d) as a result rom users adapting their demand or bandwidth when the price increases. In addition, Figure 7(a-c) reach the plateau (or lat) whenever bandwidth usage alls below the capacity limit, but change when demands go over the capacity limit. Moreover, Figure 7(c) also shows that user utility decreases as the price increases, because users obtain less bandwidth or higher price. Then, user utility in Figure 7(d) drops to zero when the price in Figure 7(b) peaks at 7 units currency, which results in unaordable service leading to zero transaction. This also means no revenue or both the and the, as described in Figure 7(a). In conclusion, a achieves higher shared revenue when there is high demand or bandwidth until the price becomes unaordable, but this is also at the cost o lower user utility. On the other hand, we also demonstrate that a also can obtain higher shared revenue and allow an to gain higher revenue while achieving high user utility, when the bandwidth usage nears the limit capacity while keeping the price stable. Similar outcome is expected when an price is increased beyond users aordability except higher shared revenue will apportioned to an relative to a. VI. CONCLUSION In this paper, we propose a Shapley value based revenue sharing scheme and a NUM based dynamic pricing strategy to provide incentives or and to oer additional bandwidth to their users. We explored the revenue sharing model in two alternative scenarios, cooperative and noncooperative, and discovered that the cooperative model oers better incentives or. In the cooperative revenue sharing setting, will be aware o s inal sale price to users, which gives better understanding o the market and more control over pricing. Importantly, our revenue sharing model is able to address critical concerns such as traic management. Additionally, our model also captures the conditions in which one o the parties ( or ) receives a higher portion o the revenue. For instance, the sharing model apportions a larger share o the revenue to when generates lower revenue, but avors when it brings higher revenue. When contributes a signiicant portion o the revenue, the division o revenue eventually converges to a stable value, which gives larger share to. We also demonstrate it is possible or a and an to achieve higher revenue while attain high user utility. In our uture work, we will investigate whether the economic interplay and negotiation between, s, and users can reach an equilibrium. Appendix Proo Theorem. By deinition deined in e.q. () that g s λ s, λ s g s. Thus, by comparing λ s g s and R({w}) in e.q. (8), we have the ollowing equality. (λ s g s ) (λ s g s ) max(log(g w ), β). (8) Observe that in the equality above, as the g w = g s increases, the right side o the equality decreases quicker than the let side. Next, the equality (8) can be derived urther as ollows. λ s g s (λ s g s ) max(log(g w ), β), Which is also g s λ s s w (λ s g s ) max(log(g w ), β). By considering bandwidth x s allocated or every user s that receives service rom w, equality (8) also implies (x s g s ) (x s λ s ) (λ s g s ) x s max(log(g w ), β). (9) s w Now, consider combining (3) with (5), (6), and (8), the revenue shared apportion to is φ i = (x s g s ) + ( (x s λ s ) (λ s g s ) x s ). () max(log(g w ), β) s w Next, we substitute (9) to () and then we have φ i (x s g s ) + (x s g s ) = (x s g s ). Thus, φ i (x s g s ), which is the revenue shared apportion to covers the minimum cost. Acknowledgement. This research was supported in part by the NSF under Awards CNS-9536, CNS-5733, and CNS REFERENCES [] E. J. Friedman and D. C. Parkes, Pricing WiFi at Starbucks: issues in online mechanism design, ACM Electronic Commerce, 3. [] F. P. Kelly, A. Maullo, D. 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