10.1.1 Research Questions

The concept of sponsored content introduces the following set of research questions. In this chapter, we shall mostly focus on the first one.

• What is the proper way to design a contract between the service provider and the content provider for sponsored content? The service provider needs to design the contract in such a way that induces the content provider to participate in sponsoring and make decisions that improve the service provider's profit. The main contribution of this chapter is the design of a contract that not only does this but also maximizes the gain to the entire system, while at the same time transferring a significant share of the gain to the service provider itself. Moreover, we will show that the contract is win–win–win for the service provider, the content provider and the EUs in the sense that if sponsoring occurs, then all participants in the system will be better off than if there were no sponsoring.
• What are the main types of content for which the sponsored content concept is most applicable? Our model will shed some light on this problem because it will generate a set of conditions regarding when the content provider will decide to sponsor. At a crude level, the concept makes most sense for content that generates significant economic value to the content provider on each view. Some examples include advertising (especially advertising for luxury items), shopping sites (where the content provider cost of sponsoring could be wrapped into the purchase), large content such as movies (especially for sites where contentmust be purchased because again the cost of sponsoring could be wrapped into the cost of the purchase) and applications such as games that include “in-app purchases.”
• To what extent should consumers be informed that sponsored content is free to them and if so, how should this information be communicated? We believe that the sponsored content concept has value even if the EU is unaware of which content is sponsored because it would still prevent a big depletion of quota for large content that the EU would prefer to not pay for. However, it is likely that the dynamics of the system would be significantly transformed if the users do know what content is free to them.
• How can sponsored content be implemented at scale? Realizing the concept at a small scale is simple because all we need to do is inspect packets within the network to decide whether the EU will be charged or not. [This could for example be done on the basis of Internet Protocol (IP) address.] In addition, we would need a way to manage the payments from the content provider to the service. Achieving all this on the scale of a large service provider without bringing significant extra signaling into the network is an important challenge.
• What are the “net-neutrality” implications of sponsored content? The topic is relevant because if a content provider sponsors its content, then the service provider will treat that content differently than the content of other content providers. Hence, the service provider would not be treating the content of all content providers in an identical manner which is required under some definitions of network neutrality.

10.1.2 Previous Work

Networks that allow the option of content provider pricing were studied in References 2 and 3. The first paper considers a network utility maximization (NUM) setting where both the content provider and the EU have a utility and we wish to set prices at both end points and route traffic so that the aggregate utility minus the cost of the network is maximized. This setup was considered for both an Internet Service Provider (ISP) in a competitive market where the prices are determined by the market as well as a monopolistic ISP that has complete freedom to set prices. The second paper [3] considers a model where there is one local ISP for the content provider and one local ISP for the EUs. Two mechanisms are studied in this setting. In the first, there is no collusion and each ISP tries to selfishly maximize profit. In the second, a Nashbargaining solution is used to determine the profit division between the two ISPs.

There have also been a number of studies motivated by the question of network neutrality and some of these are related to the concept of sponsored content. In Reference 4, Economides and Hermalin consider a situation where the service provider partitions bandwidth and charges content providers for access to a given bandwidth partition. Conditions are presented for which a single partition is welfare maximizing. Mitra and Wang [5] study a model where the service provider maintains two pipes that can be accessed by content providers: a best-effort pipe and a managed bandwidth pipe that provides improved quality for an additional fee. In this setting, the service provider optimizes over the amount of best-effort bandwidth and the price of managed bandwidth. A key feature of this model is that when new applications enter the market, they typically rely on the best-effort pipe and so the rate of new service generation critically depends on the amount of best-effort bandwidth that is available. Lastly, in Reference 6, Njoroge et al. consider a model where each service provider controls access to a certain subset of EUs. Moreover, each service provider can charge a content provider for access to “its” consumers. The paper describes a setting in which this nonneutral regime can drive higher investment and, hence, maximize social welfare.

As already discussed, much of the focus of this chapter relates to how contracts should be designed between a content provider and a service provider. Similar issues of contract design have been discussed in a different context in the marketing discipline under the banner of “channel coordination” [7] and have been widely addressed in the supply chain literature (e.g., see Reference 8 for review). More recent work in References 9 and 3 has started the consideration of coordinating contracts in the network setting. Our paper fits closely with this stream of thoughts. In particular, our contracting arrangement is equivalent to the stylized buyback contract discussed in both References 7 and 8.

10.1.3 Designing Contracts Under Uncertain Demand

As already discussed, the focus of our presentation is on designing contracts between the service provider and content provider so that there is a win–win–win for all parties in the system (including the EUs). By this, we mean that all parties are better off than if the content was not sponsored. Our model differs from the prior models discussed earlier in that the underlying demand from the end users is uncertain. It is not simply a function of price and user/content provider utility. (In addition, the NUM model of Reference 2 assumes strictly concave utility functions as a consequence of demand being elastic with respect to price and, hence, does not capture a natural situation where the content provider is paid a fixed price per view by advertisers.) Lastly, our model extends beyond simple per-byte pricing and attempts to capture the notion of EU quotadynamics.

The fact that we treat underlying demand as a random variable has two effects on our analysis. First, the problem faced by the content provider is similar to the “Newsvendor” problem that is common in supply chain analysis. (In a Newsvendor problem, a retailer must purchase inventory to cover uncertain demand over a fixed time period. When the time period is over, the inventory only has a salvage value that is well below the purchasing price.) In our setting, the Newsvendor problem arises because the content provider must decide how much content to sponsor in a time period without knowing what the EU demand is. Second, the uncertain demand coupled with a reservation fee paid in advance will allow the service provider to control how much content is sponsored by the content provider, even when the latter's revenue grows in proportion to the number of views of its content.

We model the interaction between the service and the content providers as a Stackelberg game in which the service provider offers a contract parameterized by two fixed fees: a reservation fee proportional to the maximum number of views to be sponsored and a usage fee for each sponsored view that actually takes place. By accepting this contract, the content provider determines the maximum number of sponsored views and pays the corresponding reservation fee in advance, and assumes the payment of the usage fee for each view of its content by EUs, up to the aforementioned maximum.

We divide our discussions into two parts that reflect different ways of modeling EU payments.

• In Section 10.2, we present a simple model in which service provider congestion costs, EU bandwidth costs, and the price that the content provider must pay for sponsoring content are all determined on a per-byte basis. A key feature of this model is that the underlying demand from the EUs is a random variable but the service provider would like to control the amount of bandwidth it has to provide.

  We focus on the relationship between the service provider and a single content provider. We show that the aforementioned two-fee contract is incentive compatible: by charging a proper reservation fee, the content provider will be induced to choose the maximum number of sponsored views to optimize the total expected profit of both parties. It is also in the service provider's best interest to charge such a fee to bring about this outcome, because it can then use the per-use fee to transfer the profit to itself. In Section 10.2.5, we present a numerical example to demonstrate how the optimization might work in practice.

• In Section 10.3, we indicate how the results can be adapted for the case of EU quotas. In most current wireless data plans, the EUs pay a certain fee for a fixed quota of data. They do not pay on a byte-by-byte basis. This has a significant effect on the model because it is now much less explicit howmuch EU revenue the service provider is giving up when content is sponsored. In particular, we model an EU quota via a Markov Chain and describe the dynamics of the process according to whether the content is sponsored.

10.1.4 The Models

In this paper, we consider a contractual relationship between a single service provider (SP) and a single content provider (CP) in offering sponsored views of content (e.g., a webpage, an advertisement, or an online video). The situation is formally modeled as a Stackelberg game in which the SP is the leader who sets price parameters of the contract and the CP is the follower who responds by determining the maximum number of views it is willing to sponsor within a fixed period, for example, monthly. The purpose of sponsoring is to raise revenue by increasing the number of views of the said content. To model this effect, we assume EU will always access the said content if it is sponsored and with a smaller probability if it is not.

This problem can be naturally extended to the case of multiple CPs competing for the attentions of the EUs by sponsoring their own content. That situation leads to interesting competitive dynamics between the content providers and we leave its analysis for future work.

We define two basic models. In the first, the EUs pay for bandwidth on a per-byte “pay-as-you-go” basis. In the second model, we aim to capture the more common situation in which EUs pay for bandwidth via monthly quotas.

10.1.4.1 Model of Sponsored Content with Per-Byte End-User Costs

The EUs generate N (a random variable) potential views in a period for content items that for ease of exposition are all assumed to have the same size θ. (It would not be difficult to extend to a situation where θ is the mean size of heterogeneous content.) Let F be the cumulative distribution function of N and let . If the content is sponsored, it is viewed with probability 1. If content is not sponsored, it is viewed with probability . (The parameter q here captures the strategic behavior of the EUs.) Let denote a binomial random variable with trials and success probability q. Then .

The SP charges only the CP for sponsored content and the EUs for nonsponsored content, all on a per-byte basis. As we assume constant size for content, we denoteEUs’ payment per view for nonsponsored content by r. (The fact that an EU does not have to pay this amount for sponsored content is the main reason why the probability (=1) of viewing sponsored content is more than the probability (=q) of viewing nonsponsored content. The CP's decision is denoted by B, defined as the maximum number of views the CP is willing to sponsor. The actual number of sponsored views is, therefore, and the total number of views is . As mentioned earlier, the payment from the CP to the SP is structured as an ex ante reservation fee and an ex post usage fee. We define c to be the reservation fee per view and b to be the usage fee per view. Hence, the total revenue that the SP collects from the CP in a given period is .

It remains to define the advertising revenue earned by CP and the bandwidth cost incurred by SP. We assume that CP earns revenue a for each view and, hence, its total revenue is . (We assume that all parameters are known by the SP and leave the interesting case where a and q are private information of the CP for future work.) The cost for the SP is dependent on the total congestion on its network, which is given by a nondecreasing function . We let be the total load on the network excluding the EU's views of the CP's content. The total load without sponsoring is

and the total load with a sponsoring level of B is

So the expected congestion cost paid by the SP is

10.1

Our goal is to determine the maximum number of views that the CP should sponsor to maximize the total profit of both CP and SP. We also study the fees charged by SP that can induce this outcome.

10.2.1 Content Provider's Problem

We start with the simplest situation in which the reservation fee . Recall that B denotes the maximum number of sponsored views, denotes the (advertising) revenue to the CP of each view, and denotes the usage fee per sponsored view paid by the CP to the SP. The revenue received by the CP is and the cost paid by the CP to the SP is . The net revenue to the CP is

10.2

where , and we have used . Let denote the maximizing value of B for given b. Then if and if . If , the CP's net revenue function becomes a constant, and hence, the CP is indifferent between any choice of . In other words, if the CP does not need to pay a reservation fee in advance for sponsoring but price b is paid for each view of sponsored content, then the CP's optimal choice of is either zero or infinity with a transition point where the CP is indifferent between sponsoring any content or not.

Now, consider the case with a per-unit reservation fee . Then CP's revenue function becomes

10.3

This is a standard Newsvendor model. If , then , that is, the CP will not sponsor any content viewing if the combined reservation and usage fees exceed the additional revenue from advertisement. If N has a continuous distribution function (F has no jumps), then

10.4

In our setting, N is a discrete random variable, so F has jumps, and there may not be a such that Eq. (10.3) holds exactly. On the other hand, N is likely to be an extremely large integer (in our numerical Example, is on the order of ), so Eq. (10.3) will hold almost exactly. In particular, because is defined by

the error we make in assuming that Eq. (10.3) holds is miniscule and will henceforth be ignored.

10.2.2 Service Provider's Problem

First, consider the case with no contract cost (i.e., ) and no revenue from EUs (i.e., ). The SP's revenue from the CP is . The SP pays a congestion cost, given by a function C. Recall that is the “baseline” congestion without the EU, and the congestion cost is given by Eq. (10.1). We remark that congestion cost may not be a convex function of B even if C is linear because is concave.

The SP wants to choose b to maximize

Recall that with , , and with , . Thus the SP wants to choose either b as large as possible subject to , in which case the SP's profit is

or , in which case the SP's profit is .The SP will choose the alternative yielding the higher profit.

Now consider the case with fixed contract cost . The SP's revenue from the CP is . So the SP wants to choose c and b to maximize

Given the relationship from Eq. (10.3), the SP's problem is equivalent to choosing and to maximize

We now consider the optimal b for a given B. Looking at the first-order derivative of the profit function

we conclude that SP wants to set b as high as possible such that . Thus with B fixed, the SP's profit is

so that the optimal profit is attained using given by

Of course, in practice the limit cannot be attained: the SP needs to keep to induce the CP to choose the SP's desired . Thus there is some small such that and , that is, while a positive reservation fee is necessary to induce optimal B, the SP is better off to keep it as low as possible and derive all its profit by setting b as high as possible.

We also remark that because of Eq. (10.3), when finding we must optimize over the support of N. In reality, we would typically wish to restrict the optimization further to between (say) and because otherwise the system would be overly sensitive to the exact values of b and c.

10.2.2.1 Revenue from EUs

Suppose that SP earns revenue from the EUs, that is, where r is the revenue rate. So the SP wants to choose c and b to maximize

If , it is not beneficial for the SP to offer sponsored content option to CP because the additional revenue from CP is not high enough to compensate for the loss in revenues from the EUs . This is the case if content revenues are low (i.e., for low a values) and/or the content is popular (i.e., for high q values).

Now, consider the case with . Similarly as above, the SP's problem is equivalent to choosing B and b to maximize

Checking the derivative with respect to b, we conclude that SP wants to set b as high as possible such that as above. We can again optimize over B, the only difference being the additional term .

10.2.3 A Pareto Analysis of the Two-Parameter Contract

The system performance, that is, the aggregate profit achieved by the SP and the CP, is given by

and the SP takes the following share

Let denote the system optimal number of sponsored views, that is, . The increase of the total expected profit from sponsoring is

and from the system's perspective, sponsoring only makes sense if

From the earlier discussion, we know that the inequality is not satisfied if . However, we remark that even if , sponsored content might not generate sufficient advertising revenue to offset thecombined effect of losing EU revenue and increasing congestion cost. Such situations will be identified by the optimization of when the optimal solution . This will happen if the congestion function increases steeply, for example, if,

where,

is an increasing and convex function of B, in which case for all .

Assume now that . As the system profit is maximized at and the SP's share is increasing with b for any given B (and, hence, CP's share is decreasing with b), a contract is Pareto efficient if and only if . Therefore, Pareto efficient contracts can be characterized by the single parameter where . Under the set of Pareto efficient contracts, any allocation of additional system profit can be possible. The SP's share of profit will have a range of , whereas CP's profit will have a range of . We remark that for CP to achieve profit of , CP needs to negotiate from SP the most favorable per-unit price b such that

When r is small, b that satisfies this equality might be negative.

10.2.4 Summary of the Analysis with a Contract Price c and Additional Revenue from End Users

The findings from the above analysis can be summarized as follows.

• The system performance, that is, the total expected profit for both the SP and the CP, is given by
  

  Optimizing the above determines whether sponsoring should take place.

• Although, as noted above, the system profit function is not necessarily a concave function, finding the system optimal B is not a hard problem given that is defined by one variable.
• Charging a single usage fee b is not enough to enforce a sponsored view to the CP. SP needs to charge a reservation fee c to induce the optimal limit on the sponsored views. By keeping c as low as possible and b as high as possible, the SP transfers all the expected gains from sponsoring to itself.
• Under any coordinating contract, the system profit is maximized (i.e., achieves Pareto optimum of the CP and the SP profits). Moreover, any allocation of additional profits is possible. Such a contract is definitely a win–win–win contract for CP, SP, and EUs.

10.2.5 Numerical Example

We now present a numerical example to illustrate the above concepts. Consider the case of a large CP for which N has a truncated normal distribution with mean views per month. (The distribution is truncated to two standard deviations on each side.) The size of the content θ is 7.416 Mbit and the CP receives $0.0125 profit for each view (before paying any sponsoring charge to the SP). We assume EUs pay at a rate $10/GB for nonsponsored content and so this translates to a cost per view of . For the SP congestion cost, we set the baseline congestion and use a piecewise linear function given by

(This stylized cost function reflects, in a simple manner, the additional costs, such as lost customer good will, of exceeding the nominal system capacity.) We set , that is, an EU is five times as likely to view the content when it is free to them than they are when they have to pay for the bandwidth. In Figures 10.1 and 10.2, we show system profit as a function of B when the standard deviation of the underlying normal distribution is and , respectively. We can see that as the uncertainty in N increases (i.e., the standard deviation increases), the optimal amount of content to sponsor decreases because there is more likelihood that the realization of N will correspond to the steep part of the SP congestion cost curve. We can also see that although the system profit is not concave, it is simple to identify the optimal value of B.

In Figure 10.3, we fix B to its optimal value (in this case, views) for the case that the standard deviation is . We then plot both SP profit and CP profit as a function of b. (Recall that c is then determined from b and B via Eq. (10.3). In particular, as b increases from 0 to , c decreases from to 0.) As b increases, more of the excess system profit generated from the sponsored content is transferred from CP to SP. As a comparison, we also plot the baseline profit for SP and CP that would occur in the case that no content is sponsored (i.e., ).

10.3.1 Case 1: Sponsorship-Insensitive Transition Probabilities

We begin with the case in which the Markov Chain transition probabilities do not change when CP's content is sponsored (i.e., the users simply switch their viewing from another content provider). We can obtain similar conclusions as before with Q playing the role of q. In particular, the CP's expected profit is given by

As in Section 10.2.1, this is again a standard Newsvendor model and so the CP decision leads to a relationship of the form

10.5

The SP choice of b and c is, therefore, equivalent to a choice of b and B so long as . (Once again, therefore, we need in order for the SP to be able to control the system.)

Similar to the per-byte cases, the system profit for a fixed value of B is

Hence, as in the previous model, we can optimize system profit via a univariate optimization over B. Once the optimal value of the B has been obtained, the split between the SP and CP can be controlled by an appropriate choice of b.

10.3.2 Case 2: Sponsorship-Sensitive Transition Probabilities

The above analysis assumed that sponsoring content does not have a material affect on how fast the EUs consume their quota. It just causes the EUs to consume additional bandwidth corresponding to the sponsored content. In reality, of course, the knowledge that the CP's content is sponsored may affect the dynamics of quota usage. In particular, sponsoring may slow the rate at which quota is consumed, thereby lowering the probability that a user has to refill. In this case, the sponsoring of the content is cannibalizing the revenue that the SP obtains from the EUs.

A general analysis of this case is beyond the scope of this chapter. Here we take an initial step in the following by using a simple case to highlight issues involved. In particular, we consider a two-state model as in Figure 10.4. EUs are in state 0 if they have available quota to use and in state 1 if they do not. We define as EUs’ transition rate out of state 0 and assume it is a decreasing function of B, that is, EUs exhaust their quotas more slowly if they get more sponsored bandwidth. Let be the (constant) fraction of EUs who do not refill their quotas, so is EUs’ transition rate into state 1. We also define as the transition rate at which EUs move from state 1 back to state 0 as a result of monthly replenishment of quotas. We assume to be an increasing function of B. As more content is sponsored, those who run out of their quotas will do so later in their monthly cycles, hence, get replenishment sooner and move back to state 0 faster.

Following the above definitions, the steady-state probability for EUs to be in states 0 and 1 are

10.6

Obviously, and () are transition rates and steady-state probabilities, respectively, for the case without sponsorship. Observe that is the rate at which an EU moves from state 1 back to state 0. As more sponsored content results in fewer EUs in state 1, it is natural to assume that and should be such that decreases in B.

As before, we define as the subscription revenue that SP receives from the EUs to pay for their monthly quotas. Define

to be the rate at which EUs refill their quota “early.” For the convenience of discussion, we denote as the probability that EUs access nonsponsored content. Let . Given B, the expected profit of the system is

Compare the above with the case without sponsorship, the difference in profit is

Examining each component in the above,

10.7

is the increase of advertising revenue because of sponsoring, which increases in B, that is, more sponsoring leads to higher advertisement revenue. The incremental cost from sponsoring contents

always increases in B. The change of the refill revenue

10.8

is always negative because from Eq. (10.6),

and the right-hand side decreases in B.

In comparison with Case 1, the additional advertisement revenue in Eq. (10.7) is higher here because increases in B instead of being fixed. This extra reward is accrued by the CP. On the other hand, the last component Eq. (10.8) shows an additional negative profit impact of content sponsoring, the cannibalization of the SP's refill revenue because of slower use of EUs’ quotas. Like the bandwidth cost, this loss of revenue is assumed by the SP. To recoup its loss and share the extra gain, it is in the SP's best interest to require a more demanding transfer payment than that in Case 1 from the CP.