Profit Sharing in a Closed Content Market

Abstract

Many media industries can be characterized as a closed content market in which only subscribers of the distribution network operator (Network Provider [NP]) have access to the content provided by a content provider (CP). In these markets, the NP frequently charges the CP for providing billing and connectivity services to potential customers. Due to this carriage payment, the closed content market has structural similarity to the coalitional form game. Consequently, concepts of superadditivity, the core, and the Shapley value can be applied to determine what constitutes a sustainable and fair share of the CP's profit that could be paid to the NP as a carriage payment. This article addresses issues concerning the existence of the sustainable and fair profit allocation in a closed content market like the one described previously.

Notes

This assumption ignores the possibility that the NP and the CP might advertise content to audiences outside the NP's existing subscribers. However, this article focuses on understanding the impact of the profit sharing scheme, not the content advertisement strategy. Thus, the model does not consider this possibility of advertisement outside the NP's existing consumers. Alternatively, one can imagine a closed content market that is stable due to market saturation, and so forth. Then, the possibility of outside advertisement will not affect results of this article significantly.

The expressions for the network and content demands of (1) and (2) need a careful interpretation. In this article, it is assumed that the network service demand of (1) includes consumers’demand for the “right to access” the CP's content. To fully justify this assumption, (1) needs to be a function of also the CP's price, pC. This interpretation issue is critical for two reasons. First, in making the NP's pricing decision, the NP needs to factor in the pricing decision of the CP not only due to the sharing contract, but also due to this option for accessing the content. Although such cross-price interaction is not explicitly incorporated in this article's model, the reader should be aware of such possibility in the real world environment. Second, the assumption of inclusion of “right of access” in the network demand is critical in the context of the network neutrality issue mentioned in the Introduction section. By assuming that the network service demand inherently includes the right of access to content, the Internet ISP s’ recent claim for the right to discriminate among online content providers loses much of its force. An extension of this article to discuss the network neutrality issue in these regards is currently under development.

Alternatively, one might envision a situation in which one player (say, the NP) sets both pN and pC and this player pays the other player (say, the CP) a fixed amount of compensation, say, T. Such an arrangement will maximize the sum of both players’profits since it enables the NP to internalize the CP's profit. In addition, a calibration of T can render the resulting profit allocation fair and sustainable. In practice we tend not to observe compensation schemes of this nature. A possible explanation is that a compensation scheme independent of the partner's profit size requires an estimation of this player's profit potential before the contract setup, which is also a frequent source of dispute.

Because content costs are assumed not to vary with the number of content subscribers and there are no other content-related variable costs, this fairly standard assumption of a concave profit function rules out certain commonly-used demand functions, such as a unit elastic demand function, for which revenue at some point does not begin to decline as unit sales increase.

Price reaction functions can be derived from first-order optimality conditions such as (11) and (12). For example, the price reaction function of the NP in response to changes in the CP's pricing decision can be derived by rearranging (11) so that a network pricing decision is expressed as a function of the content price level.

For a review of coalitional form games, including concepts of superadditivity, the core and the Shapley value, see, for example, Eichberger (1993).

For this particular model of a two-player game environment, superadditivity is ensured if the sum of profits for the two players is largest when they form an alliance. The superadditivity property of this model allows the application of the core and the Shapley value concepts for further analysis.

Thus, any profit allocation that belongs to the core has a property that all alliance members are better off compared to their profit levels prior to the alliance. Consequently, the alliance is “sustainable.”

This condition, the so-called Inada condition (Inada, 1964), is an assumption frequently made by economists. I am grateful to referees of JME for pointing out the necessity of the Inada condition for establishing Theorem 1.

The Shapley value concept derives a particular fair allocation outcome deduced from a set of desirable requirements (axioms) that an outcome of a bargaining process should possess. An alternative approach of specifying the details of the bargaining process also yields the same allocation outcome in our context in which case a formulation of this context as a coalitional form game is not necessary. As a hybrid approach, Nash (1953) suggested that any axiomatic approach to predict an outcome of a bargaining process be accompanied by a bargaining procedure that yields the same outcome. For expositional simplicity and the modeling consistency, this article adopts the Shapley value approach without an accompaniment of a description of the bargaining process.

Intuitively, this 50–50 split rule is more compelling with the bargaining process approach discussed in Footnote 9. This context's bargaining procedure proceeds with alternating offerings of a sharing proportion between two players and two rational players will realize that, without evidence of asymmetric contributions to the generation of the total profit, they will be better off by settling down with half of the additional joint profits created jointly than not.

Profit Possibility Frontier in our context is a range of profit combinations among industry players that are achievable through adjustment of actual proportion of profit transfer. For more information on the PPF, see, for example, Schmalensee (1987).