This paper analyzes the effects of direct interconnection agreements in the Internet backbone on content quality investment for content providers (CPs). The model assumes that when the Internet service provider (ISP) has a vertical affiliation with one CP, the ISP directly interconnects the affiliated CP’s traffic to its network for free while collecting a direct interconnection fee from the unaffiliated CP. If the unaffiliated CP’s traffic is indirectly interconnected to the ISP’s network via a third party transit provider, its network quality is lower than that via a direct interconnection. For the CPs’ content quality investments, I find that the affiliated CP invests more in content when the rival indirectly interconnects, leading to a higher total level of content investment. Accordingly, there is a condition under which the ISP does not want to offer direct interconnection to the unaffiliated CP. However, consumers are not always worse off from this interconnection foreclosure. Thus, the regulation of a paid direct interconnection does not necessarily enhance welfare in terms of consumer surplus.
A Further Discussion
A.1 Opportunity Cost of Free Direct Interconnection to
When directly interconnecting the affiliated ’s content, the ISP faces an opportunity cost: if the cost of direct interconnection is high, the ISP might not want to offer free direct interconnection even for . To guarantee that the ISP is incentivized to provide direct interconnection for free to , I assume that the associated cost K is sufficiently low throughout the paper.
Specifically, I consider the case in which ’s content is indirectly interconnected even with its affiliation status. Given that ’s content can be either directly or indirectly interconnected, the equilibrium fee charged to for direct interconnection is different, as follows.
where is the fee charged if is directly (indirectly) interconnected. Assuming that , the set of equilibrium can be derived by the same logic in the main model. From the equilibrium profits for , I first derive the profit difference with and without direct interconnection as follows.
where represents ’s profit difference with and without direct interconnection given that is directly interconnected. Similarly, is the profit difference given that is indirectly interconnected. From Equation (14), the threshold on K below which ’s profit from direct interconnection is greater than another for each case can be derived: if , while if . First, it can be easily shown that by the concavity condition. Thus, the condition guaranteeing that the ISP offers free in-house direct interconnection to is given by , which is assumed to hold throughout the paper.
Additionally, I show that in Proposition 3 is always smaller than : , which can be shown to be positive under the interior solution assumption. Per Proposition 3, if , the ISP wants to offer direct interconnection to at the fee. Given that , whenever is directly interconnected, so is ; thus, symmetric network quality specifications for both CPs emerge in equilibrium. Also, if , which leads to indirect interconnection with , an asymmetric network quality specification (direct interconnection for but the reverse for ) can prevail in equilibrium under . That is, the implication in Proposition 3 still holds with the additional assumption on K.
A.2 Partial Market Coverage
By backward induction, CPs solve their profit maximization problem, considering the Internet market size, or , as given. Using the same logic as in the main analysis, the set of content market equilibrium as a function of S and is derived as follows. Note that is assumed.
Given the content market equilibrium, the ISP solves its joint profit maximization problem to set S as follows.
Both Figures plot how the equilibrium levels change as α increases. For example, the equilibrium Internet subscription fee is higher in the direct interconnection agreement, and the gap between two fees becomes wider as α increases. Similar patterns can be observed from other comparisons.
A.3 Bargaining Power
Denoting the ISP’s bargaining power β where , the equilibrium fee charged to for direct interconnection is given by , where is given in Equation (6). Although the set of equilibrium in the indirect interconnection agreement does not change, that in the direct interconnection agreement is different because the amount of content-specific investment is now a function of β. Assuming that , the equilibria and , where the superscript B denotes the model with bargaining power, are derived as follows.
Comparing to as in Equation (7), it is immediately clear that if . Even if CPs’ investments in content quality increase, the equilibrium for price and market share is the same as in the main model; i.e., two CPs equally split the market by charging the content price of one to consumers because of the symmetry in content quality investment. Additionally, I find the following results.
From Equation (18), it is easy to see that Propositions 1 and 2 still hold in this extension. Given that the set of equilibria in the indirect interconnection agreement does not change, Corollary 1 remains the same. After some algebra, I can also show that Propositions 3 and 4 hold even if the quantitative threshold on K is different from .
For the welfare implications, consumer surplus in the indirect interconnection agreement is the same as before, whereas that in the direct interconnection agreement changes because of β: . From , it can be observed that, as β increases, i.e., as has less advantage in negotiation, consumer surplus from the direct interconnection agreement decreases. From the comparison of and , I find a threshold on α, as in Proposition 5, below which is greater than . The threshold on α, denoted , is given as follows.
It can be verified that , which suggests that, as gains more bargaining power, increases, implying that is more likely to be greater than .
A.4 Multiplicative Utility
From the utility specification, as in Equation (11), the indifferent consumer type is given as follows: . From each CP’s profit maximization problem, the optimal price and market share are derived as follows.
By the same logic as in the main analysis, the equilibrium fee charged to for direct interconnection is derived by as follows:
Assuming that , the set of equilibria is given as follows.
After some algebraic manipulation, I find the following results.
Under the interior solution condition, , and the concavity condition, , Equation (23) shows that Propositions 1 and 2 still hold in this extension. Additionally, the comparison between and also shows that is dominant in terms of market share in the indirect interconnection agreement. From the profit comparison between and , I derive a threshold on K, denoted as , below which wants to offer direct interconnection to , as shown in Proposition 3. The welfare implication also qualitatively holds.
B Proofs of the Propositions
Proof of Lemma 1
First, let ,,, and . It can be shown that
By the conditions in (4) and (5), and . Then, = if either strategic effect is positive, or it is negative but with a small effect compared to the interconnection spillover effect. Similarly, if the strategic effect is negative. If the inequality holds, by the concavity of profit functions, is non-increasing; therefore, and . □
Proof of Proposition 1
From the proof of Lemma 1, it can be shown that where , i.e., and are strategic substitutes. Here, the positive interconnection spillover effect for leads to . This outcome suggests that the strategic effect for is positive, implying that. □
Proof of Proposition 2
It can be shown by the proof of Lemma 1. Also, under the parametric example of, it is readily shown that , which is positive for . □
Proof of Corollary 1
It is obvious from Equation (6) and by Proposition 1 that . □
Proof of Proposition 3
The profit comparison for with and without the direct interconnection agreement is shown as follows.
The threshold is the solution to . Under the parametric example of , the profit comparison for with and without the direct interconnection agreement is shown as follows.
From Equation (26), I find the threshold, denoted , as follows.
Given , it is easy to show that if and vice versa. □
Proof of Proposition 4
Given derived from Equation (25), the comparative statics with respect to α can be simplified by applying the implicit function theorem to and, as defined in the proof of Lemma 1, which is given as follows.
where holds by the concavity condition. Thus, as long as α is sufficiently large, such that , is negative. For instance, under the parametric example, the threshold on K is given as in Equation (27). The comparative statics with respect to α is given as follows.
After some algebraic manipulation, it can be shown that Equation (29) is negative as long as α is larger than . The interior solution condition, i.e., , guarantees that . □
Proof of Proposition 5
Equation (9) can be further simplified as follows.
Under the parametric example of , consumer surplus levels with and without the direct interconnection agreement are derived as follows.
From Equation (31), the difference between the two levels is obtained as follows.
It can be immediately shown that if . Under the interior solution condition, is larger than one, indicating that can prevail in equilibrium if  □
I would like to thank Jay Pil Choi, Thomas Jeitschko, John Wilson, and Aleksandr Yankelevich; and the participants at the Red Cedar Conference at Michigan State University, the Fall 2016 Midwest Economic Theory Conference, and the Eastern Economic Association 2017 Conference. I am also grateful to the editor and two anonymous referees for their constructive comments, which greatly improved this paper.
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