Fear of Discrimination: Net Neutrality and Product Differentiation on the Internet

Xingyi Liu

doi:10.1515/rne-2017-0010

Abstract

We study the impact of net neutrality on the content market with endogenous product differentiation. We show that when the Internet service provider is allowed to offer different connection qualities to content providers, it has incentives to favor contents that have a broader market feature. This biases content providers towards choosing those broader products, which may result in too little product differentiation in the content market. By eliminating the possibility of discrimination, net neutrality can reduce such distortion in the content market, and induce more efficient product choices. Net neutrality also raises social welfare if the extent of discrimination is relatively small compared to the extent of product differentiation.

Keywords: Net Neutrality; Product Differentiation; Quality Discrimination

JEL Classification: D4; L1; L52; L86

Acknowledgments

I am especially grateful to Patrick Rey and Wilfried Sand-Zantman for their encouragement and guidance. I wish to thank Jacques Crémer, Pedro Pereira, Florian Englmaier, Jan Krämer, Régis Renault, Mike Riordan and participants in conferences and seminars at London, Leuven, Munich, Toulouse and Würzburg, for their comments and suggestions. All remaining errors are mine.

Appendix: Omitted Proofs

1 Proof of Proposition 1

When two CPs choose the same design s, the profit function of the ISP with a discrimination policy δ≥0 (due to symmetry, it suffices to consider δ≥0) is given by

(5)π0δ=p⋅[1−F(p−δ; s)F(p+δ; s)]

Keeping p fixed, differentiating with respect to δ yields

(6)∂π0δ(δ)∂δ=p(f(p−δ; s)F(p+δ; s)−f(p+δ; s)F(p−δ; s)).

Therefore, ∂π0δ(δ)/∂δ=0 at δ=0; and ∂π0δ(δ)/∂δ>0 for δ>0 if

fF(p−δ; s)>fF(p+δ; s),

which is satisfied when F(v; s) is log-concave in v.

When two CPs choose different designs, say s₁<s₂, we first show that the profit is higher when the ISP favors CP₁ than when it chooses a neutral network. The profit of the ISP is

π0δ=p(1−F(p−δ; s1)F(p+δ; s2))

If δ=0, the network is neutral; if δ>0, the ISP favors CP₁. Fix p, take FOC w.r.t. δ,

∂π0δ∂δ=p(f(p−δ; s1)F(p+δ; s2)−f(p+δ; s2)F(p−δ; s1))sign{∂π0δ∂δ}=sign{fF(p−δ; s1)−fF(p+δ; s2)}

If F(v; s) satisfies both log-concavity and log-submodularity, we have

fF(p−δ; s1)>fF(p−δ; s2)>fF(p+δ; s2) for all δ∈[0, Δ]

Thus, we have ∂π0δ/∂δ>0 for all δ∈[0, Δ]. Therefore, the ISP prefers a maximum discriminatory network which favors CP₁ to a neutral network.

Then we show that a discriminatory network favoring CP₁ is preferred to a network favoring CP₂. It suffices to show that for a given p and δ≥0,

F(p−δ; s1)F(p+δ; s2)<F(p+δ; s1)F(p−δ; s2)

which is equivalent to

F(p−δ; s1)F(p−δ; s2)<F(p+δ; s1)F(p+δ; s2)

which in turn is satisfied if F(x; s₁)/F(x; s₂) is increasing in x,

sign{∂F(x; s1)F(x; s2)∂x}=sign{fF(x; s1)−fF(x; s2)}

which is positive when F(v; s) is log-submodular. Thus, favoring CP₁ is better for the ISP than favoring CP₂.

2 Proof of Proposition 2 and Corollary 1

It is easy to show that (s, s) is not an equilibrium for any s>B. Suppose not, at s₁=s₂=s, the ISP will randomly favor one of the two CPs. Then by choosing a design slightly broader s′i=s−ϵ, CP_i induces a negligible change in the total demand from the consumer; however, this slight change of design induces the ISP to favor CP_i with probability 1, and thus CP_i can get a larger share of the demand. Therefore this constitutes a profitable deviation for CP_i.

Thus, the only candidate for pure strategy symmetric equilibrium is (B, B). If both CPs choose the broadest design, each CP is favored by the ISP with the same probability; any CP deviating to a more niche design will be discriminated against for sure. Thus, if there exists an s such that D(B, B)<D^−Δ(s, B), such deviation is profitable, and then no pure strategy symmetric equilibrium exists; on the contrary, if D(B, B)>D^−Δ(s, B) for all s>B, there is no profitable deviation and (B, B) constitutes the only equilibrium.

3 Proof of Proposition 3

For each CP_i, given the price p and the discrimination policy δ, its profit is πiδ(si, sj; p)=mDi(si, sj; δ; p). Thus,

∂πiδ∂si=m∂Di(si, sj; δ; p)∂si.

Notice that ∂D∂si=∂Di∂si+∂Dj∂si, together with |∂Di∂si|≥|∂Dj∂si|, this means that if ∂D∂si>0, we must have ∂Di∂si>0 and vice versa. That is, when a change in s_i increases the profit of the ISP, it also increases the profit of CP_i. From Assumption 2, the profit of ISP is increasing in s_i, and thus the profit of CP_i is also increasing in s_i. Therefore, both CPs will choose design N.

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Supplemental Material:

The online version of this article offers supplementary material (https://doi.org/10.1515/rne-2017-0010).

Published Online: 2017-12-7

Published in Print: 2016-12-20

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Supplementary material

Fear of Discrimination: Net Neutrality and Product Differentiation on the Internet

Abstract

Acknowledgments

Appendix: Omitted Proofs

1 Proof of Proposition 1

2 Proof of Proposition 2 and Corollary 1

3 Proof of Proposition 3

References

Supplemental Material:

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Fear of Discrimination: Net Neutrality and Product Differentiation on the Internet

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Abstract

Acknowledgments

Appendix: Omitted Proofs

1 Proof of Proposition 1

2 Proof of Proposition 2 and Corollary 1

3 Proof of Proposition 3

References

Supplemental Material:

Supplementary Material

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