Market structure and technological progress, a differential games approach 

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The benchmark: Net neutrality

In this section we set as benchmark the net neutrality regime where the content provider does not participate on the investment process. The timing of the game is as follows (1) Investment, quality of service levels {αi, αj } are set by access providers non-cooperatively (2) Access competition, access prices {pi, pj } are fixed by access providers non-cooperatively.
In this regime, the content provider plays a passive role in the game. There is no relation between the network operators and the content provider, there are no fees for content access nor fees for network usage, and all decisions are made by access providers only. However the content still generates advertising profits as a consequence of global connectivity.
Access competition The solution concept is sub-game perfect Nash equilibria. Given qualities {αi, αj } set at stage (1), provider ISPi sets at stage (2) his price pi, taking pj as given, to maximize his profits 1 max πi = pi 1 − γ2 (αi − pi − γ(αj − pj )) − I(αi) pi. The first order condition gives rise to the following reaction function Rip(pj ) = 12 (αi − γ (αj − pj )). Notice that when γ is small ISPi can price consumers proportionally to the quality he sets, but when γ increases price competition in the access market intensifies and prices adjust to the rival’s offer. Solving the system of reaction functions there exists a unique price equilibrium given by: p∗ = p(α , α ) ≡ 1 − γ α + γ (α i − α ) (1.1)
2 − γ 4−γ2 i i j i j.
This prices are the equilibria as long as qualities are sufficiently close such that both operators are active in the market and as long as operators make positive profits.10 Equilibrium prices at this stage are determined by two factors. The first one accounts for the direct effect that the access provider’s quality of service has on consumers and the second one accounts for the quality difference with its rival. Remark that the quality difference has a bigger impact on prices as access by both providers become more sub-stitutes. Further, given that quality costs are fixed and do not depend on consumption levels, equilibrium prices do not depend on the investment cost of quality. At equilibrium, network operators’ profits from access to content depend on their qualities only πi = π(αi, αj ) ≡ p(αi, αj )q ((αi, p(αi, αj )), (αj , p(αj , αi))) − I(αi).

No Regulation

With no regulation, the content provider can participate on the investment process. The investment stage of the game is subdivided in two periods (1) Investment. The content provider CP proposes to negotiate an investment agree-ment over the terms of a quality level αi and a fixed monetary transfer Ti to either:
– Both access providers, having simultaneous contracts
– One access provider only, where CP enters into a quality exclusive agreement
– None of them, and access providers invest by their own means, as in the net neutrality regime (2) Access competition. access prices {pi, pj } for consumers are fixed non-cooperatively by ISPi and ISPj .
Given that the transfer fee T negotiated in stage (1.2) is fixed, it does not impact prices set by access providers in stage (2). So the access price equilibrium is the same as in the net neutrality regime, as in equation (1.1). Total profits for the providers are profits from content access or advertising at the agreed quality levels plus or minus the agreed monetary transfer: Πi = Π(αi, αj ; Ti) ≡ π(αi, αj ) + Ti, Πc(αi, αj ; Ti, Tj ) ≡ πc(αi, αj ) − Ti − Tj If there is no agreement Ti = 0 and the quality αi is set unilaterally by the access provider. The outcome of the negotiation process between the content provider and access providers is taken to be the Nash equilibrium of simultaneous generalized Nash bargain-ing problems.

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Simultaneous contracts

Suppose that CP has decided to negotiate with both access providers, and that both access providers decide to enter into negotiation.
Bargaining framework There are four assumptions that determine the solution of the bargaining process. First, as it is usual in the literature of vertical relations for its tractability, the model supposes that negotiations between the pair {CP , ISP1} and the pair {CP , ISP2} occur simultaneously.11 The equilibrium concept that is used is somehow close to the contract equilibrium first formalized by Cr´emer and Riordan (1987). This means that at equilibrium, the contract agreed by the pair {CP , ISPi} must be immune to unilateral deviations. Second, the solution supposes that contracts negotiated are not contingent on rival pair’s disagreement.12 This means that the bargaining pair {CP , ISPi} cannot implement a contract that specifies another outcome if the bargaining process of the other pair {CP , ISPj } has failed. Third, as a consequence of the last-mile control property, the model supposes that the outside option αi for the access provider ISPi is a best response to the other pair’s agreed quality αj . This assumption implies that the equilibrium outcome is sub-game perfect. And finally, the model supposes that access providers are completely symmetric, this means that the content provider has the same exogenous bargaining power β ∈ (0, 1) with respect to each one of them. Having this said, the program that the pair {CP , ISPi} solves in this simultaneous setting taking the rival pair’s contract {αj∗, Tj∗} as given is

Table of contents :

Acknowledgements
General presentation
Introduction
Network Neutrality
Next generation access networks
Technological progress
1 Bargaining power and the net neutrality debate 
1.1 Introduction
1.2 The Model
1.3 The benchmark: Net neutrality
1.4 No Regulation
1.5 Competition policy implication
1.6 Extensions
1.7 Discussion
1.8 Appendix: Proofs of Propositions
2 Investment with commitment contracts: the role of uncertainty 
2.1 Introduction
2.2 The model
2.3 Benchmark: Perfect information
2.4 Uncertainty
2.5 Access charge levels and the role of commitment
2.6 Welfare implications
2.7 Conclusion
2.8 Appendix: Proofs of Propositions
2.9 Appendix: Graphical representation of the game tree
3 Market structure and technological progress, a differential games approach 
3.1 Introduction
3.2 Microeconomic foundations and the static model
3.3 The dynamic model
3.4 Comparative statics analysis
3.5 The time path
3.6 Spillovers
3.7 Discussion
3.8 Appendix: Proofs of propositions
3.9 Appendix: A robustness analysis
Bibliography of the chapter

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