Competition in Prices and Service Level Guarantees

34 Pages Posted: 15 Oct 2007

See all articles by Ramesh Johari

Ramesh Johari

Stanford University

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University; Columbia University - Columbia Business School - Decision Risk and Operations

Date Written: September 2007

Abstract

In this paper we study the implications of service level guarantees (SLGs) in a model of oligopoly competition where providers compete to deliver a service to congestion-sensitive consumers. The SLG is a contractual obligation on the part of the service provider: regardless of how many customers subscribe, the firm is responsible for investing in infrastructure, capacity, or service quality so that the congestion experienced by all subscribers is equal to the SLG. First, we analyze a game where firms compete by setting prices and SLGs simultaneously. We establish that this game can be reduced to standard oligopoly models of price competition, greatly simplifying the analysis of this otherwise complex competitive scenario. Notably, we find that when costs in the original game are convex, the resulting equivalent pricing game also has convex costs. Further, for a broad class of models exhibiting constant returns to investment, the resulting pricing game is equivalent to a standard price game with constant marginal costs; many loss systems, such as those modeled by the Erlang loss formula, exhibit constant returns to investment. We then consider another commonly used contractual agreement between firms and customers: firms first set prices and investment levels simultaneously, and then consumers choose where to subscribe. In this case, firms provide the best possible service given their infrastructure, but without an explicit guarantee. Using the Nash equilibria of the games played by firms, we compare this competitive model with the model where firms set prices and SLGs, in terms of the resulting prices, service levels, firms' profits, and consumers' surplus.

Keywords: Competition, game theory, congestion, contracting, pricing

JEL Classification: D43, L13, L96, M21

Suggested Citation

Johari, Ramesh and Weintraub, Gabriel Y., Competition in Prices and Service Level Guarantees (September 2007). NET Institute Working Paper No. 07-21. Available at SSRN: https://ssrn.com/abstract=1021449 or http://dx.doi.org/10.2139/ssrn.1021449

Ramesh Johari (Contact Author)

Stanford University ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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