Pricing and dimensioning competing large-scale service providers

The literature on many-server approximations provides significant simplifications toward the optimal capacity sizing of large-scale monopolists, but falls short of providing similar simplifications for a competitive setting in which each firm's decision is affected by its competitors' actions. In this paper, we introduce a framework that combines many-server heavy-traffic analysis with the notion of epsilon-Nash equilibrium and apply it to the study of equilibria in a market with multiple large-scale service providers that compete on both prices and response times. In an analogy to fluid and diffusion approximations for queueing systems, we introduce the notions of fluid game and diffusion game. The proposed framework allows us to provide first-order and second-order characterization results for the equilibria in these markets. We use our results to provide insights into the price and service-level choices in the market and, in particular, into the impact of market scale on the interdependence between these two strategic decisions.