Endogenous Capacities and Price Competition: The Role of Demand Uncertainty

Abstract

This paper analyzes a model of capacity choice followed by price competition under demand uncertainty. Under various assumptions regarding the nature and timing of demand realizations, we obtain general predictions concerning the role of demand uncertainty on equilibrium outcomes. We show that it reduces the multiplicity of equilibria, it may rule out the existence of symmetric equilibria, and it leads to endogenous capacity asymmetries even though firms are ex-ante symmetric. Furthermore, as compared to the certainty equivalent game, demand uncertainty reduces prices and increases consumer surplus, but it also decreases total welfare because of the emergence of idle capacity. By relying on the analysis of firms' reaction functions as well as on the theory of submodular games, we are able to show that a subgame perfect equilibrium always exists and to fully characterize it.

Keywords: Demand uncertainty, investment, price competition, submodular game

JEL Classification: D43, D80, L11