Stability of Nash Equilibrium: The Multiproduct Case
Posted: 23 Oct 1996
Date Written: July 1996
Abstract
This paper examines the stability conditions of Cournot-Nash equilibria in models in which each firm produces multiple outputs in m-related markets. Using a discrete adjustment process, we establish sufficient and necessary conditions for stability. We derive further specialized stability conditions for three important cases, namely, multiproduct duopoly, multiproduct oligopoly with homogeneous products, and single-product oligopoly with product heterogeneity. The paper shows that stability conditions of the m-markets individually are in general neither sufficient nor necessary for the stability of the m-markets as a group. In addition, an example is given of how the stability conditions can be applied to determine comparative statistics for multiproduct oligopoly.
JEL Classification: L13
Suggested Citation: Suggested Citation