Approximate Bertrand Equilibria in a Replicated Industry

Abstract

This paper considers the existence and properties of approximate Bertrand equilibria in a replicated industry. Price setting firms produce a homogeneous product with weakly convex costs. The main results are that: (a) Given ɛ > 0, an ɛ -equilibrium exists if the industry is large enough; (b) If the ɛ is small enough, and the industry large enough, any ɛ -equilibrium is approximately competitive. These results depend on how contingent demand is specified.