On the existence of coalition-proof Bertrand equilibrium

Abstract

Bertrand equilibrium with arbitrary sharing rules were provided. Here, sufficient conditions for the existence of a coalition-proof Bertrand equilibrium with an arbitrary tie-breaking rule are provided. A classical Bertrand game in which sellers have convex costs is analyzed and sufficient conditions for the existence of coalition-proof Bertrand equilibrium which admit discontinuities in tied payoffs and a general class of tie-breaking rules are stated. Finally, an example is provided where one of the conditions is violated and there is non-existence of coalition-proof Bertrand equilibrium. This work generalizes an existence result of Chowdhury and Sengupta (Econ Theory 24:307-324, 2004).