We establish the existence results for the Allaz–Vila [B. Allaz, J.-L. Vila, Cournot competition, forward markets and efficiency, J. Econ. Theory 59 (1993) 1–16] forward market equilibrium model when the M producers have different linear cost functions. We also consider an example with three asymmetric producers. The computational results supplement the conclusion in that the forward trading would increase market efficiency. © 2006 Elsevier B.V. All rights reserved.