Allaz-Vila competition with non-linear costs or demands

If Cournot oligopolists may sell their output prior to its production (forward trading), competition intensifies. Potentially, it may intensify so far as to imply convergence to the Bertrand equilibrium, as shown by Allaz and Vila (1993) for the case of linear demand and costs. The present paper analyzes the limiting outcome if demand or costs are non-linear, which still are open problems. Specifically, I consider a general family of convex demands and increasing marginal costs. In both cases, the limiting outcomes are strictly between Cournot and Bertrand. This shows that competitive futures markets improve welfare (upon Cournot) also for non-linear costs or demands, but they do generally not imply social efficiency.