On the generic inefficiency of differentiable market games

Abstract

It is shown that a differentiable market game remains generically inefficient when its strategic outcome function is perturbed smoothly. The proof is based on Thom's transversality theorem and removes any restriction regarding the dimension of the strategy spaces. A converse result is that almost all efficient market games that are competitive are characterized by Bertrand-like non-differentiabilities. Finally a synthesis between the Cournot-and-Bertrand-type approaches to Walrasian equilibrium, as recently developed in the literature, is suggested.