Can we view the monopolistic competition equilibrium (a la Dixit-Stigliz) as the limit case of a Bertrand competition with an infinite number of firms providing differentiated products, where the resulting equilibrium is a Nash equilibrium in prices?
I am looking for references on this topic. Thanks.
The following paper compares the efficiency of the Bertrand and Cournot game in the case of product differentiation. However, their utility function is more general than the Dixit/Stiglitz case. You also do not have an infinite number of firms competing in each differentiated product but just one firm per differentiated product (the number of differentiated products however may be infinite).
Vives, Xavier. "On the efficiency of Bertrand and Cournot equilibria with product differentation." Journal of Economic Theory 36.1 (1985): 166-175.
