In this paper, we show that, in markets with a continuum of traders and atoms, the set of Cournot-Walras equilibria and the set of Cournot equilibria may be disjoint. We show also that, when the preferences of the traders are represented by Cobb-Douglas utility functions, the set of Cournot-Walras equilibria and the set of Cournot equilibria have a nonempty intersection.
Codognato, G. (1995). Cournot-walras and Cournot Equilibria in Mixed Markets - a Comparison. Economic Theory, 5(2), 361-370. https://doi.org/10.1007/BF01215210 (Original work published 1995)