  The aim of this paper is to discuss in some detail the two different quantum
schemes for duopoly problems. We investigate under what conditions one of the
schemes is more reasonable that the other one. Using the Cournot's duopoly
example we show that the current quantum schemes require a slight refinement so
that they output the classical game in a particular case. Then we show how the
amendment changes the way of studying the quantum games with respect to Nash
equilibria. Finally, we define another scheme for the Cournot's duopoly in
terms of quantum computation.
