Can we use the term "Cournot Game" to describe a competition with output quantity in general? Or, does "Cournot Game" only refer to the game studied by Cournot? For example, if we study a dynamic competition on output quantity, but with very different price functions and some added constraints, can we say it is a Cournot game?
Similarly, can we use the term "Bertrand Game" to describe a competition with price in general?