Numerical search of equilibrium in Cournot model with $S$-like costs functions

The Cournot model with the linear demand function and $S$-like costs functions given by $3$-degree polynomials is described and reduced to maximization of a single function – the potential. It is shown that this optimization problem may have more than one stationary point. Hence the model may have more than one equilibrium. Methods based on using of concave support functions for search of the potential's stationary points are suggested. Numerical comparing of methods is given. Tab. 1, bibliogr. 30.