  We consider Nash-Cournot oligopolistic equilibrium models involving separable
concave cost functions. In contrast to the models with linear and convex cost
functions, in these models a local equilibrium point may not be a global one.
We propose algorithms for finding global and local equilibrium points for the
models having separable concave cost functions. The proposed algorithms use the
convex envelope of a separable concave cost function over boxes to approximate
a concave cost model with an affine cost one. The latter is equivalent to a
strongly convex quadratic program that can be solved efficiently. To obtain
better approximate solutions the algorithms use an adaptive rectangular
bisection which is performed only in the space of concave variables
Computational results on a lot number of randomly generated data show that the
proposed algorithm for global equilibrium point are efficient for the models
with moderate number of concave cost functions while the algorithm for local
equilibrium point can solve efficiently the models with much larger size.
