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

Algorithms for finding global and local equilibrium points of Nash-Cournot equilibrium models involving concave cost