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On Nash-Cournot oligopolistic market equilibrium models with concave cost functions. (English) Zbl 1146.91029
In this paper oligopolistic market equilibrium models are considered, where the cost functions are assumed to be piecewise linear concave. It is shown, that the task, to find a global equilibrium strategy, can be formulated as a mixed variational inequality problem over a bounded rectangle. An equilibrium point need not exist. The authors prove using (upper semicontinuous mappings and) Kakutani’s fixed point theorem conditions, such that an equilibrium point exists and give a decomposition algorithm in order to find a global equilibrium point (if there is one). This method proceeds by dividing the strategy feasible rectangle set into subrectangles, on each of them the cost function is affine. They test their algorithm for more than 20 problems and show, that it is efficient when the number of the firms with concave cost functions is not too big.

MSC:
91B52 Special types of economic equilibria
49J40 Variational inequalities
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