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Evolutionary variational formulation for oligopolistic market equilibrium problems with production excesses. (English) Zbl 1273.91202

The authors describe a time-dependent spatial oligopolistic market model with shipment and storage costs. It is formulated as a dynamic Cournot-Nash equilibrium problem and transformed into an evolutionary variational inequality by taking proper derivatives. The authors give conditions which provide equivalence to optimality conditions and prove existence results under continuity and pseudo-monotonicity assumptions. Some sufficient conditions for continuity of solutions are also obtained. The results are illustrated by a numerical example of an oligopolistic market.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91A22 Evolutionary games
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