Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses

Annamaria Barbagallo () and Paolo Mauro
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Annamaria Barbagallo: University of Naples “Federico II”
Paolo Mauro: University of Catania

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 16, 288-314

Abstract: Abstract The paper is devoted to generalize a previous model of the dynamic oligopolistic market equilibrium problem allowing the presence of production excesses and assuming, in a more reasonable way that the total amounts of commodity shipments from a firm to all the demand markets be upper bounded. First, we give equilibrium conditions in terms of the well-known dynamic Cournot–Nash equilibrium principle. Then we show that such conditions can be expressed in terms of Lagrange multipliers; namely, by means of an utility function, prove that both equilibrium conditions can be equivalently expressed by a variational inequality. The variational formulation allows us to provide existence theorems and qualitative properties for equilibrium solutions. At last, a numerical example illustrates the results obtained.

Keywords: Dynamic oligopolistic market equilibrium problem; Production excess; Dynamic Cournot–Nash equilibrium; Evolutionary variational inequality; Lagrange variables; Assumption S (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10957-012-0056-z

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