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Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses

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  • Annamaria Barbagallo
  • Paolo Mauro

Abstract

The paper is concerned with the variational formulation of the oligopolistic market equilibrium problem in presence of both production and demand excesses. In particular, we generalize a previous model in which the authors, instead, considered only the problem with production excesses, by allowing also the presence of demand excesses. First we examine the equilibrium conditions in terms of the well-known dynamic Cournot-Nash principle. Next, the equilibrium conditions will be expressed in terms of Lagrange multipliers by means of the infinite dimensional duality theory. Then, we show the equivalence between the two conditions that are both expressed by an appropriate evolutionary variational inequality. Moreover, thanks to the variational formulation, some existence and regularity results for equilibrium solutions are proved. At last, a numerical example, which illustrates the features of the problem, is provided.

Suggested Citation

  • Annamaria Barbagallo & Paolo Mauro, 2012. "Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-35, July.
    • Handle: RePEc:hin:jnlaaa:651975
    DOI: 10.1155/2012/651975
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    Cited by:

    1. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2018. "A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 325-354.
    2. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.
    3. Annamaria Barbagallo & Bruno Antonio Pansera & Massimiliano Ferrara, 2024. "Notes on random optimal control equilibrium problem via stochastic inverse variational inequalities," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.

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