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Variational Inequalities and Networks in the Formulation and Computation of Market Equilibria and Disequilibria: The Case of Direct Demand Functions

Author

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  • Anna Nagurney

    (University of Massachusetts, Amherst, Massachusetts 01003)

  • Lan Zhao

    (State University of New York, College at Old Westbury, Old Westbury, New York 11568-0210)

Abstract

In this paper we introduce competitive spatial market models with direct demand functions, which permit policy interventions in the form of price controls. We derive variational inequality formulations of the governing economic conditions and establish existence and uniqueness results. A decomposition algorithm that exploits the network structure is proposed and convergence results given. The algorithm is then interpreted as an adjustment process to highlight the underlying economic behavior. Finally, numerical results for a variety of problems are presented.

Suggested Citation

  • Anna Nagurney & Lan Zhao, 1993. "Variational Inequalities and Networks in the Formulation and Computation of Market Equilibria and Disequilibria: The Case of Direct Demand Functions," Transportation Science, INFORMS, vol. 27(1), pages 4-15, February.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:1:p:4-15
    DOI: 10.1287/trsc.27.1.4
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    Citations

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    Cited by:

    1. Nagurney, Anna & Ke, Ke, 2006. "Financial networks with intermediation: Risk management with variable weights," European Journal of Operational Research, Elsevier, vol. 172(1), pages 40-63, July.
    2. Nagurney, Anna & Cruz, Jose & Dong, June & Zhang, Ding, 2005. "Supply chain networks, electronic commerce, and supply side and demand side risk," European Journal of Operational Research, Elsevier, vol. 164(1), pages 120-142, July.
    3. Yamada, Tadashi & Imai, Koji & Nakamura, Takamasa & Taniguchi, Eiichi, 2011. "A supply chain-transport supernetwork equilibrium model with the behaviour of freight carriers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 887-907.
    4. Hamdouch, Younes & Ghoudi, Kilani, 2020. "A Supply Chain Equilibrium Model with General Price-Dependent Demand," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Dong, June & Zhang, Ding & Nagurney, Anna, 2004. "A supply chain network equilibrium model with random demands," European Journal of Operational Research, Elsevier, vol. 156(1), pages 194-212, July.
    6. Saberi, Sara, 2018. "Sustainable, multiperiod supply chain network model with freight carrier through reduction in pollution stock," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 421-444.
    7. Nagurney, Anna & Besik, Deniz & Dong, June, 2019. "Tariffs and quotas in world trade: A unified variational inequality framework," European Journal of Operational Research, Elsevier, vol. 275(1), pages 347-360.
    8. June Dong & Ding Zhang & Hong Yan & Anna Nagurney, 2005. "Multitiered Supply Chain Networks: Multicriteria Decision—Making Under Uncertainty," Annals of Operations Research, Springer, vol. 135(1), pages 155-178, March.
    9. Younes Hamdouch & Qiang Patrick Qiang & Kilani Ghoudi, 2017. "A Closed-Loop Supply Chain Equilibrium Model with Random and Price-Sensitive Demand and Return," Networks and Spatial Economics, Springer, vol. 17(2), pages 459-503, June.
    10. Qiang Qiang & Ke Ke & Yihong Hu, 2013. "Financial networks with socially responsible investing," Computational Management Science, Springer, vol. 10(2), pages 231-252, June.
    11. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach," Annals of Operations Research, Springer, vol. 261(1), pages 1-43, February.
    12. Anna Nagurney & Jon Loo & June Dong & Ding Zhang, 2002. "Supply Chain Networks and Electronic Commerce: A Theoretical Perspective," Netnomics, Springer, vol. 4(2), pages 187-220, November.

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