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Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information

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  • Igor Konnov

Abstract

We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a quasi-variational inequality that enables us to establish existence results for the model in different settings. We also describe dynamic processes, which fall into information exchange schemes of the proposed market model. In particular, we propose an iterative solution method for quasi-variational inequalities, which is based on evaluations of the proper market information only in a neighborhood of the current market state without knowledge of the whole feasible set and prove its convergence.

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  • Igor Konnov, 2020. "Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information," Papers 2006.01178, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:2006.01178
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    1. I. V. Konnov, 2019. "Equilibrium formulations of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 137-152, August.
    2. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    3. I. V. Konnov, 2016. "Selective bi-coordinate variations for resource allocation type problems," Computational Optimization and Applications, Springer, vol. 64(3), pages 821-842, July.
    4. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    5. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    6. Elisabetta Allevi & Adriana Gnudi & Igor V. Konnov & Giorgia Oggioni, 2017. "Dynamic Spatial Auction Market Models with General Cost Mappings," Networks and Spatial Economics, Springer, vol. 17(2), pages 367-403, June.
    7. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    8. Igor Konnov, 2009. "Decomposition Approaches for Constrained Spatial Auction Market Problems," Networks and Spatial Economics, Springer, vol. 9(4), pages 505-524, December.
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