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Economic Problems with Constraints: How Efficiency Relates to Equilibrium

Author

Listed:
  • Jacek B. Krawczyk

    (Victoria University of Wellington, Wellington, New Zealand)

  • Mabel Tidball

    (Institut National de Recherche en Agronomie, LAMETA, Montpellier, France)

Abstract

We consider situations, in which socially important goods (like transportation capacity or hospital beds) are supplied by independent economic agents. There is also a regulator that believes that constraining the goods delivery is desirable. The regulator can compute a constrained Pareto-efficient solution to establish optimal output levels for each agent. We suggest that a coupled-constraint equilibrium (also called a “generalized†Nash or “normalized†equilibrium à la Rosen) may be more relevant for market economies than a Pareto-efficient solution. We examine under which conditions the latter can equal the former. We illustrate our findings using a coordination problem, in which the agents’ outputs depend on externalities. It becomes evident that the correspondence between an efficient and equilibrium solutions cannot be complete if the agents’ activities generate both negative and positive externalities at the same time.

Suggested Citation

  • Jacek B. Krawczyk & Mabel Tidball, 2016. "Economic Problems with Constraints: How Efficiency Relates to Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-19, December.
  • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:04:n:s0219198916500110
    DOI: 10.1142/S0219198916500110
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Krawczyk, Jacek B. & Vallée, Thomas, 2010. "Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1813-1835, September.
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    3. J. Contreras & J. B. Krawczyk & J. Zuccollo, 2016. "Economics of collective monitoring: a study of environmentally constrained electricity generators," Computational Management Science, Springer, vol. 13(3), pages 349-369, July.
    4. Dávila, J. & Eeckhout, J., 2008. "Competitive bargaining equilibrium," Journal of Economic Theory, Elsevier, vol. 139(1), pages 269-294, March.
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    6. Krawczyk, Jacek B., 2005. "Coupled constraint Nash equilibria in environmental games," Resource and Energy Economics, Elsevier, vol. 27(2), pages 157-181, June.
    7. Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
    8. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    9. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
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    Cited by:

    1. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.

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    More about this item

    Keywords

    Coupled constraints; generalized Nash equilibrium; Pareto-efficient solution; game engineering;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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