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Sensitivity analysis of boundary equilibria

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  • Alan Beggs

    (Oxford University)

Abstract

This paper studies the sensitivity of economic equilibria to perturbations when the implicit function theorem cannot be applied on account of the presence of boundaries. It presents results from the mathematical programming literature which provide conditions under which equilibria are robust to perturbation and are locally unique Lipschitz continuous functions of parameters. Economic applications include search equilibrium, Cournot equilibrium and general equilibrium.

Suggested Citation

  • Alan Beggs, 2018. "Sensitivity analysis of boundary equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 763-786, October.
    • Handle: RePEc:spr:joecth:v:66:y:2018:i:3:d:10.1007_s00199-016-0987-y
    DOI: 10.1007/s00199-016-0987-y
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967.
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    6. J. M. Bonnisseau & J. Rivera-Cayupi, 2006. "Constrained Consumptions, Lipschitzian Demands, and Regular Economies," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 179-193, November.
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    8. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-1232, July.
    9. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    10. Shu Lu & Stephen M. Robinson, 2008. "Variational Inequalities over Perturbed Polyhedral Convex Sets," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 689-711, August.
    11. Beggs, A.W., 2015. "Regularity and robustness in monotone Bayesian games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 145-158.
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    Cited by:

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    2. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.

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    More about this item

    Keywords

    Sensitivity analysis; Implicit function theorem; Equilibria; Variational inequalities; Boundaries;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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