IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v66y2018i3d10.1007_s00199-016-0987-y.html
   My bibliography  Save this article

Sensitivity analysis of boundary equilibria

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-016-0987-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-016-0987-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, January.
    2. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 399-404.
    3. 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.
    4. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 441-463.
    5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    6. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    7. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-1232, July.
    8. Charles D. Kolstad & Lars Mathiesen, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 681-690.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hal:spmain:info:hdl:2441/10287 is not listed on IDEAS
    2. Rabah Amir & Filomena Garcia & Malgorzata Knauff, 2006. "Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities," Working Papers Department of Economics 2006/29, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    3. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    4. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    5. Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1968-1986, September.
    6. Citanna, Alessandro & Cres, Herve & Dreze, Jacques & Herings, P. Jean-Jacques & Villanacci, Antonio, 2001. "Continua of underemployment equilibria reflecting coordination failures, also at Walrasian prices," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 169-200, December.
    7. repec:spo:wpecon:info:hdl:2441/10287 is not listed on IDEAS
    8. Alan Beggs & A.W. Beggs, 2011. "Regularity and Stability in Monotone Bayesian Games," Economics Series Working Papers 587, University of Oxford, Department of Economics.
    9. Christensen, Finn & Cornwell, Christopher R., 2018. "A strong correspondence principle for smooth, monotone environments," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 15-24.
    10. Alessandro Citanna & Herve Cres & Antonio Villanacci, "undated". "Underemployment of resources and self-fulfilling beliefs: Nonwalrasian allocations at walrasian prices," GSIA Working Papers 11, Carnegie Mellon University, Tepper School of Business.
    11. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    12. Beggs, A.W., 2015. "Regularity and robustness in monotone Bayesian games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 145-158.
    13. repec:hal:wpspec:info:hdl:2441/10287 is not listed on IDEAS
    14. Bruinshoofd, W.A. & Letterie, W.A., 2001. "Comovement of sales, retention practice and financing constraints in Dutch manufacturing," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Bill Dupor, 2005. "Keynesian Conundrum: Multiplicity and Time Consistent Stabilization," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(1), pages 154-177, January.
    16. Ennis, Huberto M. & Keister, Todd, 2005. "Government policy and the probability of coordination failures," European Economic Review, Elsevier, vol. 49(4), pages 939-973, May.
    17. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2013. "The empirical content of Cournot competition," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1552-1581.
    18. Cumbul, Eray & Virág, Gábor, 2018. "Multilateral limit pricing in price-setting games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 250-273.
    19. David Bowman, 1995. "Constrained suboptimality in economies with limited communication," International Finance Discussion Papers 497, Board of Governors of the Federal Reserve System (U.S.).
    20. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-533, May.
    21. Krishnendu Ghosh Dastidar & Sugata Marjit, 2022. "Market size, entry costs and free entry Cournot equilibrium," Journal of Economics, Springer, vol. 136(2), pages 97-114, July.
    22. Keiran Sharpe, 2006. "Effective demand in a stylised Keynesian model of growth," Review of Political Economy, Taylor & Francis Journals, vol. 18(2), pages 173-191.
    23. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:66:y:2018:i:3:d:10.1007_s00199-016-0987-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.