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A note on local uniqueness of equilibria: How isolated is a local equilibrium?

Author

Listed:
  • Stefano Matta

    (University of Cagliari)

Abstract

The motivation of this note is to show how singular values affect local uniqueness. More precisely, Theorem 3.1 shows how to construct a neighborhood (a ball) of a regular equilibrium whose diameter represents an estimate of local uniqueness, hence providing a measure of how isolated a (local) unique equilibrium can be. The result, whose relevance in terms of comparative statics is evident, is based on reasonable and natural assumptions and hence is applicable in many different settings, ranging from pure exchange economies to non-cooperative games.

Suggested Citation

  • Stefano Matta, 2023. "A note on local uniqueness of equilibria: How isolated is a local equilibrium?," Economics Bulletin, AccessEcon, vol. 43(3), pages 1389-1394.
    • Handle: RePEc:ebl:ecbull:eb-22-00049
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2023/Volume43/EB-23-V43-I3-P118.pdf
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    References listed on IDEAS

    as
    1. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    2. Andrea Loi & Stefano Matta, 2016. "On the topology of the set of critical equilibria," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(2), pages 107-126, June.
    3. Balasko, Yves, 1978. "Equilibrium analysis and envelope theory," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 153-172, September.
    4. Yves Balasko, 2011. "General Equilibrium Theory of Value," Economics Books, Princeton University Press, edition 1, number 9482.
    5. Loi, Andrea & Matta, Stefano, 2010. "A note on the structural stability of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 591-594, July.
    6. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
    7. Garratt, Rod & Goenka, Aditya, 1995. "Income redistributions without catastrophes," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 441-455.
    8. Balasko, Yves, 1978. "The Transfer Problem and the Theory of Regular Economies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 687-694, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Comparative statics; regularity; singular values; local uniqueness.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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