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A Strong Correspondence Principle for Smooth, Monotone Environments

Author

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  • Finn Christensen

    (Department of Economics, Towson University)

  • Christopher Cornwell

    (Department of Mathematics, Towson University)

Abstract

In discrete time dynamic systems that are locally monotone, we show that comparative statics are well-behaved if and only if equilibrium is exponentially stable. In addition, subject to boundary conditions but without local monotonicity, we show that the number of equilibria is finite and odd, and if every equilibrium is stable then there is exactly one. The results, which are applied to best response dynamics and adaptive dynamics, expand the scope of the correspondence principle to include a relationship between stability and uniqueness.

Suggested Citation

  • Finn Christensen & Christopher Cornwell, 2016. "A Strong Correspondence Principle for Smooth, Monotone Environments," Working Papers 2016-05, Towson University, Department of Economics, revised Mar 2017.
    • Handle: RePEc:tow:wpaper:2016-05
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    References listed on IDEAS

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    Cited by:

    1. Christensen, Finn, 2017. "A necessary and sufficient condition for a unique maximum with an application to potential games," Economics Letters, Elsevier, vol. 161(C), pages 120-123.
    2. 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.
    3. Barthel, Anne-Christine & Hoffmann, Eric, 2022. "On dynamic adjustment and comparative statics via the implicit function theorem," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 52-57.
    4. Christensen, Finn, 2022. "Streaming Stimulates the Live Concert Industry: Evidence from YouTube," International Journal of Industrial Organization, Elsevier, vol. 85(C).
    5. Finn Christensen, 2023. "Comparative Statics for Difference-in-Differences," Working Papers 2023-08, Towson University, Department of Economics, revised Nov 2023.
    6. 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

    correspondence principle; stability; comparative statics; uniqueness; best response dynamics; adaptive dynamics; M-matrix.;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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