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On dynamic adjustment and comparative statics via the implicit function theorem

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  • Barthel, Anne-Christine
  • Hoffmann, Eric

Abstract

The implicit function theorem (IFT) offers a way of deriving a correspondence between the parameter space and the Nash equilibria of a game. However, which equilibrium will actually emerge after a parameter change involves a dynamic adjustment process, which may significantly differ from IFT predictions. Utilizing the notion of local uniform contraction mappings, we show that IFT predictions are consistent with economic behavior at locally contraction stable equilibria, which is both a necessary and sufficient condition in games of strategic complements. When best response functions are monotone, we can address the convergence of play under more general adaptive dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:115:y:2022:i:c:p:52-57
    DOI: 10.1016/j.mathsocsci.2021.12.004
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    References listed on IDEAS

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    1. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
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    5. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
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