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Fixed Points of Parameterized Perturbations

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Abstract

The effect of perturbing a parameter—comparative statics—is, of course, a familiar and important issue in economic analysis. Perfection of a single Nash equilibrium (Selten (1975)) is defined by requiring that at least some perturbations in a given class give rise to perturbed games that have nearby equilibria. Roughly, Kohlberg and Mertens (1986) define strategic stability of a set of equilibria by requiring that for all sufficiently small perturbations, the perturbed games have equilibria near the set. This note presents a topological result concerning the behavior of such nearby equilibria when there is a function from a neighborhood of the relevant set of equilibria to the space of perturbations.

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  • Andrew McLennan, 2014. "Fixed Points of Parameterized Perturbations," Discussion Papers Series 526, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:526
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    File URL: https://economics.uq.edu.au/files/46015/526.pdf
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    1. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    2. McLennan, Andrew, 1989. "Fixed Points of Contractible Valued Correspondences," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 175-184.
    3. Yehuda John Levy & Andrew McLennan, 2015. "Corrigendum to “Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples”," Econometrica, Econometric Society, vol. 83(3), pages 1237-1252, May.
    4. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
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    1. Yehuda John Levy & Andrew McLennan, 2015. "Corrigendum to “Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples”," Econometrica, Econometric Society, vol. 83(3), pages 1237-1252, May.

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