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Continuity and sensitivity analysis of parameterized Nash games

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  • Zachary Feinstein

    (Stevens Institute of Technology)

Abstract

In this paper we consider continuity of the set of Nash equilibria and approximate Nash equilibria for parameterized games. For parameterized games with unique Nash equilibria, the continuity of this equilibrium mapping is well-known. However, when the equilibria need not be unique, there may exist discontinuities in the equilibrium mapping. Because the parameters of a game need to be estimated in practice, these discontinuities can result in an incorrect understanding of the Nash equilibria and, thus also, the decision-making of the players. The focus of this work is to summarize continuity properties for parameterized Nash equilibria and prove continuity via the approximate Nash game with uniformly continuous objective functions over potentially non-compact strategy spaces. That is, we consider a robust representation for the set of Nash equilibria so that small perturbations in the parameters lead to small changes in the set of Nash equilibria.

Suggested Citation

  • Zachary Feinstein, 2022. "Continuity and sensitivity analysis of parameterized Nash games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 233-249, October.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:2:d:10.1007_s40505-022-00228-0
    DOI: 10.1007/s40505-022-00228-0
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    References listed on IDEAS

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    2. Tathagata Banerjee & Zachary Feinstein, 2019. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," Papers 1910.12130, arXiv.org, revised Feb 2021.
    3. Banerjee, Tathagata & Feinstein, Zachary, 2021. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1147-1160.
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    12. Zachary Feinstein, 2017. "Obligations with Physical Delivery in a Multi-Layered Financial Network," Papers 1702.07936, arXiv.org, revised May 2019.
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    Cited by:

    1. Zachary Feinstein & Niklas Hey & Birgit Rudloff, 2023. "Approximating the set of Nash equilibria for convex games," Papers 2310.04176, arXiv.org, revised Apr 2024.
    2. Natalia Novikova & Irina Pospelova, 2022. "Germeier’s Scalarization for Approximating Solution of Multicriteria Matrix Games," Mathematics, MDPI, vol. 11(1), pages 1-28, December.

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