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A Reformulation-Based Simplicial Homotopy Method for Approximating Perfect Equilibria

Author

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  • Yin Chen

    (City University of Hong Kong)

  • Chuangyin Dang

    (City University of Hong Kong)

Abstract

As a strict refinement of Nash equilibrium, the concept of perfect equilibrium was formulated by Selten (Int J Game Theory 4(1):25–55, 1975). A well-known application of this concept is that every perfect equilibrium of the agent normal form game of an extensive form game with perfect recall yields a trembling-hand perfect equilibrium (consequently a sequential equilibrium). To compute a perfect equilibrium, this paper extends Kohlberg and Mertens’s equivalent reformulation of Nash equilibrium to a perturbed game. This extension naturally leads to a homotopy mapping on the Euclidean space. With this homotopy mapping and a triangulation, we develop a simplicial homotopy method for approximating perfect equilibria. It is proved that every limit point of the simplicial path yields a perfect equilibrium. Numerical results further confirm the effectiveness of the method.

Suggested Citation

  • Yin Chen & Chuangyin Dang, 2019. "A Reformulation-Based Simplicial Homotopy Method for Approximating Perfect Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 877-891, October.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:3:d:10.1007_s10614-018-9847-0
    DOI: 10.1007/s10614-018-9847-0
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    References listed on IDEAS

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    Cited by:

    1. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1026-1062, June.
    2. Peixuan Li & Chuangyin Dang & P. Jean-Jacques Herings, 2024. "Computing perfect stationary equilibria in stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 347-387, September.
    3. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.
    4. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.

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    More about this item

    Keywords

    Perfect equilibrium; Nash equilibrium; Equivalent reformulation; Homotopy mapping; Simplicial path-following method;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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