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Perfect Quasi-Perfect Equilibrium

Author

Listed:
  • Blume, Larry

    (Cornell University and Institute for Advanced Studies)

  • Meier, Martin

    (University of Bath and Institute for Advanced Studies)

Abstract

In strategic-form games Selten's (1975) perfect equilibria are admissible. This is not true for extensive-form perfection. Quasi-perfect equilibria solves this problem using Selten's (1975) trembles to introduce a refinement of Nash equilibrium wherein each player puts infinitesimal weight on other players's strategies, but not her own. One might be sure of oneself, while (infinitesimally) unsure of others. However, also quasi-perfection itself is not without problems, precisely because it ignores future infinitesimal uncertainties in one's own play. We introduce a refinement; perfect quasi-perfect equilibrium, to capture the best of both concepts. Our idea is to force each player to consider infinitesimal deviations in her own future play, but to make them so unlikely that they are infinitely less likely than the combined likelihood of deviations by all other players. Our refinement uses only strategies that are neither weakly dominated in the strategic form nor in the agent normal form.

Suggested Citation

  • Blume, Larry & Meier, Martin, 2019. "Perfect Quasi-Perfect Equilibrium," IHS Working Paper Series 4, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihswps:4
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    File URL: https://irihs.ihs.ac.at/id/eprint/4970/
    File Function: First version, 2019
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    References listed on IDEAS

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    1. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
    2. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
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    Cited by:

    1. Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).

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