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Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games

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  • Eibelshäuser, Steffen
  • Poensgen, David

Abstract

We formally define Markov quantal response equilibrium (QRE) and prove existence for all finite discounted dynamic stochastic games. The special case of logit Markov QRE constitutes a mapping from precision parameter ... to sets of logit Markov QRE. The limiting points of this correspondence are shown to be Markov perfect equilibria. Furthermore, the logit Markov QRE correspondence can be given a homotopy interpretation. We prove that for all games, this homotopy contains a branch connecting the unique solution at ...to a unique limiting Markov perfect equilibrium. This result can be leveraged both for the computation of Markov perfect equilibria, and also as a selection criterion.

Suggested Citation

  • Eibelshäuser, Steffen & Poensgen, David, 2019. "Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203603, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc19:203603
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    References listed on IDEAS

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    Cited by:

    1. Li, Peixuan & Dang, Chuangyin & Herings, P.J.J., 2023. "Computing Perfect Stationary Equilibria in Stochastic Games," Discussion Paper 2023-006, Tilburg University, Center for Economic Research.
    2. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.

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    More about this item

    Keywords

    Homotopy continuation; Stationary equilibrium; Logit choice;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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