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Using Simulated Annealing to Calculate the Trembles of Trembling Hand Perfection

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  • Stuart, McDonald
  • Liam, Wagner

Abstract

Within the literature on non-cooperative game theory, there have been a number of algorithms which will compute Nash equilibria. This paper shows that the family of algorithms known as Markov chain Monte Carlo (MCMC) can be used to calculate Nash equilibria. MCMC is a type of Monte Carlo simulation that relies on Markov chains to ensure its regularity conditions. MCMC has been widely used throughout the statistics and optimization literature, where variants of this algorithm are known as simulated annealing. This paper shows that there is interesting connection between the trembles that underlie the functioning of this algorithm and the type of Nash refinement known as trembling hand perfection. This paper shows that it is possible to use simulated annealing to compute this refinement.

Suggested Citation

  • Stuart, McDonald & Liam, Wagner, 2003. "Using Simulated Annealing to Calculate the Trembles of Trembling Hand Perfection," MPRA Paper 89127, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:89127
    as

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    File URL: https://mpra.ub.uni-muenchen.de/89127/2/0309016.pdf
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    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
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    Cited by:

    1. Stuart McDonald & Liam Wagner, 2010. "The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing," Risk & Uncertainty Working Papers WPR10_1, Risk and Sustainable Management Group, University of Queensland, revised Apr 2010.
    2. Jasmin Wachter & Stefan Rass & Sandra König, 2018. "Security from the Adversary’s Inertia–Controlling Convergence Speed When Playing Mixed Strategy Equilibria," Games, MDPI, vol. 9(3), pages 1-15, August.

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    More about this item

    Keywords

    Trembling Hand Perfection; Equilibrium Selection and Computation; Simulated Annealing; Markov Chain Monte Carlo;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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