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The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing

Author

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  • Stuart McDonald

    (Department of Economics, University of Queensland)

  • Liam Wagner

    (Department of Economics, University of Queensland)

Abstract

This paper exploits an analogy between the “trembles” that underlie the functioning of simulated annealing and the player “trembles” that underlie the Nash refinements known as perfect and proper equilibrium. This paper shows that this relationship can be used to provide a method for computing perfect and proper equilibria of n-player strategic games. This paper also shows, by example, that simulated annealing can be used to locate a perfect equilibrium in an extensive form game.

Suggested Citation

  • 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.
    • Handle: RePEc:rsm:riskun:r10_1
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    File URL: http://www.uq.edu.au/rsmg/WP/WPR10_1.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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    3. Koller, Daphne & Megiddo, Nimrod, 1996. "Finding Mixed Strategies with Small Supports in Extensive Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 73-92.
    4. Doup, T.M. & Talman, A.J.J., 1984. "A new variable dimension simplicial algorithm to find equilibria on the product space of unit simplices," Research Memorandum FEW 146, Tilburg University, School of Economics and Management.
    5. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    6. van den Elzen, A.H. & Talman, A.J.J., 1988. "A procedure for finding Nash equilibria in bi-matrix games," Other publications TiSEM 580d39b9-a174-4eaa-842a-d, Tilburg University, School of Economics and Management.
    7. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
    8. Doup, T.M. & Talman, A.J.J., 1985. "A continuous deformation algorithm on the product space of unit simplices," Research Memorandum FEW 168, Tilburg University, School of Economics and Management.
    9. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    10. G. van der Laan & A. J. J. Talman, 1982. "On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 1-13, February.
    11. Doup, T.M. & Talman, A.J.J., 1987. "A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices," Other publications TiSEM 398740e7-fdc2-41b6-968f-4, Tilburg University, School of Economics and Management.
    12. Talman, A.J.J. & van der Laan, G., 1979. "A restart algorithm for computing fixed points without an extra dimension," Other publications TiSEM 1f2102f8-e6da-4e9c-a2ed-9, Tilburg University, School of Economics and Management.
    13. Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June.
    14. Stuart, McDonald & Liam, Wagner, 2003. "Using Simulated Annealing to Calculate the Trembles of Trembling Hand Perfection," MPRA Paper 89127, University Library of Munich, Germany.
    15. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142, Elsevier.
    16. Stuart McDonald, 2002. "Using Simulated Annealing to Compute the Trembles of Trembling Hand Perfection," Computing in Economics and Finance 2002 220, Society for Computational Economics.
    17. van den Elzen, Antoon & Talman, Dolf, 1999. "An Algorithmic Approach toward the Tracing Procedure for Bi-matrix Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 130-145, July.
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    Cited by:

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    2. 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.

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    More about this item

    Keywords

    Game Theory;

    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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