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

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  • McDonald, Stuart
  • Wagner, Liam

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

  • McDonald, Stuart & Wagner, Liam, 2010. "The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing," Risk and Sustainable Management Group Working Papers 151191, University of Queensland, School of Economics.
  • Handle: RePEc:ags:uqsers:151191
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    References listed on IDEAS

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    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, January.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
    8. 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.
    9. 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.
    10. 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.
    11. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    12. 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.
    13. Talman, A.J.J. & Doup, T.M., 1987. "A continuous deformation algorithm on the product space of unit simplices," Other publications TiSEM 0f7c777f-9ae5-4218-b3bd-2, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    Game Theory; Institutional and Behavioral Economics; C72; C73;

    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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