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

  • Stuart McDonald

    ()

    (Department of Economics, University of Queensland)

  • Liam Wagner

    ()

    (Department of Economics, University of Queensland)

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.

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File URL: http://www.uq.edu.au/rsmg/WP/WPR10_1.pdf
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Paper provided by Risk and Sustainable Management Group, University of Queensland in its series Risk & Uncertainty Working Papers with number WPR10_1.

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Date of creation: Jan 2010
Date of revision: Apr 2010
Handle: RePEc:rsm:riskun:r10_1
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  1. von Stengel, B. & van den Elzen, A.H. & Talman, A.J.J., 1997. "Computing normal form perfect equilibria for extensive two-person games," Research Memorandum 752, Tilburg University, School of Economics and Management.
  2. 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.
  3. 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, June.
  4. 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.
  5. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March.
  6. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Koller, Daphne & Megiddo, Nimrod, 1996. "Finding Mixed Strategies with Small Supports in Extensive Form Games," International Journal of Game Theory, Springer, vol. 25(1), pages 73-92.
  12. von Stengel, B. & van den Elzen, A.H. & Talman, A.J.J., 2002. "Computing normal form perfect equilibria for extensive two-person games," Other publications TiSEM 9f112346-b587-47f3-ad2e-6, Tilburg University, School of Economics and Management.
  13. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
  14. 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.
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