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

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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.

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Bibliographic Info

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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Keywords: Game Theory;

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  1. 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.
  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. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  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. 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.
  6. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
  7. Stengel, B. von & Elzen, A.H. van den & Talman, A.J.J., 2002. "Computing normal form perfect equilibria for extensive two-person games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88290, Tilburg University.
  8. 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.
  9. Doup, T.M. & Talman, A.J.J., 1986. "A continuous deformation algorithm on the product space of unit simplices," Research Memorandum 219, Tilburg University, Faculty of Economics and Business Administration.
  10. Talman, A.J.J. & Laan , G. van der, 1982. "On the computation of fixed points on the product space of unit simplices and an application to noncooperative N-person games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153028, Tilburg University.
  11. Talman, A.J.J. & Laan, G. van der, 1979. "A restart algorithm for computing fixed points without an extra dimension," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153012, Tilburg University.
  12. Doup, T.M. & Talman, A.J.J., 1987. "A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices," Open Access publications from Tilburg University urn:nbn:nl:ui:12-148734, Tilburg University.
  13. 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.
  14. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, January.
  15. Talman, A.J.J. & Elzen , A.H. van den, 1991. "A procedure for finding Nash equilibria in bi-matrix games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153117, Tilburg University.
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