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Computing normal form perfect equilibria for extensive two-person games

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  • Stengel, B. von
  • Elzen, A.H. van den
  • Talman, A.J.J.

    (Tilburg University, Faculty of Economics and Business Administration)

Abstract

This paper presents an algorithm for computing an equilibrium of an extensive two-person game with perfect recall. The method is computationally efficient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear path in the sequence form strategy space from an arbitrary starting vector. If the starting vector represents a pair of completely mixed strategies, then the equilibrium is normal form perfect. Computational experiments compare the sequence form and the reduced normal form, and show that only the sequence form is tractable for larger games. Copyright The Econometric Society 2002.

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Bibliographic Info

Paper provided by Tilburg University, Faculty of Economics and Business Administration in its series Research Memorandum with number 752.

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Date of creation: 1997
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Handle: RePEc:dgr:kubrem:1997752

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Web page: http://www.tilburguniversity.edu/nl/over-tilburg-university/schools/economics-and-management/

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References

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  1. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
  2. Stengel, B. von & Elzen, A.H. van den & Talman, A.J.J., 1997. "Computing normal form perfect equilibria for extensive two-person games," Research Memorandum 752, Tilburg University, Faculty of Economics and Business Administration.
  3. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Wilson, Robert, 1992. "Computing Simply Stable Equilibria," Econometrica, Econometric Society, vol. 60(5), pages 1039-70, September.
  10. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
  11. Kamiya, K. & Talman, D., 1990. "Linear Stationary Point Problems," Papers 9022, Tilburg - Center for Economic Research.
  12. Elzen, A.H. van den & Talman, A.J.J., 1988. "A procedure for finding Nash equilibria in bi-matrix games," Research Memorandum 334, Tilburg University, Faculty of Economics and Business Administration.
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Citations

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Cited by:
  1. F. Forges & B. von Stengel, 2002. "Computionally Efficient Coordination in Games Trees," THEMA Working Papers 2002-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. Yukio KORIYAMA & Matias NUNEZ, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Stuart McDonald & Liam Wagner, 2013. "A Stochastic Search Algorithm for the Computation of Perfect and Proper Equilibria," Discussion Papers Series 480, School of Economics, University of Queensland, Australia.
  5. 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.
  6. Federico Echenique, 2002. "Finding All Equilibria," Levine's Working Paper Archive 506439000000000059, David K. Levine.
  7. 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.
  8. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.

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