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Computing Normal Form Perfect Equilibria for Extensive Two-Person Games

  • Bernhard von Stengel

    ()

    (Department of Mathematics, London School of Economics, Houghton St, London WC2A 2AE, United Kingdom)

  • Antoon van den Elzen

    ()

    (Div. of Humanities and Social Sciences 227-88, California Institute of Technology, Pasadena, CA 91125, U.S.A.)

  • Dolf Talman

    ()

    (Div. of Humanities and Social Sciences 227-88, California Institute of Technology, Pasadena, CA 91125, U.S.A.)

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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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 2 (March)
Pages: 693-715

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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:693-715
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  1. 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.
  2. 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.
  3. Itzhak Gilboa & Eitan Zemel, 1988. "Nash and Correlated Equilibria: Some Complexity Considerations," Discussion Papers 777, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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, March.
  5. Kamiya, K. & Talman, A.J.J., 1990. "Linear stationary point problems," Discussion Paper 1990-22, Tilburg University, Center for Economic Research.
  6. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
  7. Dai, Y. & Talman, A.J.J., 1990. "Linear stationary point problems on unbounded polyhedra," Discussion Paper 1990-67, Tilburg University, Center for Economic Research.
  8. 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.
  9. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
  10. Talman, A.J.J. & van den Elzen, A.H., 1991. "A procedure for finding Nash equilibria in bi-matrix games," Other publications TiSEM 14df3398-1521-43ad-8803-a, 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;Game Theory Society, vol. 25(1), pages 73-92.
  12. 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.
  13. Wilson, Robert, 1992. "Computing Simply Stable Equilibria," Econometrica, Econometric Society, vol. 60(5), pages 1039-70, September.
  14. Robert Wilson, 1972. "Computing Equilibria of Two-Person Games from the Extensive Form," Management Science, INFORMS, vol. 18(7), pages 448-460, March.
  15. Talman, A.J.J. & Dai, Y., 1993. "Linear stationary point problems on unbounded polyhedra," Other publications TiSEM 17e8253b-bf0f-4b64-82fb-7, Tilburg University, School of Economics and Management.
  16. 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.
  17. Selten,Reinhard, 1986. "Evolutionary stability in extensive two-person games correction and further development," Discussion Paper Serie A 70, University of Bonn, Germany.
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