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Stable Outcomes of Generic Games in Extensive Form

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  • Govindan, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)

Abstract

We apply Mertens' dedinition of stability for a game in strategic form to a game in extensive form with perfect recall. We prove that if payoffs are generic then the outcomes of stable sets of equilibria defined via homological essentiality by Mertens coincide with those defined via homotopic essentiality. This implies that for such games various definitions of stability in terms of perturbations of players' strategies as in Mertens or best-reply correspondences as in Govindan and Wilson yield the same outcomes. A corollary yields a computational test that usually suffices to identify the stable outcomes of such a game.

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Bibliographic Info

Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1933r.

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Date of creation: May 2007
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Handle: RePEc:ecl:stabus:1933r

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  1. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  2. 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.
  3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  4. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  5. Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-71, March.
  6. 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.
  7. Jean-François Mertens, 2004. "Localization of the degree on lower-dimensional sets," International Journal of Game Theory, Springer, vol. 32(3), pages 379-386, 06.
  8. Govindan, Srihari & Wilson, Robert B., 2007. "Metastable Equilibria," Research Papers 1934r, Stanford University, Graduate School of Business.
  9. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  10. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
  11. Srihari Govindan & Robert Wilson, 2006. "Essential Equilibria," Levine's Bibliography 122247000000001035, UCLA Department of Economics.
  12. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. MERTENS, Jean-François, 1990. "The "small worlds" axiom for stable equilibria," CORE Discussion Papers 1990007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November.
  15. Hillas, John & Kohlberg, Elon, 2002. "Foundations of strategic equilibrium," 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 42, pages 1597-1663 Elsevier.
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Cited by:
  1. Govindan, Srihari & Wilson, Robert B., 2007. "Metastable Equilibria," Research Papers 1934r, Stanford University, Graduate School of Business.

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