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Stable Outcomes of Generic Games in Extensive Form

Author

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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.

Suggested Citation

  • Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:1933r
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    References listed on IDEAS

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    14. 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.
    15. John Hillas & Mathijs Jansen & Jos Potters & Dries Vermeulen, 2001. "On the Relation Among Some Definitions of Strategic Stability," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 611-635, August.
    16. 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. Srihari Govindan & Robert Wilson, 2006. "Metastable Equilibria," Levine's Bibliography 122247000000001211, UCLA Department of Economics.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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