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Stable Outcomes of Generic Games in Extensive Form

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Author Info
Govindan, Srihari (U of Iowa)
Wilson, Robert B. (Stanford U)

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

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  1. 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. [Downloadable!] (restricted)
  2. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November. [Downloadable!] (restricted)
  3. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06. [Downloadable!] (restricted)
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  4. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Govindan, Srihari & Wilson, Robert B., 2007. "Metastable Equilibria," Research Papers 1934r, Stanford University, Graduate School of Business. [Downloadable!]
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  6. Srihari Govindan & Robert Wilson, 2006. "Essential Equilibria," Levine's Bibliography 122247000000001035, UCLA Department of Economics. [Downloadable!]
  7. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
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  12. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June. [Downloadable!] (restricted)
  13. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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