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Sufficient conditions for stable equilibria

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

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Abstract

A refinement of the set of Nash equilibria that satisfies two assumptions is shown to select a subset that is stable in the sense defined by Kohlberg and Mertens. One assumption requires that a selected set is invariant to adjoining redundant strategies and the other is a strong version of backward induction. Backward induction is interpreted as the requirement that each player's strategy is sequentially rational and conditionally admissible at every information set in an extensive-form game with perfect recall, implemented here by requiring that the equilibrium is quasi-perfect. The strong version requires 'truly' quasi-perfection in that each strategy perturbation refines the selection to a quasi-perfect equilibrium in the set. An exact characterization of stable sets is provided for two-player games.

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Publisher Info
Article provided by Society for Economic Theory in its journal Theoretical Economics.

Volume (Year): 1 (2006)
Issue (Month): 2 (June)
Pages: 167-206
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Handle: RePEc:the:publsh:159

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Related research
Keywords: Game theory; equilibrium selection; stability;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
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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. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May. [Downloadable!] (restricted)
  3. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January. [Downloadable!] (restricted)
  4. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  5. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May. [Downloadable!] (restricted)
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  6. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  7. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine. [Downloadable!]
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  2. Govindan, Srihari & Wilson, Robert B., 2008. "Axiomatic Theory of Equilibrium Selection in Signaling Games with Generic Payoffs," Research Papers 2000, Stanford University, Graduate School of Business. [Downloadable!]
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  3. Srihari Govindan & Robert Wilson, 2006. "Metastable Equilibria," Levine's Bibliography 122247000000001211, UCLA Department of Economics. [Downloadable!]
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  4. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business. [Downloadable!]
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