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Sufficient Conditions for Stable Equilibria

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  • Srihari Govindan
  • Robert Wilson

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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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000267.

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Date of creation: 03 Mar 2006
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Handle: RePEc:cla:levrem:784828000000000267

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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.
  2. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  4. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  5. Damme, E.E.C. van, 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154427, Tilburg University.
  6. Banks, Jeffrey S. & Sobel, Joel., 1985. "Equilibrium Selection in Signaling Games," Working Papers 565, California Institute of Technology, Division of the Humanities and Social Sciences.
  7. Srihari Govindan & Tilman Klumpp, 2003. "Perfect equilibrium and lexicographic beliefs," International Journal of Game Theory, Springer, vol. 31(2), pages 229-243.
  8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  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.
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Cited by:
  1. Srihari Govindan & Robert Wilson, 2007. "On Forward Induction," Levine's Bibliography 321307000000000788, UCLA Department of Economics.
  2. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, 07.
  3. Govindan, Srihari & Wilson, Robert B., 2007. "Metastable Equilibria," Research Papers 1934r, Stanford University, Graduate School of Business.
  4. Breitmoser, Yves, 2012. "Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma," MPRA Paper 41731, University Library of Munich, Germany.
  5. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
  6. 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.

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