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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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  • Srihari Govindan & Robert Wilson, 2006. "Sufficient Conditions for Stable Equilibria," Levine's Bibliography 784828000000000267, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:784828000000000267
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    1. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    2. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    3. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    4. 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.
    5. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    6. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
    7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    Cited by:

    1. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    2. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    3. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    4. Vida, Péter & Honryo, Takakazu, 2021. "Strategic stability of equilibria in multi-sender signaling games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 102-112.
    5. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    6. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    7. Srihari Govindan & Robert Wilson, 2008. "Axiomatic Theory of Equilibrium Selection in Signalling Games with Generic Payoffs," Levine's Working Paper Archive 122247000000002381, David K. Levine.
    8. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    9. Gatti, Nicola & Gilli, Mario & Marchesi, Alberto, 2020. "A characterization of quasi-perfect equilibria," Games and Economic Behavior, Elsevier, vol. 122(C), pages 240-255.
    10. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    11. 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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