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Refinements of Nash Equilibrium


  • Govindan, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)


This paper describes ways that the definition of an equilibrium among players' strategies in a game can be sharpened by invoking additional criteria derived from decision theory. Refinements of John Nash's 1950 definition aim primarily to distinguish equilibria in which implicit commitments are credible due to incentives. One group of refinements requires sequential rationality as the game progresses. Another ensures credibility by considering perturbed games in which every contingency occurs with positive probability, which has the further advantage of excluding weakly dominated strategies.

Suggested Citation

  • Govindan, Srihari & Wilson, Robert B., 2005. "Refinements of Nash Equilibrium," Research Papers 1897, Stanford University, Graduate School of Business.
  • Handle: RePEc:ecl:stabus:1897

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    References listed on IDEAS

    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
    3. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October.
    4. Drew Fudenberg & David M. Kreps & David K. Levine, 2008. "On the Robustness of Equilibrium Refinements," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 5, pages 67-93 World Scientific Publishing Co. Pte. Ltd..
    5. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    6. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
    7. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
    8. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 179-221.
    9. 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.
    10. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    11. 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.
    12. 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. Lupia, Arthur & Levine, Adam Seth & Zharinova, Natasha, 2008. "When Should Political Scientists Use the Self-Confirming Equilibrium Concept? Benefits, Costs, and an Application to Jury Theorems," MPRA Paper 8643, University Library of Munich, Germany.
    2. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.

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