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On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games

Author

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  • John Hillas

    (SUNY at Stony Brook)

Abstract

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not true. An example of a normal form game is given in which there is an equilibrium that is quasi-perfect in any extensive form game having a given normal form but not proper.

Suggested Citation

  • John Hillas, 1996. "On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games," Game Theory and Information 9605002, University Library of Munich, Germany, revised 14 May 1996.
    • Handle: RePEc:wpa:wuwpga:9605002
    Note: Type of Document - AMSLaTeX2e; prepared on IBM PC - emTeX; to print on PostScript; pages: 1 + 9 ; figures: included
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. MERTENS, Jean-François, 1989. "Stable equilibria - a reformulation. Part I. Definition and basic properties," LIDAM Reprints CORE 866, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mailath, George J. & Samuelson, Larry & Swinkels, Jeroen M., 1997. "How Proper Is Sequential Equilibrium?," Games and Economic Behavior, Elsevier, vol. 18(2), pages 193-218, February.
    4. MERTENS, Jean-François, 1991. "Stable equilibria - a reformulation. Part II. Discussion of the definition, and further results," LIDAM Reprints CORE 960, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.

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    More about this item

    Keywords

    perfect equilibrium; quasi-perfect equilibrium; proper equilibrium; strategicý equilibrium.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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