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How Proper Is Sequential Equilibrium?

Author

Listed:
  • Mailath, G.J.
  • Samuelson, L.
Abstract
We show that a strategy profile of a normal form game is proper if and only if it is quasi-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit.

Suggested Citation

  • Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611, Wisconsin Madison - Social Systems.
    • Handle: RePEc:att:wimass:9611
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    References listed on IDEAS

    as
    1. Mailath George J. & Samuelson Larry & Swinkels Jeroen M., 1994. "Normal Form Structures in Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 64(2), pages 325-371, December.
    2. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    3. Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
    4. 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..
    5. 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.
    6. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    8. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1997. "The Loser's Curse and Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 65(6), pages 1247-1282, November.
    9. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    10. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Citations

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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. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    3. Asheim,G.B. & Perea,A., 2000. "Lexicographic probabilities and rationalizability in extensive games," Memorandum 38/2000, Oslo University, Department of Economics.
    4. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    5. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    6. 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.
    7. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    8. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    9. Petri, Henrik, 2020. "Lexicographic probabilities and robustness," Games and Economic Behavior, Elsevier, vol. 122(C), pages 426-439.
    10. John Hillas & Mathijs Jansen & Jos Potters & Dries Vermeulen, 2001. "On the Relation Among Some Definitions of Strategic Stability," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 611-635, August.

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    More about this item

    Keywords

    GAMES; GAME THEORY;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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