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The Algebraic Geometry of Perfect and Sequential Equilibrium

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  • Blume, Lawrence E
  • Zame, William R

Abstract

Two of the most important refinements of the Nash equilibrium concept for extensive form games are (trembling hand) perfect equilibrium and sequential equilibrium. It is shown here that, for almost all assignments of payoffs to outcomes, the sets of sequential and perfect equilibrium strategy profiles are identical. This result is obtained by exploiting the semialgebraic nature of equilibrium correspondences, following from a deep theorem of mathematical logic. Copyright 1994 by The Econometric Society.

Suggested Citation

  • Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
  • Handle: RePEc:ecm:emetrp:v:62:y:1994:i:4:p:783-94
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Roger B. Myerson, 1986. "Axiomatic Foundations of Bayesian Decision Theory," Discussion Papers 671, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    4. Simon, Leo K., 1987. "Basic Timing Games," Department of Economics, Working Paper Series qt8kt5h29p, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    5. 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..
    6. McLennan, Andrew, 1989. "Consistent Conditional Systems in Noncooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 141-174.
    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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    More about this item

    JEL classification:

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

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