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The Algebraic Geometry of Perfect and Sequential Equilibrium

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Author Info
Blume, Lawrence E
Zame, William R

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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.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 62 (1994)
Issue (Month): 4 (July)
Pages: 783-94
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Handle: RePEc:ecm:emetrp:v:62:y:1994:i:4:p:783-94

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Leo K. Simon., 1987. "Basic Timing Games," Economics Working Papers 8745, University of California at Berkeley.
  2. McLennan, Andrew, 1989. "Consistent Conditional Systems in Noncooperative Game Theory," International Journal of Game Theory, Springer, vol. 18(2), pages 141-74.
  3. Roger B. Myerson, 1986. "Axiomatic Foundations of Bayesian Decision Theory," Discussion Papers 671, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  4. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January. [Downloadable!] (restricted)
  5. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  6. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January. [Downloadable!] (restricted)
  7. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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  1. Carlos Pimienta & Cristian Litan, 2008. "Conditions for equivalence between sequentiality and subgame perfection," Economic Theory, Springer, vol. 35(3), pages 539-553, June. [Downloadable!] (restricted)
  2. Eddie Dekel & Drew Fudenberg & David K. Levine, 1999. "Payoff Information and Self-Confirming Equilibrium," Levine's Working Paper Archive 172, UCLA Department of Economics. [Downloadable!]
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  3. Predtetchinski,Arkadi, 2004. "A General Structure Theorem for the Nash Equilibrium Correspondence," Research Memoranda 023, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  4. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, EconWPA, revised 18 Sep 1996. [Downloadable!]
  5. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer, vol. 34(4), pages 561-581, November. [Downloadable!] (restricted)
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  6. Francesco De Sinopoli & Giovanna Iannantuoni, 2003. "On the Generic Strategic Stability of Nash Equilibria if Voting is Costly," CEIS Research Paper 41, Tor Vergata University, CEIS. [Downloadable!]
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  7. Vermeulen,Dries & Jansen,Mathijs, 2004. "On the computation of stable sets for bimatrix games," Research Memoranda 020, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  8. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  9. Carlos Pimienta, 2007. "Generic Finiteness of Outcome Distributions for Two Person Game Forms with Three Outcomes," Discussion Papers 2007-20, School of Economics, The University of New South Wales. [Downloadable!]
  10. Felix Kuber & Karl Schmedders, 2007. "Competitive Equilibria in Semi-Algebraic Economies," PIER Working Paper Archive 07-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  11. Voorneveld, Mark, 2003. "Probabilistic choice in games: properties of Rosenthal's t-solutions," Working Paper Series in Economics and Finance 542, Stockholm School of Economics, revised 31 Oct 2003. [Downloadable!]
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  12. Carlos Pimienta, 2007. "Generic Determinacy of Nash Equilibrium in Network Formation Games," Discussion Papers 2007-31, School of Economics, The University of New South Wales. [Downloadable!]
  13. J. Carlos Gonzalez-Pimienta & Cristian M. Litan, 2005. "On The Equivalence Between Subgame Perfection And Sequentiality," Economics Working Papers we052616, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  14. Borm, P. & Vermeulen, D. & Voorneveld, M., 1998. "The structure of the set of equilibria for two person multicriteria games," Discussion Paper 75, Tilburg University, Center for Economic Research. [Downloadable!]
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  15. Joseph Halpern, 2009. "A nonstandard characterization of sequential equilibrium, perfect equilibrium, and proper equilibrium," International Journal of Game Theory, Springer, vol. 38(1), pages 37-49, March. [Downloadable!] (restricted)
  16. Raymond Wladimir & Mohnen, Pierre & Palm, Franz & Schim, van der Loeff, Sybrand, 2006. "Persistence of Innovation in Dutch Manufacturing: Is it Spurious?," Research Memoranda 009, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  17. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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