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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.

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Bibliographic 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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  1. 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.
  2. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  3. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  5. Roger B. Myerson, 1986. "Axiomatic Foundations of Bayesian Decision Theory," Discussion Papers 671, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. McLennan, Andrew, 1989. "Consistent Conditional Systems in Noncooperative Game Theory," International Journal of Game Theory, Springer, vol. 18(2), pages 141-74.
  7. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  8. Leo K. Simon., 1987. "Basic Timing Games," Economics Working Papers 8745, University of California at Berkeley.
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