International Journal of Game Theory

, Volume 43, Issue 2, pp 395–402 | Cite as

On the equivalence between (quasi-)perfect and sequential equilibria

  • Carlos PimientaEmail author
  • Jianfei Shen


We prove the generic equivalence between quasi-perfect equilibrium and sequential equilibrium. Combining this result with Blume and Zame (Econometrica 62:783–794, 1994) shows that perfect, quasi-perfect and sequential equilibrium coincide in generic games.


Backwards induction Perfect equilibrium Quasi-perfect equilibrium Sequential equilibrium Lower-hemicontinuity Upper-hemicontinuity 

JEL Classification




We thank Priscila Man, the associate editor and two anonymous reviewers for thoughtful comments that improved the presentation and content of the paper. Carlos thanks financial support from UNSW ASBRG 2010. Jianfei thanks financial support from Shandong University grants IFYT12071 and 2013HW006. The usual disclaimer applies.


  1. Aliprantis C, Border K (2006) Infinite dimensional analysis: a hitchhiker’s guide. Springer, BerlinGoogle Scholar
  2. Blume L, Zame W (1994) The algebraic geometry of perfect and sequential equilibrium. Econometrica 62(4):783–794CrossRefGoogle Scholar
  3. Bochnak J, Coste M, Roy M (1998) Real algebraic geometry. Springer, BerlinCrossRefGoogle Scholar
  4. Elmes S, Reny J (1994) On the strategic equivalence of extensive form games. J Econ Theory 62(1):1–23CrossRefGoogle Scholar
  5. Govindan S, Wilson R (2006) Sufficient conditions for stable equilibria. Theor Econ 1(2):167–206Google Scholar
  6. Govindan S, Wilson R (2012) Axiomatic equilibrium selection for generic two-player games. Econometrica 80(4):1639–1699CrossRefGoogle Scholar
  7. Hillas J, Kao T, Schiff A (2002) A semi-algebraic proof of the generic equivalence of quasi-perfect and sequential equilibria. University of Auckland, MimeoGoogle Scholar
  8. Kreps D, Wilson R (1982) Sequential equilibria. Econometrica 50:863–894CrossRefGoogle Scholar
  9. Kuhn H (1953) Extensive games and the problem of information. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol 2. Princeton University Press, Princeton, pp 193–216Google Scholar
  10. Mertens J-F (1995) Two examples of strategic equilibrium. Games Econ Behav 8(2):378–388CrossRefGoogle Scholar
  11. Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, CambridgeGoogle Scholar
  12. Reny J (1992) Backward induction, normal form perfection and explicable equilibria. Econometrica 60(3):627–649CrossRefGoogle Scholar
  13. Seidenberg A (1954) A new decision method for elementary algebra. Ann Math 60(2):365–374CrossRefGoogle Scholar
  14. Selten R (1975) Re-examination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4:24–55CrossRefGoogle Scholar
  15. Tarski A (1951) A decision method for elementary algebra and geometry, 2nd edn. University of California Press, BerkeleyGoogle Scholar
  16. Thompson FB (1952) Equivalence of games in extensive form. RAND research, Memorandum 759.Google Scholar
  17. van Damme E (1984) A relation between perfect equilibria in extensive form games and proper equilibria in normal form games. Int J Game Theory 13(1):1–13Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of EconomicsThe University of New South WalesSydneyAustralia
  2. 2.School of EconomicsShandong UniversityJinanChina

Personalised recommendations