A Strong Anti-Folk Theorem

Original Article


We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. Our second main result is a strong anti-Folk Theorem, since, in contrast to what is described by the Folk Theorem, the set of equilibrium payoffs does not expand when the game is repeated.


Nash equilibrium Complexity Stability Social institutions 


  1. Abreu D, Rubinstein A (1988) The structure of nash equilibrium in repeated games with finite automata. Econometrica 56:1259–1281CrossRefGoogle Scholar
  2. Al-Najjar N, Smorodinsky R (2001) Large nonanonymous repeated games. Games Econ Behav 37:26–39CrossRefGoogle Scholar
  3. Aumann R (1981) Survey of repeated games. In: Essays in game theory and mathematical economics in honor of Oskar Morgenstern. Bibliographisches Institut, MannheimGoogle Scholar
  4. Aumann R, Brandenburger A (1995) Epistemic conditions for Nash equilibrium. Econometrica 63:1161–1180CrossRefGoogle Scholar
  5. Banks J, Sundaram R (1990) Repeated games, finite automata, and complexity. Games Econ Behavio 2:97–117CrossRefGoogle Scholar
  6. Barlo M, Carmona G (2002) Strategic behavior in non-atomic games: a refinement of nash equilibrium. University of Minnesota, Minneapolis Universidade Nova de Lisboa, mimeo, LisboaGoogle Scholar
  7. Carmona G (2002a) Essays on the theory of social institutions, with special emphasis on monetary trading. Ph.D. thesis, University of Minnesota, MinneapolisGoogle Scholar
  8. Carmona G (2002b) Monetary trading: an optimal exchange system. Working Paper 420, Universidade Nova de Lisboa, LisboaGoogle Scholar
  9. Fudenberg D, Maskin E (1986) The Folk Theorem in repeated games with discounting and incomplete information. Econometrica 54:533–554CrossRefGoogle Scholar
  10. Fudenberg D, Tirole J (1991) Game Theory. The MIT Press, CambridgeGoogle Scholar
  11. Green E (1980) Non-cooperative price taking in large dynamic markets. J Econ Theory 22:155–182CrossRefGoogle Scholar
  12. Hopcroft J, Ullman J (1979) Introduction to automata theory, language, and computation. Addison-Wesley, New YorkGoogle Scholar
  13. Jacobsen H (1996) On the foundations of Nash equilibrium. Econ Philos 12:67–88CrossRefGoogle Scholar
  14. Kalai E (1990) Bounded rationality and strategic complexity in repeated games. In: Game theory and applications; Tatsuro Ichiishi AN, Tauman Y, (eds) Academic Press, New YorkGoogle Scholar
  15. Kalai E, Stanford W (1988) Finite rationality and interpersonal complexity in repeated games. Econometrica 56:397–410CrossRefGoogle Scholar
  16. Kandori M (1992) Social Norms and Community Enforcements. Rev Econ Stud 59:63–80CrossRefGoogle Scholar
  17. Lipman B, Srivastava S (1990) Informational requirements and strategic complexity in repeated games. Games Econ Behav 2:273–290CrossRefGoogle Scholar
  18. McCulloch W, Pitts W (1943) A logical calculus for the ideas immanent in nervous activity. Bull Math Biophys 5:115–133CrossRefGoogle Scholar
  19. Nash J (1950) Non-cooperative games. Ph.D. thesis, Princeton University, PrincetonGoogle Scholar
  20. Okuno-Fujiwara M, Postlewaite A (1995) Social norms and random matching games. Games Econ Behav 9:79–109CrossRefGoogle Scholar
  21. Piccione M (1992) Finite automata equilibria with discounting. J Econ Theory 56:180–193CrossRefGoogle Scholar
  22. Rubinstein A (1979) Equilibrium in supergames with the overtaking criterion. J Econ. Theory 21:1–9CrossRefGoogle Scholar
  23. Rubinstein A (1986) Finite automata play the repeated prisoner’s dilemma. J Econ Theory 39:83–96CrossRefGoogle Scholar
  24. Rubinstein A (1998) Modeling bounded rationality. The MIT Press, CambridgeGoogle Scholar
  25. Sabourian H (1990) Anonymous repeated games with a large number of players and random outcomes. J Econ Theory 51:92–110CrossRefGoogle Scholar
  26. Schotter A (1981) The economic theory of social institutions. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  1. 1.Faculdade de Economia, Campus de CampolideUniversidade Nova de LisboaLisboaPortugal

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