Economic Theory

, Volume 37, Issue 3, pp 357–394 | Cite as

A “Super” Folk Theorem for dynastic repeated games

  • Luca Anderlini
  • Dino Gerardi
  • Roger Lagunoff
Research Article


We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.”


Dynastic repeated games Private communication Social memory Folk theorem 

JEL Classification

C72 C73 D82 


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  1. 1.
    Abreu D., Dutta P.K. and Smith L. (1994). The folk theorem for repeated games: a neu condition. Econometrica 62: 939–948 CrossRefGoogle Scholar
  2. 2.
    Aliprantis C.D., Camera G. and Puzzello D. (2007). Anonymous markets and monetary trading. J Monet Econ 54: 1905–1928 CrossRefGoogle Scholar
  3. 3.
    Aliprantis C.D., Camera G. and Puzzello D. (2007). Contagion equilibria in a monetary model. Econometrica 75: 277–282 CrossRefGoogle Scholar
  4. 4.
    Anderlini, L., Gerardi, D., Lagunoff, R.: Social memory and evidence from the past. Mimeo (2007)Google Scholar
  5. 5.
    Anderlini, L., Gerardi, D., Lagunoff, R.: A ‘Super’ Folk Theorem in dynastic repeated games. Mimeo, Georgetown University and the Cowles Foundation Discussion Paper No 1490. (2005)
  6. 6.
    Anderlini L. and Lagunoff R. (2005). Communication in dynastic repeated games: ‘whitewashes’ and ‘coverups’. Econ Theory 26: 265–299 CrossRefGoogle Scholar
  7. 7.
    Ben-Porath E. and Kahneman M. (1996). Communication in repeated games with private monitoring. J EconTheory 70: 281–297 Google Scholar
  8. 8.
    Bergin J. (2006). The folk theorem revisited. Econ Theory 27: 321–332 CrossRefGoogle Scholar
  9. 9.
    Bhaskar V. (1998). Informational constraints and the overlapping generations model: folk and anti-folk theorems. Rev Econ Studies 65: 135–149 CrossRefGoogle Scholar
  10. 10.
    Chaudhuri A., Schotter A. and Sopher B. (2001). Talking ourselves to efficiency: coordination in inter- generational minimum games with private, almost common and common knowledge of advice. New York University, Mimeo Google Scholar
  11. 11.
    Compte O. (1998). Communication in repeated games with imperfect private monitoring. Econometrica 66: 597–626 CrossRefGoogle Scholar
  12. 12.
    Corbae D., Temzelides T. and Wright R. (2001). Endogenous matching and money. Univeristy of Pennsylvania, Mimeo Google Scholar
  13. 13.
    Cremer J. (1986). Cooperation in ongoing organizations. Q J Econ 101: 33–49 CrossRefGoogle Scholar
  14. 14.
    Ellison G. (1994). Cooperation in the Prisoner’s dilemma with anonymous random matching. Rev Econ Stud 61: 567–588 CrossRefGoogle Scholar
  15. 15.
    Farrell J. (1993). Meaning and credibility in cheap talk games. Games Econ Behav 5: 514–531 CrossRefGoogle Scholar
  16. 16.
    Fudenberg D. and Maskin E.S. (1986). The Folk theorem in repeated games with discounting or with incomplete information. Econometrica 54: 533–556 CrossRefGoogle Scholar
  17. 17.
    Games and Economic Behavior.: Special Issue on Imperfect Recall, vol. 20, no. 1. New-York: Academic (1997)Google Scholar
  18. 18.
    Johnson P., Levine D.K. and Pesendorfer W. (2001). Evolution and information in a gift giving game. J Econ Theory 100: 1–22 CrossRefGoogle Scholar
  19. 19.
    Kandori M. (1992). Repeated games played by overlapping generations of players. Rev Econ Studies 59: 81–92 CrossRefGoogle Scholar
  20. 20.
    Kandori M. (1992). Social norms and community enforcement. Rev Econ Stud 59: 63–80 CrossRefGoogle Scholar
  21. 21.
    Kandori M. and Matsushima H. (1998). Private Observation, communication and collusion. Econometrica 66: 627–652 CrossRefGoogle Scholar
  22. 22.
    Kobayashi H. (2003). Folk Theorem for Infinitely Repeated Games Played by Organizations with Short-Lived Members. Osaka Prefecture University, mimeo Google Scholar
  23. 23.
    Kocherlakota N. (1998). Money is memory. J Econ Theory 81: 232–251 CrossRefGoogle Scholar
  24. 24.
    Kocherlakota N. and Wallace N. (1998). Incomplete record keeping and optimal payout arrangements. J Econ Theory 81: 272–289 CrossRefGoogle Scholar
  25. 25.
    Kreps D.M. and Wilson R. (1982). Sequential equilibria. Econometrica 50: 863–894 CrossRefGoogle Scholar
  26. 26.
    Lagunoff R. and Matsui A. (2004). Organizations and overlapping generations games: memory, communication and altruism. Rev Econ Design 8: 383–411 CrossRefGoogle Scholar
  27. 27.
    Mailath, G.J., Samuelson, L.: Repeated Games and Reputations: long-run relationships. Oxford: Oxford University Press (2006, forthcoming)Google Scholar
  28. 28.
    Maskin E.S. (1999). Nash equilibrium and welfare optimality. Rev Econ Studies 66: 23–38 CrossRefGoogle Scholar
  29. 29.
    Mattehws S., Okuno-Fujiwara M. and Postlewaite A. (1991). Refining cheap-talk equilibria. J Econ Theory 55: 247–273 CrossRefGoogle Scholar
  30. 30.
    Piccione M. and Rubinstein A. (1997). On the interpretation of decision problems with imperfect recall. Games Econ Behav 20: 3–24 CrossRefGoogle Scholar
  31. 31.
    Salant D. (1991). A repeated game with finitely lived overlapping generations of players. Games Econ Behav 3: 244–259 CrossRefGoogle Scholar
  32. 32.
    Schotter A. and Sopher B. (2001). Advice and behavior in intergenerational ultimatum games: an experimental approach. New York University, Mimeo Google Scholar
  33. 33.
    Schotter A. and Sopher B. (2001). Social lerning and coordination conventions in inter-generational games: an experimental study. New York University, Mimeo Google Scholar
  34. 34.
    Smith L. (1992). Folk theorems in overlapping generations games. Games Econ Behav 4: 426–449 CrossRefGoogle Scholar
  35. 35.
    Wallace N. (2001). Whither monetary economics?. Int Econ Rev 42: 847–869 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of EconomicsGeorgetown UniversityWashingtonUSA
  2. 2.Department of EconomicsYale UniversityNew HavenUSA

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