The Folk Theorem in Dynastic Repeated Games

78 Pages Posted: 24 Nov 2004

See all articles by Luca Anderlini

Luca Anderlini

Georgetown University - Department of Economics

Dino Gerardi

Yale University - Cowles Foundation

Roger Lagunoff

Georgetown University - Department of Economics

Date Written: October 2004

Abstract

A canonical interpretation of an infinitely repeated game is that of a dynastic repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players.

In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors.

Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior.

Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players' equilibrium beliefs may violate Inter-Generational Agreement.

Keywords: Dynastic Repeated Games, Private Communication, Folk Theorem

JEL Classification: C72, C73, D82

Suggested Citation

Anderlini, Luca and Gerardi, Dino and Lagunoff, Roger, The Folk Theorem in Dynastic Repeated Games (October 2004). Available at SSRN: https://ssrn.com/abstract=624662

Luca Anderlini

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States
202-687-6361 (Phone)
202-687-6102 (Fax)

HOME PAGE: http://www.georgetown.edu/faculty/la2/

Dino Gerardi (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3562 (Phone)
203-432-5779 (Fax)

Roger Lagunoff

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States
202-687-1510 (Phone)
202-687-6102 (Fax)