IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Purification in the Infinitely-Repeated Prisoners' Dilemma

  • V. Bhaskar

    (University College London)

  • George J. Mailath

    (University of Pennsylvania)

  • Stephen Morris

    (Princeton University)

This paper investigates the Harsanyi (1973)-purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of one-period memory mixed strategy equilibria used by Ely and Valimaki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that any such strategy profile is not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable. (Copyright: Elsevier)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Access to full texts is restricted to ScienceDirect subscribers and institutional members. See for details.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 11 (2008)
Issue (Month): 3 (July)
Pages: 515-528

in new window

Handle: RePEc:red:issued:07-130
Contact details of provider: Postal: Marina Azzimonti, Department of Economics, Stonybrook University, 10 Nicolls Road, Stonybrook NY 11790 USA
Web page:

More information through EDIRC

Order Information: Web: Email:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. V. Bhaskar & Ichiro Obara, 2000. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Econometric Society World Congress 2000 Contributed Papers 1330, Econometric Society.
  2. Bhaskar, V. & van Damme, E.E.C., 2002. "Moral hazard and private monitoring," Other publications TiSEM 432fc615-feb9-4c90-8a14-e, Tilburg University, School of Economics and Management.
  3. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  4. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  5. V Bhaskar & George J. Mailath & Stephen Morris, 2006. "Purification in the Infinitely Repeated Prisoner's Dilemma," Levine's Bibliography 321307000000000170, UCLA Department of Economics.
  6. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  7. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  8. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
  9. repec:oup:restud:v:65:y:1998:i:1:p:135-49 is not listed on IDEAS
  10. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
  11. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
  12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, July.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:red:issued:07-130. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christian Zimmermann)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.