The Folk Theorem with Private Monitoring and Uniform Sustainability
This paper investigates infinitely repeated prisoner-dilemma games where the discount factor is less than but close to 1. We assume that monitoring is truly imperfect and truly private, there exist no public signals and no public randomization devices, and players cannot communicate and use only pure strategies. We show that implicit collusion can be sustained by Nash equilibria under a mild condition. We show that the Folk Theorem holds when players' private signals are conditionally independent. These results are permissive, because we require no conditions concerning the accuracy of private signals such as the zero likelihood ratio condition. We also investigate the situation in which players play a Nash equilibrium of a machine game irrespective of their initial states, i.e., they play a uniform equilibrium. We show that there exists a unique payoff vector sustained by a uniform equilibrium, i.e., a unique uniformly sustainable payoff vector, which Pareto-dominates all other uniformly sustainable payoff vectors. We characterize this payoff vector by using the values of the minimum likelihood ratio. We show that this payoff vector is efficient if and only if the zero likelihood ratio condition is satisfied. These positive results hold even if each player has limited knowledge on her opponent's private signal structure. Keywords: Repeated Prisoner-Dilemma Games, Private Monitoring, Conditional Independence, Folk Theorem, Uniform Sustainability, Zero Likelihood Ratio Condition, Limited Knowledge.
|Date of creation:||Jul 2000|
|Date of revision:|
|Contact details of provider:|| Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033|
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
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.:
- Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991.
"Information and Timing in Repeated Partnerships,"
Econometric Society, vol. 59(6), pages 1713-33, November.
- Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
- David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation for Research in Economics, Yale University.
- Jeffrey Ely, 2000.
"A Robust Folk Theorem for the Prisoners' Dilemma,"
Econometric Society World Congress 2000 Contributed Papers
0210, Econometric Society.
- Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994.
"The Folk Theorem with Imperfect Public Information,"
Econometric Society, vol. 62(5), pages 997-1039, September.
- Fudenberg, D. & Levine, D.K. & Maskin, E., 1989. "The Folk Theorem With Inperfect Public Information," Working papers 523, Massachusetts Institute of Technology (MIT), Department of Economics.
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
- Green, Edward J & Porter, Robert H, 1984.
"Noncooperative Collusion under Imperfect Price Information,"
Econometric Society, vol. 52(1), pages 87-100, January.
- Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
- Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matsushima, Hitoshi, 1989. "Efficiency in repeated games with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 48(2), pages 428-442, August.
- Matsushima, Hitoshi, 2001.
"Multimarket Contact, Imperfect Monitoring, and Implicit Collusion,"
Journal of Economic Theory,
Elsevier, vol. 98(1), pages 158-178, May.
- Hitoshi Matsushima, 1998. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," CIRJE F-Series CIRJE-F-24, CIRJE, Faculty of Economics, University of Tokyo.
- Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part II: revelation through communication," Economics Letters, Elsevier, vol. 35(3), pages 257-261, March.
- Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
- Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 57-89.
When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2000cf84. 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: (CIRJE administrative office)
If references are entirely missing, you can add them using this form.