The Limits of Discrete Time Repeated Games:Some Notes and Comments
AbstractThis paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.
Download InfoIf 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.
Bibliographic InfoPaper provided by Universitat Rovira i Virgili, Department of Economics in its series Working Papers with number 2072/203171.
Date of creation: 2012
Date of revision:
Teoria de jocs; Incertesa -- Models matemàtics; Contractes -- Aspectes econòmics; 33 - Economia;
Find related papers by JEL classification:
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
- D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-11 (All new papers)
- NEP-GTH-2012-11-11 (Game Theory)
- NEP-MIC-2012-11-11 (Microeconomics)
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.:
- Drew Fudenberg & Yuhta Ishii & Scott Duke Kominers, 2012. "Delayed-Response Strategies in Repeated Games with Observation Lags," Levine's Working Paper Archive 786969000000000390, David K. Levine.
- Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
- 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.
- Drew Fudenberg & David K Levine, 2007.
"Continuous Time Limits of Repeated Games with Imperfect Public Monitoring,"
Levine's Working Paper Archive
699152000000000028, David K. Levine.
- Drew Fudenberg & David Levine, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 173-192, April.
- Fudenberg, Drew & Levine, David, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Scholarly Articles 3196334, Harvard University Department of Economics.
- Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
- Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
- Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
- Fudenberg, Drew & Levine, David, 2009.
"Repeated Games with Frequent Signals,"
3160491, Harvard University Department of Economics.
- Kawamori, Tomohiko, 2004. "Uncertainty of time intervals and possibility of collusion in infinitely repeated games," Economics Letters, Elsevier, vol. 83(3), pages 355-358, June.
- Yuliy Sannikov & Andrzej Skrzypacz, 2010.
"The Role of Information in Repeated Games With Frequent Actions,"
Econometric Society, vol. 78(3), pages 847-882, 05.
- Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers 871, Society for Economic Dynamics.
- Yuliy Sannikov & Andrzej Skrzypacz, 2007.
"Impossibility of Collusion under Imperfect Monitoring with Flexible Production,"
American Economic Review,
American Economic Association, vol. 97(5), pages 1794-1823, December.
- Yuliy Sannikov & Andrzej Skrzypacz, 2004. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," 2004 Meeting Papers 418, Society for Economic Dynamics.
- Skrzypacz, Andrzej & Sannikov, Yuliy, 2005. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," Research Papers 1887, Stanford University, Graduate School of Business.
- Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, 09.
- Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals-super-," The Quarterly Journal of Economics, MIT Press, vol. 124(1), pages 233-265, February.
- Green, Edward J. & Porter, Robert H., 1982.
"Noncooperative Collusion Under Imperfect Price Information,"
367, California Institute of Technology, Division of the Humanities and Social Sciences.
- Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, 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.
- Fudenberg, Drew & Olszewski, Wojciech, 2011. "Repeated games with asynchronous monitoring of an imperfect signal," Games and Economic Behavior, Elsevier, vol. 72(1), pages 86-99, May.
- Yasuyuki Miyahara & Tadashi Sekiguchi, 2011. "Finitely Repeated Games with Monitoring Options," Discussion Papers 2011-44, Kobe University, Graduate School of Business Administration.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ariadna Casals).
If references are entirely missing, you can add them using this form.