Common Learning

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Common Learning

Author Info

Martin W. Cripps
Jeffrey C. Ely
George J. Mailath
Larry Samuelson

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Abstract

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case. Copyright Copyright 2008 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 76 (2008)
Issue (Month): 4 (07)
Pages: 909-933
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:ecm:emetrp:v:76:y:2008:i:4:p:909-933

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Paper
- Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006. "Common Learning," Levine's Bibliography 321307000000000355, UCLA Department of Economics. [Downloadable!]
- Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006. "Common Learning," Cowles Foundation Discussion Papers 1575, Cowles Foundation, Yale University. [Downloadable!]
- Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006. "Common Learning," Cowles Foundation Discussion Papers 1575R, Cowles Foundation, Yale University, revised Jun 2007. [Downloadable!]
- Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2007. "Common Learning," PIER Working Paper Archive 07-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]

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.:

Stephen Morris, 1999. "Approximate common knowledge revisited," International Journal of Game Theory, Springer, vol. 28(3), pages 385-408. [Downloadable!] (restricted)
Other versions:
- Stephen Morris, . "Approximate Common Knowledge Revisited," Penn CARESS Working Papers 6be11f49fbded40b2a623aebf, Penn Economics Department. [Downloadable!]
- Stephen Morris, . ""Approximate Common Knowledge Revisited''," CARESS Working Papres 96-06, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences. [Downloadable!]
- Morris, S., 1999. "Approximate Common Knowledge Revisited," Papers 987r, Yale - Economic Growth Center.
Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Other versions:
- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto. [Downloadable!]
Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June. [Downloadable!] (restricted)
Martin Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 122247000000000086, UCLA Department of Economics. [Downloadable!]
Other versions:
- Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," PIER Working Paper Archive 04-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
- Martin W. Cripps & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," PIER Working Paper Archive 04-031, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2004. [Downloadable!]
- Martin W. Cripps & George J. Mailath & Larry Samuelson, 2006. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 321307000000000152, UCLA Department of Economics. [Downloadable!]
- Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May. [Downloadable!] (restricted)
Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July. [Downloadable!] (restricted)
Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September. [Downloadable!] (restricted)
Other versions:
- Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, 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.)

Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," ESE Discussion Papers 184, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
Other versions:
- Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Working Papers tecipa-330, University of Toronto, Department of Economics. [Downloadable!]
Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Other versions:
- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto. [Downloadable!]
Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," Working Papers tecipa-301, University of Toronto, Department of Economics. [Downloadable!]
Other versions:
- Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," ESE Discussion Papers 175, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
- Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," FMG Discussion Papers dp600, Financial Markets Group. [Downloadable!] (restricted)

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