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.
Volume (Year): 76 (2008)
Issue (Month): 4 (July)
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- Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
- Carlsson, Hans & van Damme, Eric, 1993.
"Global Games and Equilibrium Selection,"
Econometric Society, vol. 61(5), pages 989-1018, September.
- Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
- Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
- Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
- Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
- Stephen Morris, 1999.
"Approximate common knowledge revisited,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 28(3), pages 385-408.
- Stephen Morris, "undated". "Approximate Common Knowledge Revisited," Penn CARESS Working Papers 6be11f49fbded40b2a623aebf, Penn Economics Department.
- Morris, S., 1999. "Approximate Common Knowledge Revisited," Papers 987r, Yale - Economic Growth Center.
- Stephen Morris, "undated". ""Approximate Common Knowledge Revisited''," CARESS Working Papres 96-06, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- 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.
- Cripps,M.W. & Mailath,G.J. & Samuelson,L., 2004. "Disappearing private reputations in long-run relationships," Working papers 5, Wisconsin Madison - Social Systems.
- Martin W. Cripps & George J. Mailath & Larry Samuelson, 2006. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 321307000000000152, UCLA Department of Economics.
- Martin Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 122247000000000086, UCLA Department of Economics.
- 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.
- 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.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
- Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, March. Full references (including those not matched with items on IDEAS)
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