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Learning to agree over large state spaces

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  • Michele Crescenzi

Abstract

We study how a consensus emerges in a finite population of like-minded individuals who are asymmetrically informed about the realization of the true state of the world. Agents observe a private signal about the state and then start exchanging messages. Generalizing the classical model of rational dialogues of Geanakoplos and Polemarchakis (1982) and its subsequent extensions, we dispense with the standard assumption that the state space is a probability space and we do not put any bound on the cardinality of the state space itself or the information partitions. We show that a class of rational dialogues can be found that always lead to consensus provided that three main conditions are met. First, everybody must be able to send messages to everybody else, either directly or indirectly. Second, communication must be reciprocal. Finally, agents need to have the opportunity to engage in dialogues of transfinite length.

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  • Michele Crescenzi, 2021. "Learning to agree over large state spaces," Papers 2105.06313, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:2105.06313
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    1. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    2. Giacomo Bonanno & Klaus Nehring, "undated". "Agreeing To Disagree: A Survey," Department of Economics 97-18, California Davis - Department of Economics.
    3. Tsakas, Elias & Voorneveld, Mark, 2011. "On consensus through communication without a commonly known protocol," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 733-739.
    4. Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 1-14, August.
    5. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
    6. Michael Ostrovsky, 2012. "Information Aggregation in Dynamic Markets With Strategic Traders," Econometrica, Econometric Society, vol. 80(6), pages 2595-2647, November.
    7. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    8. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
    9. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
      • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
    10. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
    11. 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.
    12. Bergin, James, 1989. "We eventually agree," Mathematical Social Sciences, Elsevier, vol. 17(1), pages 57-66, February.
    13. ,, 2013. "A general framework for rational learning in social networks," Theoretical Economics, Econometric Society, vol. 8(1), January.
    14. WEYERS , Sonia, 1992. "Three results on communication, information and common knowledge," LIDAM Discussion Papers CORE 1992028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    16. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
    17. Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, vol. 70(1), pages 266-272, July.
    18. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
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