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Feasible Joint Posterior Beliefs

Arieli, Itai and Babichenko, Yakov and Sandomirskiy, Fedor and Tamuz, Omer (2020) Feasible Joint Posterior Beliefs. . (Unpublished)

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We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related "no trade" condition likewise provides a characterization of feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Tamuz, Omer0000-0002-0111-0418
Additional Information:This paper greatly benefited from multiple suggestions and comments of our colleagues. We are grateful (in alphabetic order) to Kim Border, Laura Doval, Sergiu Hart, Kevin He, Yuval Heller, Matthew Jackson, Benny Moldovanu, Jeffrey Mensch, Alexander Nesterov, Michael Ostrovsky, Thomas Palfrey, Luciano Pomatto, Marco Scarsini, Gabriel Ziegler, and seminar participants at HSE St. Petersburg, Bar-Ilan Univeristy, Caltech, and Stanford MS&E. Itai Arieli is supported by the Ministry of Science and Technology (#2028255). Yakov Babichenko is supported by a BSF award (#2018397). Fedor Sandomirskiy is partially supported by the Lady Davis Foundation, by Grant 19-01-00762 of the Russian Foundation for Basic Research, by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (#740435), and by the Basic Research Program of the National Research University Higher School of Economics. Omer Tamuz is supported by a grant from the Simons Foundation (#419427) and by a BSF award (#2018397).
Funding AgencyGrant Number
Ministry of Science and Technology (Israel)2028255
Binational Science Foundation (USA-Israel)2018397
Lady Davis FoundationUNSPECIFIED
Russian Foundation for Basic Research19-01-00762
European Research Council (ERC)740435
National Research University Higher School of EconomicsUNSPECIFIED
Simons Foundation419427
Record Number:CaltechAUTHORS:20200615-155012317
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103930
Deposited By: Tony Diaz
Deposited On:15 Jun 2020 23:00
Last Modified:15 Jun 2020 23:00

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