Feasible Joint Posterior Beliefs
Abstract
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.
Additional Information
© 2020 Copyright held by the owner/author(s). The 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, Aviad Heifetz, Yuval Heller, Matthew Jackson, Benny Moldovanu, Jeffrey Mensch, Alexander Nesterov, Michael Ostrovsky, Thomas Palfrey, Luciano Pomatto, Marco Scarsini, Eilon Solan, Gabriel Ziegler, and seminar participants at Bar-Ilan Univeristy, Caltech, HSE St. Petersburg, Technion, Stanford, and UC San Diego. 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).Attached Files
Published - 3391403.3399505.pdf
Submitted - 2002.11362.pdf
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Additional details
- Eprint ID
- 103930
- Resolver ID
- CaltechAUTHORS:20200615-155012317
- 2028255
- Ministry of Science and Technology (Israel)
- 2018397
- Binational Science Foundation (USA-Israel)
- Lady Davis Foundation
- 19-01-00762
- Russian Foundation for Basic Research
- 740435
- European Research Council (ERC)
- National Research University Higher School of Economics
- 419427
- Simons Foundation
- 2018397
- Binational Science Foundation (USA-Israel)
- Created
-
2020-06-15Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field