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Published July 2020 | Version Submitted + Published
Book Section - Chapter Open

Feasible Joint Posterior Beliefs

Creators

  • 1. ROR icon Technion – Israel Institute of Technology
  • 2. ROR icon California Institute of Technology

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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2002.11362.pdf

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Additional details

Identifiers

Eprint ID
103930
Resolver ID
CaltechAUTHORS:20200615-155012317

Related works

Describes
https://arxiv.org/abs/2002.11362 (URL)
https://resolver.caltech.edu/CaltechAUTHORS:20210727-175655408 (URL)

Funding

Ministry of Science and Technology (Israel)
2028255
Binational Science Foundation (USA-Israel)
2018397
Lady Davis Foundation
Russian Foundation for Basic Research
19-01-00762
European Research Council (ERC)
740435
National Research University Higher School of Economics
Simons Foundation
419427
Binational Science Foundation (USA-Israel)
2018397

Dates

Created
2020-06-15
Created from EPrint's datestamp field
Updated
2021-11-16
Created from EPrint's last_modified field

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Caltech groups
Mathematics Department