TY - JOUR
T1 - A population's feasible posterior beliefs
AU - Arieli, Itai
AU - Babichenko, Yakov
N1 - Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2024/1
Y1 - 2024/1
N2 - We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We characterize which distributions over the empirical distribution of posterior beliefs in the population are feasible. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.
AB - We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We characterize which distributions over the empirical distribution of posterior beliefs in the population are feasible. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.
KW - Bayesian persuasion
KW - Empirical distributions of posteriors
KW - Feasible posterior distribution
KW - Polarization
UR - http://www.scopus.com/inward/record.url?scp=85178341517&partnerID=8YFLogxK
U2 - 10.1016/j.jet.2023.105764
DO - 10.1016/j.jet.2023.105764
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AN - SCOPUS:85178341517
SN - 0022-0531
VL - 215
JO - Journal of Economic Theory
JF - Journal of Economic Theory
M1 - 105764
ER -