Core Concepts
Learning the true state of the world occurs with probability one in a social network setting where agents only communicate samples from their beliefs, rather than full belief distributions.
Abstract
The paper proposes a framework for social learning where agents only communicate samples from their beliefs, rather than full belief distributions. Each agent's belief is a geometric interpolation between a fully Bayesian private belief and an ensemble of empirical distributions of the actions shared by her neighbors.
Directory:
Introduction and Related Work
Discusses the body of literature on social learning, particularly within the realm of non-Bayesian models.
Highlights the importance of network structure, cognitive constraints, and the flow of information in shaping collective outcomes.
Motivates the question of whether learning with probability one is achievable if agents are only allowed to communicate samples from their beliefs.
Mathematical Model
Describes the information structure, where agents have incomplete, noisy, and heterogeneous sources of information.
Explains the belief update mechanism, where each agent's belief is a geometric interpolation between a Bayesian private belief and an ensemble of empirical distributions of neighbors' actions.
Main Results
Establishes that learning occurs with probability one under the proposed framework, assuming a strongly connected network and a "collective distinguishability" assumption.
Proves the exponential decay of private beliefs on states that are identifiable from the true state.
Derives non-trivial lower and upper bounds on the frequency of agents declaring the true state and other states, respectively.
Leverages these bounds to rigorously show the convergence of all beliefs to the true state with probability one.