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.