Value of Information in Social Learning
Hiroto Sato, Konan Shimizu
TL;DR
This paper develops a social-valued extension of Blackwell's information comparison to sequential social learning with history, introducing a binary relation $\succsim_S$ that ranks information structures by the payoffs they yield to all agents across all decision problems and equilibria. It proves that $\succsim_S$ is strictly stronger than the Blackwell order, and it characterizes when one information structure is socially more valuable than another through a necessary-and-sufficient condition tied to agents' payoffs and equilibria, plus a simple verifiable sufficient condition based on mixtures of full and no information. A key insight is that unbounded private beliefs are necessary for social superiority, and cascades under the less informative structure preclude social dominance. The paper also discusses long-run comparability and the role of equilibrium selection, showing the strong order remains informative but may prevent partial-ordering, and it offers practical criteria for designing information structures to influence herd behavior in social learning settings.
Abstract
This study extends Blackwell's (1953) comparison of information to a sequential social learning model, where agents make decisions sequentially based on both private signals and the observed actions of others. In this context, we introduce a new binary relation over information structures: an information structure is more socially valuable than another if it yields higher expected payoffs for all agents, regardless of their preferences. First, we establish that this binary relation is strictly stronger than the Blackwell order. Then, we provide a necessary and sufficient condition for our binary relation and propose a simpler sufficient condition that is easier to verify.