Characterize the weakly more socially valuable order in social learning

Determine a general characterization and develop simple sufficient conditions for the binary relation "weakly more socially valuable" (denoted \succsim_{W}) between information structures in the sequential social learning model with a binary state space, a common prior, and finite action sets, where homogeneous agents act sequentially, observe predecessors’ actions, and receive i.i.d. private signals drawn from an information structure \pi. Under this relation, \pi \succsim_{W} \pi' means that for any action set A and payoff function u, there exists an equilibrium under \pi in which the ex-ante expected payoffs for all agents are weakly higher than those in any equilibrium under \pi'.

Background

The paper introduces a new social comparison of information structures in a standard sequential social learning model with binary states, where agents act sequentially, observe past actions, and receive i.i.d. private signals. The primary binary relation, denoted \succsim_{S}, requires that one information structure yield weakly higher expected payoffs for all agents in any equilibrium and for any decision problem. The authors show \succsim_{S} is strictly stronger than Blackwell’s order, provide a full characterization, a necessary condition (unbounded beliefs), and a simple sufficient condition based on mixtures of full and no information.

Recognizing that \succsim_{S} is strong and not a partial order due to equilibrium selection issues, the authors introduce a weaker relation \succsim_{W}, which only requires the existence of at least one equilibrium under \pi with payoffs weakly higher than any equilibrium under \pi'. Although they construct examples, they explicitly state that they cannot currently provide a general characterization or a simple sufficient condition for \succsim_{W}, identifying tie-breaking across decision problems as the main obstacle and leaving this extension for future research.