Social learning with questions

In social networks, agents use information from (a) private signals (knowledge) they have, (b) learning past agents actions (observations), and (c) comments from contactable experienced agents (experts) to guide their own decisions. With fully observable history and bounded likelihood ratio of signal, Information Cascade occurs almost surely when it is optimal for agents to ignore their private signals for decision making after observing the history. Though individually optimal, this may lead to a socially sub-optimal outcome. Literature studying social learning, i.e., making socially optimal decisions, is mainly focused on using channels (a) and (b) above for Bayes-rational agents by either relaxing the assumption of bounded signal strength or allowing the distortion of the history. In this work, we enable a limited communication capacity to let Bayes-rational agents querying their predecessors, motivated by the real-world behavior that people usually consult several friends before making decisions. We allow each Bayes-rational agent to ask a single, private and finite-capacity (for response) question of each among a subset of predecessors. Note that the Maximum Aposteriori Probability (MAP) rule is still individually optimally and will be used by each agent for her decision. With an endowed communication capacity, we want to answer the following two questions: 1) What is the suitable framework to model the help that questions provide on information aggregation? 2) Can we construct a set of questions that will achieve learning by querying the minimum set of agents with the minimum capacity requirements (in terms of bits)?