Sequential Bayesian Learning with A Self-Interested Coordinator (2305.06793v1)

Abstract: Social learning refers to the process by which networked strategic agents learn an unknown state of the world by observing private state-related signals as well as other agents' actions. In their classic work, Bikhchandani, Hirshleifer and Welch showed that information cascades occur in social learning, in which agents blindly follow others' behavior, and consequently, the actions in a cascade reveal no further information about the state. In this paper, we consider the introduction of an information coordinator to mitigate information cascades. The coordinator commits to a mechanism, which is a contract that agents may choose to accept or not. If an agent enters the mechanism, she pays a fee, and sends a message to the coordinator indicating her private signal (not necessarily truthfully). The coordinator, in turn, suggests an action to the agents according to his knowledge and interest. We study a class of mechanisms that possess properties such as individual rationality for agents (i.e., agents are willing to enter), truth telling, and profit maximization for the coordinator. We prove that the coordinator, without loss of optimality, can adopt a summary-based mechanism that depends on the complete observation history through an appropriate sufficient statistic. Furthermore, we show the existence of a mechanism which strictly improves social welfare, and results in strictly positive profit, so that such a mechanism is acceptable for both agents and the coordinator, and is beneficial to the agent community. Finally, we analyze the performance of this mechanism and show significant gains on both aforementioned metrics.