Controlled Social Learning: Altruism vs. Bias

We introduce a model of controlled sequential social learning in which a planner may pay a cost to adjust the private information structure of agents. The planner may seek to induce correct actions that are consistent with an unknown true state of the world (altruistic planner) or to induce a specific action the planner prefers (biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. This sheds light on practical policy questions, such as how the socially optimal level of ad personalization changes according to current beliefs or how a political campaign may selectively illuminate or obfuscate the winning potential of its candidate among voters. We then prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from the choices they induce in the agents. Even for a planner who has equivalent knowledge to an individual, cannot lie or cherry-pick information, and is fully observable, we demonstrate that it is possible to dramatically influence social welfare in both positive and negative directions.