Multi-Objective Learning: A Unifying Framework for Collaboration, Fairness, and Robustness

We study a communication game between a sender and receiver where the sender has access to a set of informative signals about a state of the world. The sender chooses one of her signals and communicates it to the receiver. We call this an “anecdote.” The receiver takes an action. The state of the world and the receiver action are payoff relevant for both the sender and receiver. The sender and receiver are also influenced by a personal preference so that, fixing the state of the world, their preferred receiver action differs. We characterize perfect Bayesian equilibria of this game. The sender faces a temptation to persuade: she is tempted to select a more biased anecdote to influence the receiver’s action. Anecdotes are still informative to the receiver (who will debias at equilibrium) but the attempt to persuade comes at the cost of precision. This gives rise to “informational homophily” where the receiver prefers to listen to like minded senders because they provide higher-precision signals. Furthermore, this leads to a cost of informedness – fixing the personal preferences of the sender, the receiver may prefer a less-informed sender to a more-informed one for certain anecdote distributions.

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