Dynamic Information Design with Diminishing Sensitivity Over News

TL;DR

This paper explores how diminishing sensitivity to news affects agents' preferences and equilibrium outcomes in dynamic information design, highlighting the role of loss aversion and news skewness in communication strategies.

Contribution

It introduces a model of news utility with diminishing sensitivity, analyzes equilibrium behaviors in dynamic cheap-talk settings, and characterizes how loss aversion influences information transmission.

Findings

Diminishing sensitivity leads to preferences for news skewness.

Higher loss aversion can increase news utility in equilibrium.

Gradual good news equilibria involve progressively larger information releases.

Abstract

A Bayesian agent experiences gain-loss utility each period over changes in belief about future consumption ("news utility"), with diminishing sensitivity over the magnitude of news. Diminishing sensitivity induces a preference over news skewness: gradual bad news, one-shot good news is worse than one-shot resolution, which is in turn worse than gradual good news, one-shot bad news. So, the agent's preference between gradual information and one-shot resolution can depend on his consumption ranking of different states. In a dynamic cheap-talk framework where a benevolent sender communicates the state over multiple periods, the babbling equilibrium is essentially unique without loss aversion. More loss-averse agents may enjoy higher news utility in equilibrium, contrary to the commitment case. We characterize the family of gradual good news equilibria that exist with high enough loss aversion, and find the sender conveys progressively larger pieces of good news. We discuss applications to media competition and game shows.