Simple Communication
Jacopo Bizzotto, Nathan Hancart
TL;DR
This paper studies multidimensional cheap talk under a simple-language constraint by restricting the sender to communicate through a real-valued score that aggregates a two-dimensional state Θ ⊆ ℝ^2, subject to the Intermediate Value Property. It proves that equilibrium scores exist and characterizes their structure: with a general state space, equilibrium scores are either linear or coarsely linear, and revealing one dimension is only possible if certain affine conditions hold. In the special case of normal state distribution, the equilibrium linear scores correspond to the eigenvectors of the product ΦΣ, yielding exactly two equilibria—the ex-ante best and worst linear scores—whose relative performance depends on the correlation between dimensions. The analysis highlights welfare losses from strategic frictions relative to commitment and provides a clear link between information design, linearity of equilibria, and the geometry of the state space, offering implications for how language constraints shape policy advice and information transmission.
Abstract
We study multidimensional cheap talk with simple language and aligned preferences. An expert communicates with a decision-maker using a score that aggregates a multidimensional state into a one-dimensional message. Even though the expert and the decision-maker share the same payoffs, the use of simple language introduces strategic frictions. As a result, equilibrium payoffs may be lower than those achievable under commitment to a score. Additionally, under quadratic-loss utility, any equilibrium score must be linear in the state or discrete. Finally, for normally distributed states, we characterize the set of equilibrium linear scores and show that it consists of the ex-ante best and worst linear scores.