Crawford-Sobel model: when do messages convey information?
Crawford & Sobel (1982): A sender knows state θ ~ U[0,1]. Sender prefers action a = θ + b; receiver prefers a = θ.
With bias b, only partition equilibria exist: sender tells receiver "θ is in interval [t_i, t_{i+1}]". Max intervals N* = floor(−1/(4b) + √(1/(16b²)+1/2)).
The partition is uniform only when b = 0 (fully informative). As b increases, fewer intervals survive.
Applications: expert advice (analyst + CEO), political speech, medical diagnosis, strategic disclosure.