Abstract

We extend the classical Crawford–Sobel (1982) framework of strategic information transmission to a setting where the sender can generate signals at vanishing cost and the receiver bears positive verification cost per signal. Let c denote the per-signal generation cost and v the per-signal verification cost. We characterize the unique perfect Bayesian equilibrium of the multi-signal game as a function of (c, v). Three results are central. First (Proposition 1), there exists a hallucination threshold c*(v) > 0 such that for c < c*(v) the unique equilibrium is babbling-with-noise: the sender generates a continuum of signals whose informational content is statistically indistinguishable from random, and the receiver optimally verifies a vanishing fraction. Second (Proposition 2), as c → 0 with v fixed, the equilibrium mutual information I(θ; m) between the state θ and the receiver's posterior m converges to zero at rate 1/v; the receiver's expected utility converges to the no-information lower bound. Third (Proposition 3), introducing a publicly observed reputation parameter ρ that rewards truthful signaling restores positive information transmission for ρ above a critical level ρ*(c, v), generalizing the Spence (1973) signaling logic to the costless-generation case. We provide a quantitative calibration to three contemporary application domains—AI-generated content moderation, scientific peer review under LLM authorship, and social-media misinformation—and document that the parameter combinations observed in the post-November-2022 information environment fall on the babbling-with-noise side of the threshold in all three cases. We close by discussing extensions to receiver heterogeneity, dynamic reputation, and the design of intermediate institutions (editorial filters, content moderation algorithms) whose welfare properties our framework can evaluate.