Private Languages

2026-05-23

AI Summary

This study addresses strategic communication when a sender relies on unobservable private anchors and faces non-zero reporting costs. By constructing a Bayesian signaling game that incorporates private anchors and reporting costs, the work reveals how anchor heterogeneity reshapes the geometry of communication in continuous message spaces. The analysis demonstrates that even an arbitrarily small positive reporting cost can sustain near-full information disclosure, and that anchors devoid of intrinsic informativeness can still convey information through strategic distortion. It further establishes an endogenous coexistence mechanism between hard information (anchor-based reports) and soft information (cheap talk). The findings show that under low preference misalignment, all parties favor pure cheap talk—offering an explanation for organizations’ reliance on informal communication channels—and highlight the dual role of private anchors in either enhancing or impairing information transmission quality.

Abstract

Strategic communication often relies on anchors observed by the sender but not by the receiver. An analyst may report against a proprietary valuation model, an auditor against an internal score, a manager against an accounting estimate, or an institution against its own standard. I study a sender-receiver game in which reports are costly to move away from such privately observed anchors. Anchor heterogeneity changes the geometry of communication. Rather than relying on partitions, privately anchored reporting generates continuous variation in messages because different senders find different reports costly to make. This mechanism can improve information transmission, but it can also pull reports toward noisy private anchors. I show that (i) small positive reporting costs can make communication approach full revelation, even though zero costs return the model to cheap talk, (ii) uninformative anchors can transmit information through strategic distortions. Anchored reports and cheap-talk messages can coexist as endogenous hard and soft information, but cheap-talk alone is preferred by all parties under sufficiently low misalignment, explaining why organizations may rely exclusively on informal channels.

Problem

• private anchors
• strategic communication
• sender-receiver game
• reporting costs
• information transmission

Innovation

• private anchors
• strategic communication
• reporting costs
• information transmission
• cheap talk