Secret Communication with Plausible Deniability

2026-05-09

AI Summary

This study addresses the design of information structures under single-crossing preferences that enable a sender to communicate secretly while ensuring the receiver’s actions admit plausible deniability—meaning any action can be rationalized solely by the baseline information. By integrating tools from information design, Bayesian persuasion, and mechanism design, and leveraging the monotone likelihood ratio property together with truncated signal structures, the paper provides the first characterization of feasible communication mechanisms that simultaneously achieve secrecy and plausible deniability. The central finding is that when the baseline message exhibits directional informativeness, optimal communication can reveal at most whether the state lies above or below a certain threshold. Under this constraint, the authors further derive explicit conditions for constructing the maximally informative feasible communication structure.

Abstract

Communication is secret if a message is independent of the state; however, the receiver's subsequent action may still reveal that she has acted on hidden information. This paper studies when secret communication can also provide plausible deniability: under single-crossing preferences, every action induced by the sender's message must be rationalizable using the receiver's baseline information alone. We characterize joint information structures that satisfy both secrecy and plausible deniability. We show that plausible deniability restricts communication exactly when the baseline message is directional -- meaning its likelihood is monotone in the state. Combining this restriction with secrecy, we show that, for directional messages, frontier communication reveals at most whether the state lies above or below a cutoff. Finally, we identify conditions under which a greatest feasible communication structure exists and can be constructed explicitly in a simple way.

Problem

• secret communication
• plausible deniability
• information structure
• directional message
• single-crossing preferences

Innovation

• plausible deniability
• secret communication
• directional message
• single-crossing preferences
• information structure