Secret Communication with Plausible Deniability
For economists and game theorists studying communication with privacy concerns, this provides a theoretical characterization of when secret communication can also be plausibly deniable.
This paper characterizes information structures that achieve both secrecy (message independent of state) and plausible deniability (receiver's action rationalizable by baseline information alone) under single-crossing preferences. It finds that plausible deniability restricts communication only when the baseline message is directional, and the frontier communication reveals at most whether the state is above or below a cutoff.
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.