I am reading this as an instance of a telepathy problem for coalitions.
In your model, where any legible strategy can be stolen, the engineering problem is selective transparency, both internally and externally.
In the Friendly Telepath Problems, I claim that the limited transparency we have into our cognition (as explored in Parameters of Metacognition) is what makes commitments and cooperation between people who can partly read your mind possible. The hostile telepaths problem deals with the need to protect your mind from being read too much. This may be a partial problem of your conspirators in regard to adversaries, but the dynamic in your case is more a coordination problem among multiple hostile telepaths. They use their naturalasymmetric opacity, to become more transparent to each other rather than to the police.
Thru that lens, the stable equilibria in your game are less about hiding facts and more about which part of the mind becomes mutually modelable by which audience.
I am reading this as an instance of a telepathy problem for coalitions.
In your model, where any legible strategy can be stolen, the engineering problem is selective transparency, both internally and externally.
In the Friendly Telepath Problems, I claim that the limited transparency we have into our cognition (as explored in Parameters of Metacognition) is what makes commitments and cooperation between people who can partly read your mind possible. The hostile telepaths problem deals with the need to protect your mind from being read too much. This may be a partial problem of your conspirators in regard to adversaries, but the dynamic in your case is more a coordination problem among multiple hostile telepaths. They use their natural asymmetric opacity, to become more transparent to each other rather than to the police.
Thru that lens, the stable equilibria in your game are less about hiding facts and more about which part of the mind becomes mutually modelable by which audience.