Epistemic Status: Further Research Needed, would be a shorter essay if I thought about it for longer.

Conspiracies exist. Some of them are quite large, involve people who met as adults and agreed to do crimes together, and do many heinous things that multiple co-conspirators know about for years without the police noticing.

Some organised crime groups start within families. If you were all raised in the same family-first culture and they're your cousin, you can be pretty sure they're not a cop. Others start in Lawlessness. If it's the jungle and nobody is a cop, you can be pretty sure they're not a cop. These aren't the situations I want to draw attention to here.

Many groups maintain control through massive threats of violence, bribing people more than the cops could ever equal, holding loved ones as hostages, reliably killing snitches, etc. These are closer to sovereign states than shadowy conspiracies, and also not our subject today.

Today, our topic is Conspiring as an Information Theory game. I think it is a very weird game.

Theory

Let me first describe a math problem:

You are a standard economist's perfectly rational logician, in a community of other perfect logicians. You are (secretly) a Conspirator, and would like to start a conspiracy. X others in the community are also (secretly) Conspirators, and want to start the same conspiracy, but you don't know who. If the Conspirators can obtain mutual knowledge of their identities, then they win.
To stop you are Y Secret Police, whom you also do not know. They win if they can obtain knowledge of who any of the Conspirators are, or else forever stop the Conspirators from winning. If you wish, you may instead imagine these as snitches, fools, or other non-contributors who must be kept out of the group project at all costs. There are also a much larger number of Normal People, who will report you if you admit to being a Conspirator but aren't actively out to get you.
You have the full variety of communication options: You can directly message anyone under your real name, a pseudonym, or anonymously. You can start group chats. You can put up public announcements on the town notice board or anonymously graffiti information on some wall where everyone will see it. You can use powerful encryption. The Secret Police can also do all these things.
You haven't agreed on a plan with the other Conspirators in advance (how coul

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