The Vote-Left Equilibrium: A Deterministic Coordination Strategy for the Faithful in The Traitors

2026-05-12

I have always loved playing Werewolf! I was a late comer to the TV show equivalent the Traitors but having watched all the season of the British version I have now posted a preprint of a Game Theoretic analysis of the game.

You can read it here.

The basic idea is the following: everyone voting randomly is mathematically optimal since none of the faithful have any real information. The problem with this is that the Traitors can collude (which is in fact their optimal strategy) with how they vote and "hide" in the randomness. The best response by the faithful is for them to all vote in a cyclic order (for example everyone agrees to vote for the person to their left, leading to a random banishment). If they do this, this puts the traitors in a difficult position:

  1. If they deviate then they are immediately outing themselves.
  2. If they comply then they have to hope that they do not getting banished randomly.

Some of the big takeaways of this are the Faithful can improve their probability of winning quite substantially.

As well as this preprint, I also released the software I used for numeric results here.

Of course, whether or not anyone would have success proposing this strategy is another open question.

I'm looking forward to giving a talk on this paper at [The Welsh Mathematics Colloquium in Gregynog]https://gregynogwmc.github.io) next week.