Most commenters seem to completely miss the problem of agreeing on the strategy before agreeing on the color. That agreement is at least as difficult as the pro

Most commenters seem to completely miss the problem of agreeing on the strategy before agreeing on the color. That agreement is at least as difficult as the problem of agreeing on a color itself (because the space of possible strategies is, in some sense, larger than the space of colors), so this is in some sense a recursive problem. The article itself touches on this meta-strategy agreement problem, but then completely ignores it when presenting other strategies (and doesn't go above the first "meta" level). You could argue that humans have a certain inbuilt meta-strategy for agreeing on strategies and are all inherently different enough to symmetry-break the situation eventually. But the problem supposes everyone is a perfect logician (not a fallible human), and so relying on this "inbuilt meta-strategy" is as mathematically interesting as the answer "people put into this situation will often succeed". (Note that, when pairing up most top-level comments in this thread, if they were executed as written, you would end up with people either failing or never finishing.) I also think that randomness is, mathematically, a cop-out for two reasons: It requires some external source of "symmetry breaking" (although I suppose humans are decent enough at picking random numbers), and it only gives a probabilistic solution (although this will be good enough in practice). And it does not in itself contribute to solving meta-problem of strategy agreement either. In terms of a solution to the problem as posed, we can reason that, since the other side is a perfect logician, they will not choose a (meta-)*strategy that can possibly result in a "deadlock". For example, they will not choose "I wait until you write 'blue' and then say 'blue' to the host, and I will never diverge from this strategy" as this runs into a deadlock with the same strategy but different color. "Deadlock" here doesn't necessarily mean "fails to break symmetry", as some strategies don't require that ("choose the average of the two RGB values"). The question remains whether there exists any provably non-deadlockable (meta-)*strategy. If, for every communicated strategy (and this includes any level of meta-strategy), a different strategy is conceivable that results in a deadlock, the problem has no solution. I don't know the answer to this, but here are some thoughts: - Are what I called "deadlocks" above not just symmetry breaking failures on the (or a certain) meta-level? - We can average colors to avoid the need for symmetry breaking in color choice. Can we do the same on the (meta-)*strategy level somehow? - If messages must not be of finite length, it feels like there should be some trick to obtain a solution. But I guess we are interested only in finite message lengths.