If you can rely on the other player being logical (as suggested), just wait for them to suggest a colour then use it. If they do not suggest a colour (perhaps

If you can rely on the other player being logical (as suggested), just wait for them to suggest a colour then use it. If they do not suggest a colour (perhaps they are waiting for you to suggest?) then suggest a colour yourself, then the other player being as logical as you will use it. Job done. These scenarios in TFA seem to imply that both players want to be the "leader" as it were (all this talk of breaking symmetry etc) and that this is so somehow some sort of interminable problem. The problem does not seem to state any "cost" of waiting a turn, so there is no rush it seems, and there seems to be no cost of being the "leader" or "follower". This is a basic master-election issue more than anything. Solved problem ... see paxos et al (although I concede that this is more of a "how you think" question, and less about the "correct answer")