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One of the difficulties is deciding on a strategy that would work even if the other player used the exact same strategy on you. My solution is to say something

One of the difficulties is deciding on a strategy that would work even if the other player used the exact same strategy on you. My solution is to say something like: ‘I will nominate a colour next round. If we both nominate the same colour, I will say that colour and end the game next round. If anything else, I will nominate a different colour, proceeding alphabetically.’ Of course, it would depend on what message you receive that round - there’s probably no one size fits all approach, such as the issues of both people using an unyielding strategy. So maybe you’d have a clause which says, if the other player gives an ultimatum message, then you will go along with that. I don’t think there’s a perfect solution here, but I could be wrong.

mattlondon 5y ago
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")
- thaumasiotes 5y ago
  Waiting has just as much of a symmetry problem as leading does.
thaumasiotes 5y ago
That's not a difficulty. As noted in the post, you can easily solve it through the application of randomness. All you need is for one player to send an unopposed message announcing a color; at that point both players can use that color. There are only two failure states you can be in: both players can be talking, or both players can be waiting for a message. In the first case, one player needs to shut up long enough for the other player to make a choice. In the second case, one player needs to make a choice. A random approach will let these tiebreakers occur in an asymmetric way. > So maybe you’d have a clause which says, if the other player gives an ultimatum message, then you will go along with that. But that doesn't work, because both players can send such a message simultaneously, but they can't both comply simultaneously.
- throwaway73838 5y ago
  Yeah, randomness is the only way to break the symmetry problem.

mattlondon 5y ago

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")

thaumasiotes 5y ago
Waiting has just as much of a symmetry problem as leading does.

thaumasiotes 5y ago

That's not a difficulty. As noted in the post, you can easily solve it through the application of randomness. All you need is for one player to send an unopposed message announcing a color; at that point both players can use that color. There are only two failure states you can be in: both players can be talking, or both players can be waiting for a message. In the first case, one player needs to shut up long enough for the other player to make a choice. In the second case, one player needs to make a choice. A random approach will let these tiebreakers occur in an asymmetric way. > So maybe you’d have a clause which says, if the other player gives an ultimatum message, then you will go along with that. But that doesn't work, because both players can send such a message simultaneously, but they can't both comply simultaneously.

throwaway73838 5y ago
Yeah, randomness is the only way to break the symmetry problem.