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Not if we use RGB, send the color as a tuple of three numbers and average both tuples (taking the floor for example if one of the numbers is odd).
I'd presume that a logical contestant would google blue to be the most frequently chosen random colour, and the two of you would just scream "blue" at each other other and then you'd end the game.
I'm surprised more people didn't recognize the two generals problem.
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.
I'm surprised more people didn't recognize the two generals problem.
It’s not the two generals problem because you can be sure that your companion gets the message (both literally a d figuratively). The two generals problem is about inherent uncertainty, while the given problem has full transparency.
These puzzles would make horrible college admissions tests. They hardly qualify as interview questions. This typpe of problem is nearly impossible for folks that have never heard a similar test and nearly trivial for someone who has heard ~3 like it.
There's solving the problem - and there's solving the scenario. I'd presume that a logical contestant would google blue to be the most frequently chosen random colour, and the two of you would just scream "blue" at each other other and then you'd end the game.
„Imagine the stakes are very high—perhaps life and death.“ The only acceptable solution for perfectly rational players in the case of „death“ as possible down side while only having „live“ as a potential upside would be to extend the game indefinitely by telling the co-player that you will never agree on a different strategy than infinite play - all possible rewards, zero downside risk! Where can I get my ticket to O…
There's solving the problem - and there's solving the scenario. I'd presume that a logical contestant would google blue to be the most frequently chosen random colour, and the two of you would just scream "blue" at each other other and then you'd end the game.
This is not true in a live and death scenario, because with asymmetric payoffs like that - termination being the down side risk - it is not at all „rational“ to jump to the answer that gives the highest probability of success, if that answer still has a non-zero risk of death.
„Imagine the stakes are very high—perhaps life and death.“ The only acceptable solution for perfectly rational players in the case of „death“ as possible down side while only having „live“ as a potential upside would be to extend the game indefinitely by telling the co-player that you will never agree on a different strategy than infinite play - all possible rewards, zero downside risk! Where can I get my ticket to O…
Well in that case, you just don't answer. Your buddy on the other side also wouldn't be expecting you to, so they'll just leave the game running indefinitely as well.