I thought it was interesting that the article talks about "breaking the symmetry" in a fundamentally different way than I thought about it. Since the amount of

I thought it was interesting that the article talks about "breaking the symmetry" in a fundamentally different way than I thought about it. Since the amount of iterations is inconsequential, my first thought was to propose in the first iteration to play a round of stone, paper, scissors to decide who chooses a color, then continue with one of these until it is reciprocated successfully. A slightly more polite way of breaking the symmetry would be to suggest writing something along the lines of: "How about only one of us writes a message and the other [blank]? (I will write [blank] next round)". Both of these approaches of course still have the weakness of requiring consensus to break the symmetry of the requests, so I'm not sure if they are adequate ideas at all.