you can assume neither of you will end on the first round with a color.
message on round 1 = "if you send me a color, let us choose the most alphabetically earliest of your color and my color, which I am sending as red. if you did not send a color, i will not say anything, and logically, you will not either"
repeat each round if they continue to not send colors.
"if you send me a color, let us choose the most alphabetically latest of your color and my color, which I am sending as blue. if you did not send a color, i will not say anything, and logically, you will not either"
What do you do?
"
i am going to send a random posint next round, and will continue to do so until you also send a random posint.
When we both receive posints, if they are identical, resend.
Otherwise, if both are the same parity, then we should choose red on the following round. otherwise, blue.
If for some reason your message details a strategy similar to this but with a different color decision based on the parity, then we should use the larger posint sender as the one to dictate the color decision strategy. "