You are a contestant on a game show with a lump sum cash prize. A second contestant is in another room. The game is cooperative, so either you both win, or you both lose. You have never met the other contestant before, but you can assume they are just as logical as you are.
The game begins with round 1, then proceeds with rounds 2, 3, and so on, for as many rounds as need be. On each round, each contestant has two choices:
EITHER To tell the host: “I end the game” and announce a colour (any colour, of the contestant’s choice.)
OR To send a message (of any length) to the other contestant.
If you both choose to send a message, the messages are sent simultaneously, crossing in transit.
To win the game you must both end the game on the same round, announcing the same colours. If only one of you ends the game, or you both end it announcing different colours, you lose.
Round 1 is about to begin. What do you do?
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