Predict the other’s coin

Assume the following 3-player game consisting of several rounds. Players A and B build a team, they have one fair coin each, and may initially talk to each other. Before starting the first round, however, no more communication between them is allowed until the end of the game. (Imagine they are separated in different places without any communication infrastructure.) A round of the game consists of the following steps:

(1) the team gives one dollar to player C.
(2) Both A and B toss their coins independently.
(3) Both A and B try to predict the other’s coin by telling the guess to C. (No communication: A does not know the outcome of B’s coin toss, and vice versa, nor the guess).
(4) If C verifies that both A and B guess the other’s coin correctly, then C has to give 3 dollars back to the team.
Should C play this game?

Source: Raphael M. Reischuk

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