[Not game AI] Prisoner's dilemna 2

Here's a problem that's been bugging me for awhile. It came out of random reflexions. It's probably either trivial, or a known problem (possibly just a frequent variation on PD). In the latter case, could someone tell me how it's called? This is of course not Game AI per se, but I know that prisoner's dilemna has been often tackled by AI, so I thought about posting it here instead of the Lounge. Two prisoners have X years left in jail. They are kept in separate cells, and they both have a timer, a button, and a speaker-phone to talk to the other one. The speaker phone is unreliable and will only transmit the message with a probability P. They are informed that if they press the button at exactly the same time, they will both be freed. If either of them presses the button, but not the other one, the one who has pressed the button will see his time left in jail become Y (or be killed) while the one who has not will now have Z years left in jail (or even be killed, too). The problem comes from them always having an interest in cooperating, but the probability means that they can never be entirely sure that they will both press the button at the same time. Is there a way to communicate the intent to make the probability that only one of them presses the button vanishingly small? Part of me feels that, to the contrary, P < 1 is the same as P = 0, but I'm not sure why. edit: Or rather, that no amount of communication can reduce the uncertainty. P remains P. The problem that I originally envisionned was Y >> Z >= X, and P < 1. Any thoughts? Cédric [edited by - Cedric on February 8, 2004 2:28:34 PM]