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Stuart_Armstrong comments on Even with default points, systems remain exploitable - Less Wrong Discussion
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Here's another case (the worrying one): one player has much greater knowledge of the other's preferences than vice versa.
But your mutual knowledge does raise an interesting point...
I wonder if there's a way of Player X saying "I know that player Y's true valuation is BLAH", while convincing people that player X is actually telling the truth about what he thinks he knows. Maybe being completely transparent wouldn't be such a disadvantage as it seems...
If all they can do is make claims about themselves that no-one is in a position to check, then they cannot communicate anything. Non-verbal evidence of some sort has to be shown. When everyone can lie without loss, words are not evidence of anything. Language is an iterated PD.