"This kind of reasoning, when pushed to its logical limits, leads to some paradoxical conclusions. As shown by Aumann, two individuals who are commonly known to be rational, and who share a common prior belief about the likelihood of an event, cannot agree to disagree no matter how different their private information might be. That is, they can disagree only if this disagreement is itself not common knowledge. But the willingness of two risk-averse parties to enter opposite sides of a bet requires them to agree to disagree, and hence trade between risk-averse individuals with common priors is impossible if they are commonly known to be rational."
This means that they must be acting irrationally or they do not have a common prior. If they are not acting rationally, they may be noise traders. Market makers can then bring informed and uninformed traders together (taking a cut of the transfer of resources from those without information who want to trade to those with information). An alternative is that traders disagree about the implication of the common information. In the jargon, there is 'heterogeneous interpretation of public information'.