They are not necessarily related. Information symmetry just means that both parties know exactly the same information and neither knows more or less than the other. In a scenario where one or both parties have information that is not accessible to the other they can still engage in a trade in which each party, at least believes, it is better off given their information. A neutral/third-party observer may not come to the same conclusion but that is not relevant to this scenario.
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There is no such thing as information symmetry between any person
Both parties always benefit from the trade, or the trade would not have taken place
How can you say these two things, right at the same time? Does the former not contradict the latter?
They are not necessarily related. Information symmetry just means that both parties know exactly the same information and neither knows more or less than the other. In a scenario where one or both parties have information that is not accessible to the other they can still engage in a trade in which each party, at least believes, it is better off given their information. A neutral/third-party observer may not come to the same conclusion but that is not relevant to this scenario.
So what you mean is both parties think they benefit