That is, indeed, a great question, for information asymmetry is seen, in some levels, as inexorable (insiders cannot use privileged informations they have got, but that does not mean they lose these informations; even inside the firm there are, as Stiglitz has shown in his book, different levels of knowledge of informations relevant to the firm activities). How equal, then, are market conditions, that is the following question.
I did understand the question as putting asymetric information as a source of costs. Different levels of information of the parties could mean that the one with less relevant information could have a greater cost than the other one.
Assuming that internalization may relate to the management of the information asymmetry, I would consider the relation between i.a. and behaviorual uncertainty. As the latter is an attribute of the transaction, internalization relates to the alignment of the governance structure to the transaction attributes. Note that i.a. and uncertainty play a prominent role also in the ex post stage of the relationshi between the parties.
I do not know if this applies to the context of your problem, but in financial markets with market makers, information asymmetry is internalized by incresing the spread.
Sorry the answer took long. The spread is the difference between the price at which the market maker sells and the price at which the market maker buys. Knowing that there is some positive probability of meeting a trader with better information, the market maker increases the spread to compensate the expected loss of trading with the informed traders. The larger the probability attached to meeting informed traders, the larger the spread.