Essentially, a sale contract can be written in many ways, but one can show the following generally for (more or less) all such contracts: to account for the fact that the firm is missing information about the counterparty, you, it will have to pay what is referred to as "information rent" to at least some customers. The firm ends up in a "second best" outcome merely because it does not possess all information about its customers. The difference, however, is "rent" that accrues to at least some customers. That is, you, the customer, can expect to pay less for things you care about. This in particular occurs when the contract is simply a single "price". With a price, you have to find the optimum between serving many customers and selling for high prices.
One can show that without enough information, the firm can not really do better than setting a single price, which leaves rents to the consumer lest demand is lost.
In contrast, if you have full information, you can construct pricing schemes that fully extract all surplus from the consumer. You can, in essence, get higher prices without losing customers. Many pricing schemes today are trying to use more information to approximate that situation (for example auctions, anything with subscriptions, fixed components, packages etc.). It is why firms like Amazon and Google hire a lot of Economics PhDs and Game Theorists.
You will also notice that many products are pushing toward such pricing models. This is not by accident.
So, your contention is half right and half wrong. In the greater scheme of things, full information is often (but not always) efficient for total welfare. However, in such situation total welfare also may accrue entirely to firms. That means higher profits, first, and higher costs for the consumer second.
In effect, you will pay more if you are more known.
It then depends on your faith in the fairness of the ownership and distributional properties of our capitalist systems, as well as the efficiency of the markets in question (e.g. competition), whether the increased profits are eventually redistributed to you, the consumer.
It seems to me that in many of the markets in question, even the description of oligopoly would be rather charitable. In that case, latter parts of your post do not seem likely.
Edit: Since you asked for the principles. The first iteration of this you may come across is called price discrimination. At that stage, it's not about information, but you can make that link in your head quite easily: The ability to set different prices, depends of course crucially on what you know.
Next, you may hear about auctions or contract theory, where such problems are tackled explicitly. Switching the roles, you may hear about principal agent problems, where a similar (really the same thing) occurs. For full generality, you may want to read into Mechanism Design. Tillman Borgers has a great book which used to be available free as PDF and you can probably still find it. If you are interested in questions such as: "What can we say generally about any sort of sales contract", then this is a good place to start. Needs some math though.