What is the most any company has ever paid for a patent portfolio and why is a portfolio more valuable than a single patent?
The most recent sale (and probably one of the most expensive too) that I can think of is that of ARM Holdings to Softbank for US$31 billion. ARM has 4,500 granted or pending patents. ARM produces the designs (not the chips themselves) for the chips that are used in smartphones and most things IoT.
There was other IP in the sale as well, but discounting that for the sake of this discussion, the sale was for nearly US$7 million per patent. I am sure that there are sales of individual patents that sell for much more but as a whole, the patent portfolio was extremely valuable.
Most large acquisitions are around the sale of a nest (portfolio) of patents. A patent nest is often far more valuable than a single patent as it can be likened to an army. If a single patent is an assassin, even the best in the business, it can be taken out by an army of lesser patents every time because of sheer force of numbers. When it comes to patent nests, the whole is often more valuable than the sum of its parts.