Optimal licensing under incomplete information: the case of the inside patent holder

We reconsider the inside patent holders' optimal licensing problem of non-drastic and (super-) drastic innovations under incomplete information, taking into account restrictions concerning royalty rates and the use of exclusive licenses implied by antitrust rules. We employ methods developed in the analysis of license auctions with downstream interaction and optimal control theory. Our analysis differs from the literature which assumed particular patterns of cost reductions across firms induced by the innovation and either complete information or particular probability distributions.