Vertical integration and the licensing of innovation with a fixed fee or a royalty

In this paper, we analyse a situation where a patent holder is considered as an upstream firm that can license its innovation to some downstream companies that compete on a final market with differentiated products. Licensing contract may be based either on a royalty or a fixed fee. The patent holder can either be independant or vertically integrated with one of the downstream companies. We show that a licence based on a royalty works better with vertical integration, and that consequently, the patent holder have some interest to vertically integrate if it enables him to apply a royalty based license. The effect of vertical integration on the social surplus can be either positive or negative.