Licensing in an international triopoly

We study the effects of entry of two foreign firms on domestic welfare in the presence of licensing, when the incumbent is technologically superior to the entrants. We consider two different situations: (i) the cost-reducing innovation is licensed to both entrants; (ii) the cost- reducing innovation is licensed to just one of the entrants. We analyse three kind of license: (lump- sum) fixed-fee; (per-unit) royalty; and two-part tariff, that is a combination of a fixed-fee and a royalty. We prove that a two part tariff is never an optimal licensing scheme for the incumbent. Moreover, (i) when the technology is licensed to the two entrants, the optimal contract consists of a licensing with only output royalty; and (ii) when the technology is licensed to just one of the entrants, the optimal contract consists of a licensing with only a fixed-fee.