Optimal Licensing and Antitrust Policies in a Cournot Duopoly with an Upstream Monopolist

We analyse a licensing game in a downstream Cournot duopoly where a key input is supplied by an upstream monopolist. We consider two antitrust constraints: (i) the post-licensing price should not be higher than pre-licensing, and (ii) the fixed fee in the licensing contract must be non-negative. We characterise the optimal licensing strategy between a two-part per-unit royalty contract and a two-part ad valorem profit sharing contract. Further, we analyse the welfare implications of our model under different antitrust constraints and input pricing regimes. We also find a possibility of welfare-reducing licensing
in our model.