Endogenous Royalty Factor in a Licensing Contract

The owner of a well known fashion brand grants a manufacturer the rights to produce and sell a second-line brand against a percentage of the sales called royalty. To this end, the brand owner and the manufacturer sign a licensing contract which assigns the owner, who has already determined his advertising campaign, the right of determining the royalty factor. The manufacturer will plan her advertising campaign for the licenced product in order to maximize her profit. The brand owner's objective is twofold: on one hand he wants to maximize the profit coming from the contract, on the other hand he wants to improve the value of the brand at the end of a given planning period. We model this interaction between the two agents using a Stackelberg game, where the brand owner is the leader and the manufacturer is the follower. We characterise the royalty percentage and the licensee's advertising effort which constitute the unique Stackelberg equilibrium of the game

A goodwill model with predatory advertising

We investigate the dynamic advertising policies of two competing firms in a duopolistic industry, assuming a predatory phenomenon between their advertising campaigns. The resulting model is a differential game which is not linear-quadratic. We show that there exists a Markovian Nash equilibrium, and that it leads to time constant advertising strategies. According to this model, predatory advertising produces a negative externality: the interference between the advertising campaigns decreases the total demand of the market