Advertising and Price to Sustain The Brand Value in a Licensing Contract

One of the reasons that induce a brand owner to issue a licensing contract is that of improving the value of his brand. In this paper, we look at a fashion licensing agreement where the licensee produces and sells a product in a complementary business. The value of a fashion brand is sustained by both the advertising efforts of the licensor and the licensee. We assume that demand is proportional to the brand value and decreases with the price. The licensor wants to maximize his revenue coming from the royalties and to minimize his advertising costs. Moreover, he does not want his brand to be devalued at the end of the selling season. On the other hand, the licensee plans her advertising campaign in order to invest in the brand value and maximize the sales revenue. The aim of this paper is to analyze the different strategies the licensor can adopt to sustain his brand. To this end, we determine the optimal advertising policies by solving a Stackelberg differential game, where the owner of the brand acts as the leader and the licensee as the follower. We determine the equilibrium policies of the two players assuming that advertising varies over time and price is constant. We also determine a minimum selling price which guarantees brand sustainability without advertising too much.