Brand Extension Using a Licensing Contract with Uncertainty Advertising Effects

A licensing contract is studied as a Stackelberg differential game with the licensor as the leader and the licensee as the follower. We assume that both players can advertise to increase the brand value, but licensee’s advertising introduces an uncertainty effect in the brand evolution. The objective of the licensee is to maximize her expected profit, while the objective of the licensor is twofold. He wants to maximize his expected profit and at the same time he wants to extend the value of his brand. If the advertising campaign planned at the beginning of the programming interval is required to be open-loop and deterministic, then the stochastic differential game becomes deterministic. We take into account brand extension by mean of two approaches. In the first one we require the mean brand value to be greater than a given threshold, in the second one we require that the final constraint is satisfied with a given probability. We characterize the deterministic optimal strategies for both players and analyze the economic meaning of the obtained results.