• game theory;
  • differential games;
  • advertising;
  • licensing


We consider a licensing agreement where a brand owner grants to a manufacturer the rights to use his own brand on the goods she produces. The ‘royalty’ clause requires that the licensee pays a monetary compensation for having such property and it generally consists of a percentage of the licensee's sales. Furthermore, a guaranteed minimum royalty, the so-called guarantee, is also required, and it has to be paid even in the face of total failure of the property.

We take into account such clause by considering a non-differentiable term—the maximum between the guarantee and the percentage of the sales—in the payoffs of the involved parts. A Stackelberg game constituted by two non-differentiable optimal control problems is formulated in order to find the Stackelberg equilibrium open-loop advertising strategies for the licensor and the licensee. We discuss the existence conditions for such an equilibrium with respect to feasible guarantee levels, and we highlight that particular guarantee values lead to a no-equilibrium situations. Copyright © 2011 John Wiley & Sons, Ltd.