An advertising game with multiplicative interference

Two competing manufacturers provide a homogeneous market with substitutable products and want to maximize their profits. Each firm may advertise its brand, with a positive effect on its own brand and negative on the competitor’s one. Moreover, each firm may choose an advertising medium to use among several available media. We assume that the advertising effect on demand is mediated by the goodwill variable and that a competitor’s interference may be represented as a proportional reduction of the virtual goodwill. We model the manufacturers’ problem as a noncooperative game under complete information and discuss the existence and features of its Nash equilibria.