Pure-strategy Nash equilibria in an advertising game with interference

Two manufacturers produce substitutable goods for a homogeneous market. The advertising efforts of the two manufacturers determine the demand for the goods and interfere negatively with each other. The demand of each good is a piecewise linear function of the product goodwill, and the latter is a linear function of advertising efforts. In a game with two competing profit-maximizing manufacturers who have access to a set of several advertising media, the pure-strategy Nash equilibria are characterized and their existence is shown.

► We model two competing manufacturers who provide a market with substitutable goods.
► Advertising efforts determine demand and interfere negatively with each other.
► A two-player continuous game with non-smooth payoff functions.
► We characterize and prove existence of pure-strategy Nash equilibria of game.
► Each manufacturer uses only one advertising medium in equilibrium.