Optimal Timing of Advertising with Demand Spillovers

Abstract

We construct a model of a horizontally differentiated duopoly with demand spillovers in which advertising influences the willingness-to-pay of consumers for products and thereby affects not only market share, but also the level of market demand. Furthermore, firms decide the timing as well as the level of advertising. We first derive a subgame perfect Nash equilibrium and Stackelberg equilibria in the advertising competition. Then, using the framework of an endogenous timing decision game with an observable delay (i.e., Hamilton and Slutsky, Games Econ Behavior 2: 29–46, 1990), we consider the optimal timing of advertising. We demonstrate that the optimal timing depends on the degree of demand spillovers and the product substitutability. In particular, if there are sufficient asymmetric demand spillovers between firms, there is a unique Stackelberg equilibrium in the advertising competition, in which the firm providing the product with small (large) demand spillovers chooses to invest in advertising early (late), regardless of the mode of competition.