We consider a large group of consumers who can choose between two products at each purchasing occasion. Their choice is influenced by the marketing strategies of the firms, e.g., price, advertising, the reputation of the brands, and by the product reviews. The problem is modeled as a Stackelberg mean-field game, with one firm acting as leader and the consumers as followers. We determine the conditions under which an equilibrium exists and provide a numerical scheme to compute it. We give some examples to illustrate the type of insights that can be obtained with our model.
Published July 2019 , 29 pages