Dynamic marketing policies with rating-sensitive consumers: A mean-field games approach

We consider a large group of consumers who decide whether or not to buy a durable good offered by a firm. Without previous experience with the product, consumers rely on the ratings of past purchasers to evaluate the product goodwill and make optimal decisions. The consumers have heterogeneous intrinsic rating behaviors and preferences. For example, the population may include avid fans who tend to purchase at early stages and over-rate the product. What are the firm's optimal pricing and marketing strategies in the face of such heterogeneous market? To answer this question, we model the problem as a Stackelberg mean-field game, with the firm acting as leader and the consumers as followers. We determine the conditions under which a Stackelberg equilibrium exists and provide a numerical scheme to compute the optimal prices, marketing activities, aggregate rating, and market share. We provide some numerical examples to illustrate the type of insights that can be obtained with our model. For instance, we show that it is useful to compare the fairness of different rating aggregators, and can anticipate herding behavior triggered by biased raters.