Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach

Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate pricing behavior on markets with a number of firms are not well-suited to model competitive markets with a large number of firms. Using a mean-field game approach, this article develops a setting where numerous firms optimize prices for a new product. We analyze a framework à la Bass with product diffusion and experience effects. The analytical contribution of the paper is to prove the existence and uniqueness of a mean-field game equilibrium, further characterized in terms of mean tendencies and market heterogeneity. We also demonstrate the possible emergence of one or more groups of firms with regards to their pricing strategy. Numerical simulations illustrate how differences in firm experience translate into market heterogeneity in sales and profits. We show that, on a market where the absolute price effect is stronger than the relative price effect, we observe the emergence of two groups of firms, characterized by different prices, sales, and profits. Heterogeneity in firms’ prices and profits is thus compatible with competitive markets.