Innovative Dynamic Pricing: The Potential Benefits of Early-Purchase Reward Programs

We propose a scientific, game-theoretic model in which a monopolist sells a fashion product in a market consisting of strategic consumers. Research papers on this subject have studied the adverse consequences of strategic consumer behavior, and have proposed a variety of mechanisms to counteract this phenomenon. In this work, we introduce a very broad class of mechanisms which we refer to as early-purchase reward (EPR) programs. Such class includes, but is not limited to strategies such as price-matching, price commitment, and capacity rationing. Confining ourselves to a simple but tractable model, we are able to obtain a complete analytical characterization of the optimal EPR program that a seller should offer to its consumers. Such a program maintains a structure that consists of two components: (1) a promised refund ("participation bonus") that segments the market over the course of the season, and (2) a "modified price matching guarantee" that serves as a lever to counteract strategic consumer behavior. The latter component protects consumers against price drops, but charges them for the fact that they get to enjoy the product by consuming it earlier rather than later in the season. We find that optimal EPR programs are particularly valuable when the inventory and the degree of fashion are high. We have also conducted a numerical analysis to further compare an EPR program (heuristic) to an optimal price-matching strategy, in a rich modelling framework that consists of market size uncertainty, production costs, mixture of strategic and non-strategic consumers, and more. Our results suggest that EPR programs can be advantageous in settings involving modest-to-high degrees of fashion and high degrees of market size uncertainty, regardless of the percentage of strategic consumers in the market.