Dynamic Pricing With Demand Carry‐Over: Managerial Practice Versus Theory Prediction

Abstract

This paper examines how competing firms set prices over multiple periods when current‐period demand partially carries over to future periods. We first present results from a pricing experiment conducted with experienced fast‐food managers. Despite the scenario debrief providing all necessary information for participants to evaluate and forecast demand and payoff in each period, they still tended to prioritize short‐term profitability, adopting simpler, monotonic price paths for immediate gains while overlooking potential long‐term benefits. These patterns diverge from dynamic pricing strategies predicted to be optimal in competitive markets with demand carry‐over. To investigate this gap, we develop a multi‐period analytical model in which firms selling substitutable products engage in price competition to maximize total profits over the competition horizon. The model incorporates key factors, including demand carry‐over, product substitutability and the discounting of future payoffs. Analytical solutions derived from a recursive algorithm, along with numerical simulation results, suggest that, under certain market conditions the optimal policy is to reduce prices in early periods to build a strong customer base and then raise prices later to capitalize on retained demand. However, excessive reliance on carry‐over can reduce total profits if early price cuts are not offset by sufficient later‐period gains. By integrating experimental evidence with a rigorous theoretical framework, this study bridges the gap between managerial practice and optimal strategic design. The findings provide both scholarly insights into dynamic pricing with demand carry‐over and practical guidance for aligning short‐term tactics with long‐term profitability objectives in competitive marketplaces.