Dynamic Price Competition of Substitutable Perishable Products Among Multiple Sellers

ABSTRACT In this paper, we study a multi‐period price‐setting stochastic game involving multiple sellers, each offering a perishable product with limited capacity over a fixed time horizon. Employing a stylized linear demand rate model to capture consumer choice behavior, we prove the existence and uniqueness of a sub‐game perfect (normalized) Nash equilibrium. Furthermore, we show that any sub‐game perfect Nash equilibrium depends solely on state variables through the reservation costs of sellers with stock on hand. When the Nash equilibrium is interior for sellers with stock on hand, the equilibrium price set by a seller increases with all reservation costs. However, the corresponding equilibrium demand rate decreases with the seller's reservation cost while it increases with competitors' reservation costs. To demonstrate the complexity of the equilibrium behavior with respect to state variables in the stochastic game, we further examine its deterministic counterpart. Counterintuitively, in the equilibrium of the deterministic game, the prices offered by sellers holding relatively high initial inventories can increase with the initial inventories of their competitors and decrease with the horizon length. In situations with incomplete real‐time inventory information, we propose four pricing heuristics—EIP, QRIP, OLP, and r‐OLP—which estimate competitors' inventory levels using the up‐to‐date sales and price path data. These heuristics then set each seller's price by leveraging equilibrium results from the stochastic or deterministic game under complete information. Extensive numerical studies demonstrate the effectiveness of EIP and QRIP, with QRIP being robust across various market conditions. Notably, EIP and QRIP generally outperform OLP and r‐OLP, demonstrating the value of exploiting reservation costs under incomplete inventory information.